{"paper_id":"01538fa8-ab3b-4a4e-a41d-2aafa7466de7","body_text":"Foot Pressure Classification and Feature Extraction Based on Multiple Fusion Algorithms | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Foot Pressure Classification and Feature Extraction Based on Multiple Fusion Algorithms Xiaotian Bai, Xiao Hou, Yiling Song, Zhengyan Tang, Hongfeng Huo, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4108538/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Apr, 2025 Read the published version in Scientific Reports → Version 1 posted 13 You are reading this latest preprint version Abstract Objective Using multiple fusion algorithms to optimize the classification and feature extraction of foot pressure during walking stance phase in healthy people, and explore the diversity of foot pressure distribution. Methods 243 healthy young male individuals was studied to collect data on plantar impulse and maximum pressure indices from ten distinct regions of the foot during walking. Principal component analysis was utilized to reduce the dimensionality of the data. Optimized clustering and feature extraction algorithms categorized the foot pressure characteristics and extracted key indicators. Classification discriminant functions were developed using linear discriminant analysis. Analysis of variance compared the differences in features between various foot pressure distribution patterns. Results Three types of foot pressure distribution were identified by multiple fusion algorithms, and four indicators were extracted, including impulses of Toe1, Meta1, Meta5 and Midfoot. The average accuracy rates of original data and cross-validation were 89.70% and 88.50%. Based on one-way analysis of variance, the distribution types were ultimately determined as Thumb Extension Type, Midfoot-Lateral Forefoot Push-off Type, and Normal Type. Conclusion Foot pressure distribution during walking in healthy people can be categorized into Thumb Extension Type, Midfoot-Lateral Forefoot Push-off Type, and Normal Type. Among them, the impulses around the first metatarsophalangeal joint region, fifth metatarsal bone region and midfoot region showed better classification performance. It is recommended that future studies combine the current findings and use prospective studies to further analyze the relationship between gait characteristics and sports injuries. Biological sciences/Biophysics Health sciences/Signs and symptoms Physical sciences/Engineering/Biomedical engineering Gait Plantar Pressure Cluster Analysis Feature Extraction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Walking is the most common form of human locomotion, and the foot, as the organ in direct contact with the ground, interacts with the surface to generate plantar pressure during ambulation 1–3 . Research has revealed that during walking, different regions of the foot function as two distinct units: a buffering unit and a push-off unit. Each unit performs its role through the coordinated effort of various parts of the foot to execute dynamic foot functions 1 . During the cushioning process, the foot's regions bear the load, causing a continuous accumulation of force over time. This can be reflected by the impulse and pressure, which indicate the key areas for foot cushioning and those at greater risk of injury 2–4 . In the propelling phase, the impulse and maximum pressure of the foot's regions also evaluate the main supporting and key force points during foot push-off 2,5 . By examining the characteristics and distribution of plantar pressure, it is possible to diagnose foot conditions such as flatfoot, pes cavus, and hallux valgus, as well as to assess foot function in different populations 2,6,7 . Thus, the mechanical features of the foot's sole are crucial reference indicators for evaluating foot function and diagnosing diseases. In the analysis of abnormal foot types and foot diseases, existing research has developed relatively comprehensive testing methods and evaluation systems for plantar pressure 6–8 . However, for the general population, the complexity of foot types and postures, along with the variability in foot structure and morphology among individuals, leads to a diverse distribution of plantar pressure 2,9,10 . The complexity of foot structure also means that there may be redundancy in the pressure data, necessitating the extraction of data that have the most significant classification effects to ensure the accuracy and practicality of gait analysis. Although some studies have classified foot types based on morphological characteristics 11,12 , there remains a lack of systematic studies on the diversity of plantar pressure, which is the most intuitive reference for foot function. This limitation hampers our understanding of gait characteristics within the general population, and such understanding is crucial for both foot function evaluation and personalized diagnosis. To address the diversity of foot pressure during walking in the general population, this study first reduced the dimensionality of foot pressure data through principal component analysis. An optimized K-means clustering algorithm was then utilized to categorize foot pressure. Combined with correlation coefficient screening and Fisher's linear discriminant analysis, the optimal classification features were extracted to construct discriminant functions for foot pressure classification. By exploring differences in foot pressure distribution through multiple fusion algorithms, gait characteristics can be examined for varying foot types to provide a more comprehensive gait analysis toolkit. This will facilitate more personalized diagnosis and treatment suggestions regarding foot health issues. Methods 1.1 Participants 292 young male participants were recruited (age 33.76 ± 4.59 years, height 176.21 ± 5.33cm, weight 68.44 ± 5.23kg). Participants were required to be physically healthy, without lower limb surgery in the past 3 years, and have normal foot types (arch index between 0.21-0.26 13 ). Prior to testing, participants were informed of the study details and signed an informed consent form. This study was approved by the Ethics Committee of Hebei Normal University (No. 2022LLSC026), and all procedures of this experiment were in accordance with the ethical standards laid out in the 1964 Declaration of Helsinki. 1.2 Data Collection After familiarizing with the protocol and warming up, participants had their foot pressure data collected during walking using a high-frequency foot pressure plate (RSscan International, Belgium, sampling frequency 126Hz, minimum resolution 0.25N, measuring range 1-60N/cm 2 , plate length 2m with 1.5m extended runways at start and end). Three trials of foot pressure data were recorded for each participant at their self-selected walking speed. Data from trials with walking speeds between 1.1-1.3m/s and containing complete bilateral footprints were included for processing. 1.3 Data Processing 1.3.1 Data Preprocessing Based on the collected foot pressure data, the foot regions were adjusted in the instrument's built-in foot pressure analysis software (see Fig. 1 ). The peak pressures and impulses of different regions were recorded for both feet of each participant. The foot with higher total impulse across 10 regions during the stance phase was identified as the primary force-producing foot. A total of 20 parameters including peak pressures and impulses from the 10 regions of the primary force-producing foot during stance were compiled for all participants. Z-scores were calculated to exclude outliers, with any foot pressure parameter having a Z-score greater than 3 considered an outlier 14,15 . Data without outliers were retained for further analysis, resulting in a final sample size of 243 participants. 1.3.2 Principal Component Extraction The preprocessed 20 parameters underwent the Kaiser-Meyer-Olkin (KMO) and Bartlett's tests of sphericity to assess correlations and multicollinearity among the parameters. Principal components with eigenvalues greater than 1 were extracted for dimensionality reduction. To enhance interpretability, the principal components were rotated using the maximum variance method. The scores of the extracted principal components were retained. 1.3.3 Optimized Clustering Algorithm The K-means + + clustering algorithm was applied to the scores of the extracted principal components. The number of clusters ranged from 2 to n (where n is the number of extracted principal components). Compared to traditional K-means, K-means + + optimizes the selection of initial cluster centers, thereby improving clustering quality 16 . In this study, the maximum number of iterations was set to 10,000. The silhouette coefficient was introduced to optimize the iteration quality (Eq. 1 ). The silhouette coefficient ranges from − 1 to 1, where values closer to 1 indicate better clustering and negative values suggest misclassification 17,18 . The number of misclassified samples (silhouette coefficient < 0) and the average silhouette coefficient (Eq. 2 ) in each cluster were calculated to optimize each iteration. The Elbow Method is a technique to determine the optimal number of clusters by finding the \"elbow point\" of the sum of squared errors (SSE) curve. SSE represents the sum of squared distances between each sample and its nearest cluster centroid (Eq. 3 ). As the number of clusters increases, SSE gradually decreases, but after the \"elbow point,\" the reduction in SSE becomes insignificant with additional clusters. This elbow point indicates the optimal number of clusters 19 . In this study, the optimal number of clusters was determined by combining the Elbow Method and silhouette coefficients. The process of the optimized clustering algorithm is shown in Fig. 2 . $${s}_{i}=\\frac{({b}_{i}-{a}_{i})}{\\text{m}\\text{a}\\text{x}({a}_{i},{b}_{i})}$$ 1 ( \\({s}_{i}\\) is the silhouette coefficient of sample i, \\({b}_{i}\\) is the distance from i to its cluster centroid, \\({a}_{i}\\) is the distance from i to the nearest neighboring cluster centroid) $${s}_{k}=\\sum _{i=1}^{n}{s}_{i}$$ 2 (Where n is the number of samples, k is the number of clusters. \\({s}_{k}\\) is the average silhouette coefficient for that number of clusters) $$SSE=\\sum _{k=1}^{n}\\sum _{i\\in {C}_{k}}{\\left|i-{m}_{k}\\right|}^{2}$$ 3 (Where n is the number of clusters, \\({C}_{k}\\) is the k-th cluster, i is a sample point in cluster \\({C}_{k}\\) , \\({m}_{k}\\) is the centroid of the kth cluster) 1.3.4 Feature Index Selection In this study, feature indexes are selected by combining correlation coefficients and the Fisher criterion 20,21 . For plantar pressure indices, Pearson's correlation analysis is used to categorize the similarity of indicators, as shown in Eq. ( 4 ). If r ≥ 0.60, it was considered that there was redundancy between the indicators, and the highly correlated indices are grouped accordingly. $$r=\\frac{\\sum _{i=1}^{n}{(x}_{i}-\\stackrel{-}{x}\\left)\\right({y}_{i}-\\stackrel{-}{y})}{\\sqrt{\\sum _{i=1}^{n}{{(x}_{i}-\\stackrel{-}{x})}^{2}}\\sqrt{\\sum _{i=1}^{n}{{(y}_{i}-\\stackrel{-}{y})}^{2}}}$$ 4 (where \\(\\stackrel{-}{x}\\) and \\(\\stackrel{-}{y}\\) represent the mean values of the samples within the two feature sets, and the value of r ranges from [-1, 1]). For indicators with high correlation, the Fisher criterion is used for feature selection in conjunction with the classification results mentioned above. The Fisher criterion extracts the optimal feature indicators for classification by calculating the ratio of between-class variance to within-class variance, achieving the best class discrimination 20,22 . The calculation method for the Fisher criterion is as follows: If n samples belong to c categories, the calculation of the between-class distance \\({f}_{a}\\) is as shown in Eq. ( 5 ). The calculation of the between-class distance \\({f}_{b}\\) for different indicators is as shown in Eq. ( 6 ). Finally, the Fisher value \\(F\\) for each indicator is obtained, as shown in Eq. ( 7 ). $${f}_{a}=\\frac{1}{n}\\sum _{i=1}^{c}{\\sum }_{x\\in {n}_{i}}{({x}_{i}^{\\left(k\\right)}-{m}_{i}^{\\left(k\\right)})}^{2}$$ 5 (where \\({x}_{i}^{\\left(k\\right)}\\) denotes the value of the k-th feature for the i-th sample, and \\({m}_{i}^{\\left(k\\right)}\\) is the mean value of the k-th feature for the i-th sample). $${f}_{b}=\\sum _{i=1}^{c}\\frac{{n}_{i}}{n}{({m}_{i}^{\\left(k\\right)}-{m}^{\\left(k\\right)})}^{2}$$ 6 (where \\({n}_{i}\\) is the number of samples in the i-th class, n is the total number of samples, and \\({m}^{\\left(k\\right)}\\) is the mean value of the k-th feature across all samples). $$F=\\frac{{f}_{b}}{{f}_{a}}$$ 7 Higher F values indicate better separability of features and higher classification performance for the system. Among highly similar indicators, the one with the highest F value, representing the optimal classification performance, is extracted while the remaining indicators are excluded. Under the premise of relative independence among indicators, this completes the extraction of optimal foot pressure feature indicators. 1.3.5 Linear Discriminant Analysis The principle of linear discriminant analysis is based on multivariate linear regression and discriminant analysis. In this study, stepwise selection was used to exclude redundant independent variables and construct an optimal predictive model 22,23 . At each step, the contribution of an indicator to classification performance was evaluated based on the change in its F value. If p < 0.05, indicating a significant F statistic, the indicator was included in the discriminant function. Based on the foot pressure classification results, the extracted foot pressure feature indicators were used as independent variables for linear discriminant analysis to obtain the classification function coefficients and constants for each included indicator. Discriminant functions were constructed for each class. The class corresponding to the maximum value calculated from the discriminant functions determined the class membership of a given sample. This process established the discriminant functions for classifying walking foot pressure and identified the final set of feature indicators. 1.4 Statistical Methods The optimized K-means + + clustering algorithm was implemented using a custom script in MATLAB R2022b. Principal component analysis and linear discriminant analysis were performed using SPSS 25.0. For different foot pressure classification results, independent samples t-tests or Wilcoxon rank-sum tests were used for between-group comparisons if there were two classes, according to the data distribution characteristics. If there were more than two classes, one-way analysis of variance or Kruskal-Wallis H tests were used for between-group comparisons. The significance level was set at 0.05. Results 2.1 Principal Component Extraction Results The KMO value for the 20 foot pressure parameters was 0.621, and Bartlett's test of sphericity yielded an approximate chi-square of 4950.62 (P < 0.001), indicating correlations among the foot pressure parameters during the stance phase and allowing for principal component extraction. As shown in Table 1 , among the 20 foot pressure parameters, 6 principal components had eigenvalues greater than 1, accounting for 81.00% of the cumulative variance. Table 1 Principal Component Extraction Results Principal Components Initial Eigenvalues Sums of Squared Loadings Rotation Sums of Squared Loadings Eigenvalues Variance% Cumulative % Eigenvalues Variance% Cumulative % Eigenvalues Variance% Cumulative % 1 5.34 26.71 26.71 5.34 26.71 26.71 3.43 17.15 17.15 2 4.22 21.10 47.80 4.22 21.10 47.80 3.24 16.19 33.33 3 1.96 9.79 57.59 1.96 9.79 57.59 2.94 14.71 48.04 4 1.88 9.39 66.99 1.88 9.39 66.99 2.58 12.89 60.94 5 1.53 7.64 74.63 1.53 7.64 74.63 2.22 11.12 72.06 6 1.27 6.37 81.00 1.27 6.37 81.00 1.79 8.94 81.00 7 0.97 4.86 85.86 8 0.67 3.34 89.19 9 0.61 3.07 92.26 10 0.35 1.77 94.04 11 0.27 1.37 95.40 12 0.23 1.16 96.56 13 0.17 0.83 97.39 14 0.13 0.66 98.05 15 0.11 0.54 98.59 16 0.09 0.46 99.05 17 0.08 0.39 99.44 18 0.07 0.37 99.80 19 0.02 0.11 99.92 20 0.02 0.09 100.00 2.2 Foot Pressure Clustering Results The optimized clustering algorithm was executed in MATLAB using the 243×6 matrix of scores from the 6 principal components for each sample. The clustering results are shown in Fig. 3 . From Fig. 3 , it can be seen that the number of misclassifications (samples with silhouette coefficient < 0) was 0 for 2 to 5 clusters, and 3 for 6 clusters. The average silhouette coefficients ranged from 0.20 to 0.25 for 2 to 6 clusters, showing no significant difference. However, the SSE results indicate that the largest slope (414.43) occurred between 2 and 3 clusters, suggesting a deceleration in the reduction of SSE after 3 clusters as the number of clusters increased further. Therefore, the optimal number of clusters was determined to be 3. 2.3 Feature Selection Results By integrating correlation coefficients and the Fisher criterion based on the clustering results of plantar pressure, a preliminary selection yields seven indicators: Toe 1 Impulse, Meta 1 Impulse, Meta 2 Impulse, Meta 5 Impulse, Midfoot Impulse, Heel Lateral Pressure, and Toe 2–5 Pressure. The correlation coefficient matrix among these seven indicators is presented in Table 2 , indicating that the indicators are relatively independent of each other. Table 2 Correlation Coefficient Matrix of Screened Indicators Toe 1 Impulse Meta 1 Impulse Meta 2 Impulse Meta 5 Impulse Midfoot Impulse Heel Lateral Impulse Toe 2–5 Pressure Toe 1 Impulse 1.00 0.42 0.19 -0.23 -0.16 0.08 0.38 Meta 1 Impulse 1.00 0.17 -0.26 -0.09 0.08 0.11 Meta 2 Impulse 1.00 0.07 -0.03 0.15 0.14 Meta 5 Impulse 1.00 0.37 0.16 0.00 Midfoot Impulse 1.00 0.13 -0.07 Heel Lateral Impulse 1.00 0.23 Toe 2–5 Pressure 1.00 2.4 Linear Discriminant Function Results The 7 indicators including Toe 1 impulse, Meta 1 impulse, Meta 2 impulse, Meta 5 impulse, Midfoot impulse, Heel Lateral impulse, and Toe 2–5 pressure underwent stepwise linear discriminant analysis. Finally, 4 indicators were retained: Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse. The classification function coefficients are shown in Table 3 . Table 3 Linear Discriminant Function Classification Coefficients Indicators Class1 Class2 Class3 Toe 1 Impulse 0.145 0.082 0.09 Meta 1 Impulse 0.27 0.12 0.092 Meta 5 Impulse 0.115 0.047 0.088 Midfoot Impulse 0.091 0.348 0.066 Constant -13.789 -12.973 -4.422 As showed in Table 3, the linear discriminant functions for the three classifications of plantar pressure are as follows: $$\\text{C}\\text{l}\\text{a}\\text{s}\\text{s}1=0.145\\times \\text{T}\\text{o}\\text{e} 1 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.27\\times \\text{M}\\text{e}\\text{t}\\text{a} 1 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.115\\times \\text{M}\\text{e}\\text{t}\\text{a}5 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.091\\times \\text{M}\\text{i}\\text{d}\\text{f}\\text{o}\\text{o}\\text{t} \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}-13.789$$ 8 $$\\text{C}\\text{l}\\text{a}\\text{s}\\text{s}2=0.0082\\times \\text{T}\\text{o}\\text{e} 1 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.12\\times \\text{M}\\text{e}\\text{t}\\text{a} 1 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.047\\times \\text{M}\\text{e}\\text{t}\\text{a}5 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.348\\times \\text{M}\\text{i}\\text{d}\\text{f}\\text{o}\\text{o}\\text{t} \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}-12.973$$ 9 $$\\text{C}\\text{l}\\text{a}\\text{s}\\text{s}3=0.09\\times \\text{T}\\text{o}\\text{e} 1 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.092\\times \\text{M}\\text{e}\\text{t}\\text{a} 1 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.088\\times \\text{M}\\text{e}\\text{t}\\text{a}5 \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}+0.066\\times \\text{M}\\text{i}\\text{d}\\text{f}\\text{o}\\text{o}\\text{t} \\text{I}\\text{m}\\text{p}\\text{u}\\text{l}\\text{s}\\text{e}-4.422$$ 10 The classification of plantar pressure is judged according to the discriminant scores of Eq. 8 – 10 , and the accuracy of the discriminant is shown in Table 4 . As shown in Table 4 , the average evaluation accuracy of the original data of the three classifications is 89.70%, and the average accuracy of the three classifications after cross-verification is 88.5%, indicating a high linear discriminant accuracy. Table 4 Results of Linear Discriminant Classification Predicted Group Membership Information Label 1 2 3 Accuracy Original data Count 1 55 2 7 85.9% 2 3 42 6 82.4% 3 3 4 121 94.5% Cross-verification Count 1 53 3 8 82.8% 2 3 42 6 82.4% 3 3 5 120 93.8% 2.5 Foot Pressure Classification Characteristics From Fig. 4 , it can be observed that Class 1 had higher Toe1 impulse and Meta1 impulse compared to Class 2 and 3 (P < 0.05). Class 2 exhibited higher Midfoot impulse than Class 1 and 3 (P < 0.05), and higher Meta5 impulse than Class 1 (P < 0.05). Based on the characteristics of the indices for each classification, it can be determined that individuals in Class 1 primarily bear weight on the thumb and first metatarsal during walking, hence named the \"Thumb Extension Type\"; those in Class 2 mainly exert force on the midfoot and fifth metatarsal, and are termed the \"Midfoot-Lateral Forefoot Push-off Type\"; Class 3 individuals do not exhibit distinct features compared to the first two classes and are thus named the \"Normal Type\". The plantar pressure characteristics for the three types of walking are depicted in Fig. 5 . Discussion Through multiple fusion algorithms, this study classified and extracted features from the peak pressures and impulses of 10 foot regions during the stance phase of walking in 243 participants. By combining principal component analysis with a clustering algorithm optimized based on silhouette coefficients, walking foot pressure characteristics were categorized into three classes. Subsequently, redundant indicators were excluded through correlation coefficient screening and Fisher's criterion. Linear discriminant functions were constructed for the three classifications. The results revealed that Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse, effectively distinguished foot pressure characteristics during walking. Based on these features, an analysis of foot pressure differences during the stance phase of different gait patterns was conducted, providing methodological support and theoretical references for the study of foot pressure distribution characteristics and dynamic foot function analysis during walking. 3.1 Analysis of Optimized Clustering and Feature Extraction Algorithms Foot pressure is an important dynamic indicator for investigating the biomechanical characteristics of the lower limbs, and it holds significant reference value for the diagnosis of foot diseases and the analysis of lower limb force lines 2,6,8 . During physical activity, the dynamic indicators of certain foot regions exhibit coordinated characteristics to perform foot functions 1 , suggesting potential redundancy among the dynamic indicators of different foot regions in foot pressure analysis. Therefore, when classifying foot pressure, it is necessary to reduce the dimensionality of the complex dynamic information to extract effective principal components for analysis. In this study, principal component analysis was performed on 20 foot pressure parameters, and the principal components were rotated using the maximum variance method to enhance their interpretability. Ultimately, 6 principal components accounting for 81% of the cumulative variance were extracted, preserving a significant amount of the original data information. K-means is a common clustering analysis method, however, it is highly sensitive to the selection of initial cluster centers, which can lead the algorithm to converge to local optima 24 . To address this issue, K-means + + optimizes the selection of initial cluster centers in the K-means algorithm to improve clustering quality. By choosing the point farthest from existing cluster centers as the new cluster center, the initial cluster centers are distributed more evenly in the data space, avoiding convergence to local optima 16 . In this study, based on the K-means + + algorithm, the silhouette coefficient was used to optimize the iterations 17,18 . By minimizing the number of misclassified samples (those with negative silhouette coefficients) for different numbers of clusters and combining the average silhouette coefficient across samples for each number of clusters, clustering quality was improved. The elbow method was then applied to determine the optimal number of clusters 19 , resulting in three classifications of foot pressure characteristics during walking in the general population. For the three classified feature sets, this study performed an initial feature screening by combining correlation coefficient selection and Fisher's criterion 21,22 . For indicators with high Pearson correlation coefficients (threshold set at 0.60 in this study), the indicator with the maximum between-class difference and minimum within-class difference, as indicated by the Fisher value, was selected, while redundant indicators were excluded. This allowed the removal of redundant indicators while preserving complete information. Seven relatively independent pre-screened indicators were obtained: Toe 1 impulse, Meta 1 impulse, Meta 2 impulse, Meta 5 impulse, Midfoot impulse, Heel Lateral impulse, and Toe 2–5 pressure. However, although this method eliminated redundant indicators, it included indicators with minor classification impact to retain complete information. Therefore, this study employed stepwise linear discriminant analysis for the final screening, ultimately identifying four indicators: Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse. The three classifications based on linear discriminant analysis achieved an accuracy of 89.70% for the original data and 88.5% for cross-validation, both demonstrating satisfactory classification performance. This indicates that the multiple fusion algorithms used in this study maximized feature simplification while maintaining optimal classification performance. 3.2 Analysis of Different Types of Foot Pressure Characteristics By combining multiple fusion algorithms, this study screened out four indicators, Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse, from the initial 20 foot pressure parameters. However, no peak pressure indicators demonstrated satisfactory classification performance among the selected indicators. Combined with previous research, peak pressures are typically associated with foot comfort or foot injuries, suggesting that peak pressures may exhibit strong individual differences and thus may not be suitable as classification references for normative data. The 1st metatarsophalangeal joint and the hallux are crucial areas for energy absorption and propulsion during foot movement 25–27 . The Toe1 and Meta1 impulse, as derived from this study, predominantly reflect the activity of the first metatarsophalangeal joint. During the push-off phase of walking, the load is transferred medially and the foot is propelled off the ground along the axes of the metatarsophalangeal joint and the hallux 1,8 . It can be inferred that Class 1 exhibits a strong function of toe extension, hence the naming of the \"Thumb Extension Type\". During the stance phase of walking, the foot arch compresses to bear the body's weight, causing the soft tissues on the sole to lengthen and store elastic potential energy. In the push-off phase, the extension of the metatarsophalangeal joint further lengthens the plantar fascia. As the toes gradually lift off the ground, the elastic potential energy stored in the plantar fascia is released, which helps to improve the economy of movement during walking 28 . Research has found that the stiffness of the metatarsophalangeal joint is also an important indicator for evaluating symptoms of plantar fasciitis 29 . This suggests that the \"Thumb Extension Type\" gait can make full use of the function of the metatarsophalangeal joint, thereby may exhibit better gait economy. During the gait cycle, the center of pressure on the foot begins at the heel, transitions to the medial side of the forefoot, and is ultimately propelled off the ground by the hallux 30 . Research on foot function indicates that during the stance and push-off phase of walking, the forefoot primarily bears load between the second and third metatarsals 1 . This study observed that for Class 2, the gait characteristics show a significantly larger impulse in the lateral forefoot area compared to the other two classes, indicating a lateral bias in force distribution on the forefoot. Based on the above characteristics, Class 2 is named “Midfoot-Lateral Forefoot Push-off Type”. Regarding the arch of the foot, it descends to cushion the impact during weight-bearing and works in conjunction with the transverse arch to act as a rigid lever during extension 28,31 . The findings suggest that individuals with the \"Midfoot-Lateral Forefoot Push-off Type\" gait exhibit a larger impulse in the midfoot area, which may be due to lower arch stiffness in this population, leading to poorer adaptability to weight-bearing and thus a larger impulse in the midfoot region. However, since all subjects in this study had normal foot types, whether this gait pattern, which shows weaker arch function, would lead to foot injuries remains to be further confirmed with prospective studies. This study has achieved classification and feature extraction of plantar pressure based on a healthy population, and has obtained satisfactory results in classification discrimination. However, there are still some shortcomings. The linear discriminant function was used for classification prediction at the end of this paper. It is suggested that future research could construct Support Vector Machines (SVM) or Convolutional Neural Networks (CNN) to improve the accuracy of classification prediction. Additionally, this study only classified plantar pressure features in a healthy population, and the potential injury risks associated with the three gait characteristics identified need further investigation. It is recommended that future studies could expand the sample size and combine different foot conditions and lower limb injuries for prospective research to explore the relationship between different gait characteristics and sports injuries. Conclusion The plantar pressure among healthy individuals during walking can be categorized into three types: Thumb Extension Type, Midfoot-Lateral Forefoot Push-off Type, and Normal Type. Among these, the impulse in the areas around the 1st metatarsophalangeal joint, the 5th metatarsal, and the midfoot region exhibit satisfactory classification performance. It is recommended that future research should combine the results of this study and, through prospective studies, further analyze the relationship between different gait characteristics and sports injuries. Declarations Author Contribution XB and HH were in charge of designing the experiment. YS and ZT completed the data processing for this research.XB wrote the main manuscript. XH and JL revised the manuscript. All authors reviewed the manuscript. Data Availability The data supporting the findings of this study are available from the author Xiaotian Bai. However, due to the personal gait information of the subjects involved, the data from this study is not made publicly available. References Bai, X., Huo, H. & Liu, J. Analysis of Mechanical Characteristics of Walking and Running Foot Functional Units Based On Non-Negative Matrix Factorization. Front. Bioeng. Biotechnol. 11 , 1201421 (2023). Hillstrom, H. J. et al. Foot Type Biomechanics Part 1: Structure and Function of the Asymptomatic Foot. Gait Posture . 37 , 445-451 (2013). Hinz, P. et al. Analysis of Pressure Distribution Below the Metatarsals with Different Insoles in Combat Boots of the German Army for Prevention of March Fractures. Gait Posture . 27 , 535-538 (2008). Schepers, T., Van der Stoep, A., Van der Avert, H., Van Lieshout, E. M. & Patka, P. Plantar Pressure Analysis After Percutaneous Repair of Displaced Intra-Articular Calcaneal Fractures. Foot Ankle Int. 29 , 128-135 (2008). De Cock, A., De Clercq, D., Willems, T. & Witvrouw, E. Temporal Characteristics of Foot Roll-Over During Barefoot Jogging: Reference Data for Young Adults. Gait Posture . 21 , 432-439 (2005). Fernandez-Seguin, L. M. et al. Comparison of Plantar Pressures and Contact Area Between Normal and Cavus Foot. Gait Posture . 39 , 789-792 (2014). Ledoux, W. R. & Hillstrom, H. J. The Distributed Plantar Vertical Force of Neutrally Aligned and Pes Planus Feet. Gait Posture . 15 , 1-9 (2002). Hofmann, U. K. et al. Transfer of Plantar Pressure From the Medial to the Central Forefoot in Patients with Hallux Valgus. Bmc Musculoskelet. Disord. 20 , (2019). Arin-Bal, G., Livanelioglu, A., Leardini, A. & Belvedere, C. Correlations Between Plantar Pressure and Postural Balance in Healthy Subjects and their Comparison According to Gender and Limb Dominance: A Cross-Sectional Descriptive Study. Gait Posture . 108 , 124-131 (2024). Buldt, A. K., Allan, J. J., Landorf, K. B. & Menz, H. B. The Relationship Between Foot Posture and Plantar Pressure During Walking in Adults: A Systematic Review. Gait Posture . 62 , 56-67 (2018). Lee, Y. C. & Wang, M. J. Taiwanese Adult Foot Shape Classification Using 3D Scanning Data. Ergonomics . 58 , 513-523 (2015). Xu, M., Li, J. X., Hong, Y. & Wang, L. Foot Type Classification for Chinese Children and Adolescents. Kinesiology . (2019). Cavanagh, P. R. & Rodgers, M. M. The Arch Index: A Useful Measure From Footprints. J. Biomech. 20 , 547-551 (1987). Berger, A. & Kiefer, M. Comparison of Different Response Time Outlier Exclusion Methods: A Simulation Study. Front. Psychol. 12 , 675558 (2021). SHIFFLER, R. Maximum Z-Scores and Outliers. Am. Stat. 42 , 79-80 (1988). Arthur, D. & Vassilvitskii, S. K-Means++: The Advantages of Careful Seeding. Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, USA, January 7-9, 2007 , 2007. RousseeuwPeter. Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis. J. Comput. Appl. Math. (1987). Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Pérez, J. M. & Perona, I. An Extensive Comparative Study of Cluster Validity Indices. Pattern Recognit. 46 , 243-256 (2013). Nainggolan, R., Perangin-Angin, R., Simarmata, E. & Tarigan, A. F. Improved the Performance of the K-Means Cluster Using the Sum of Squared Error (Sse) Optimized by Using the Elbow Method. IOP Publishing Ltd , 2019:12015-12016. Wang, Y., Ji, J., Liang, P. & Wong, K. Feature Selection of Fmri Data Based On Normalized Mutual Information and Fisher Discriminant Ratio. J. X-Ray Sci. Technol. 24 , 467-475 (2016). Adler, J. & Parmryd, I. Quantifying Colocalization by Correlation: The Pearson Correlation Coefficient is Superior to the Mander's Overlap Coefficient. Cytom. Part A . 77a , 733-742 (2010). Fisher, R. A. The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics . 7 , 179-188 (1936). Carolyn, R., Virgina, F. & Peter, L. Bias in Error Rate Estimates in Discriminant Analysis When Stepwise Variable Selection is Employed. Commun. Stat.-Simul. Comput. 20 , 1-22 (1991). Ikotun, A. M., Ezugwu, A. E., Abualigah, L., Abuhaija, B. & Heming, J. K-Means Clustering Algorithms : A Comprehensive Review , Variants Analysis , and Advances in the Era of Big Data. Inf. Sci. 622 , 178-210 (2023). Oleson, M., Adler, D. & Goldsmith, P. A Comparison of Forefoot Stiffness in Running and Running Shoe Bending Stiffness. J. Biomech. 38 , 1886-1894 (2005). Stefanyshyn, D. J. & Nigg, B. M. Mechanical Energy Contribution of the Metatarsophalangeal Joint to Running and Sprinting. J. Biomech. 30 , 1081-1085 (1997). Stefanyshyn, D. J. & Nigg, B. M. Contribution of the Lower Extremity Joints to Mechanical Energy in Running Vertical Jumps and Running Long Jumps. J. Sports Sci. 16 , 177-186 (1998). Kelly, L. A., Cresswell, A. G., Racinais, S., Whiteley, R. & Lichtwark, G. Intrinsic Foot Muscles Have the Capacity to Control Deformation of the Longitudinal Arch. J. R. Soc. Interface . 11 , 20131188 (2014). Kim, Y., Bhatia, D., Lee, Y., Ryu, Y. & Park, H. Development and Clinical Evaluation of a Novel Foot Stretching Robot that Simultaneously Stretches Plantar Fascia and Achilles Tendon for Treatment of Plantar Fasciitis. Ieee Trans. Biomed. Eng. 69 , 2628-2637 (2022). Pataky, T. C. et al. Vector Field Statistics for Objective Center-of-Pressure Trajectory Analysis During Gait, with Evidence of Scalar Sensitivity to Small Coordinate System Rotations. Gait Posture . 40 , 255-258 (2014). Lichtwark, G. A. & Kelly, L. A. Ahead of the Curve in the Evolution of Human Feet. Nature . 579 , 31-32 (2020). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Apr, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 23 Sep, 2024 Reviews received at journal 28 Jul, 2024 Reviews received at journal 13 Jul, 2024 Reviews received at journal 06 Jul, 2024 Reviewers agreed at journal 04 Jul, 2024 Reviewers agreed at journal 28 Jun, 2024 Reviewers agreed at journal 28 Jun, 2024 Reviewers agreed at journal 21 Jun, 2024 Reviewers invited by journal 21 Jun, 2024 Editor assigned by journal 19 Jun, 2024 Editor invited by journal 01 Apr, 2024 Submission checks completed at journal 27 Mar, 2024 First submitted to journal 15 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-4108538\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":284484509,\"identity\":\"18c9fc60-d553-4f72-8c8d-2d1b3f18b5c6\",\"order_by\":0,\"name\":\"Xiaotian Bai\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Department of Physical Education, Tsinghua University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Xiaotian\",\"middleName\":\"\",\"lastName\":\"Bai\",\"suffix\":\"\"},{\"id\":284484510,\"identity\":\"0f44f07d-87bc-46f8-8ed2-45a2e4ded81f\",\"order_by\":1,\"name\":\"Xiao Hou\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"School of Sport Science, Beijing Sport University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Xiao\",\"middleName\":\"\",\"lastName\":\"Hou\",\"suffix\":\"\"},{\"id\":284484511,\"identity\":\"171ad555-4811-483e-9a1e-3359afa72f1e\",\"order_by\":2,\"name\":\"Yiling Song\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Department of Physical Education, Tsinghua University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Yiling\",\"middleName\":\"\",\"lastName\":\"Song\",\"suffix\":\"\"},{\"id\":284484512,\"identity\":\"38b3cc99-373f-47d0-9025-1d08f15de6b7\",\"order_by\":3,\"name\":\"Zhengyan Tang\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Department of Physical Education, Tsinghua University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Zhengyan\",\"middleName\":\"\",\"lastName\":\"Tang\",\"suffix\":\"\"},{\"id\":284484513,\"identity\":\"bdd81915-e62f-4992-9a91-a39a11886c22\",\"order_by\":4,\"name\":\"Hongfeng Huo\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"College of Physical Education, Hebei Normal University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Hongfeng\",\"middleName\":\"\",\"lastName\":\"Huo\",\"suffix\":\"\"},{\"id\":284484514,\"identity\":\"fd7de84e-d1bc-4d5b-86b7-cd0981422e37\",\"order_by\":5,\"name\":\"Jingmin Liu\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFklEQVRIie3RMUvDQBTA8XcEmiXY9S3Sr5ASkELFL9IlR6Fdcl0EqSDypusiuGYyXyHFxfFCwMXErkId/Ahx6xDEu2CXktqOgvcnHJfjfrzhAGy2P9gJKABG5wCOQ/ofm0/n7CUdQzKa6DuM9P4oAobkYGYZfgRhL6Hz+bQadReMnKoezHqju34F8yEnt1TtU8oUsmIt4lxPySRe9t+LAKGYcvJm4X4i14IaQsiXceQjkzkn9PxfyKtIDFF1Q4IN+zpIlEgb0kGeYHSGjA6QUo7FUhNVSuQpTq4G4fM0kF7USrqoybW8EA+rPPuY17c8icePb9XN8PTeLVoJoHI3270yi2/WEH6erHUM7Rz0dg9sNpvt3/cNH2pqt5S1XH8AAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Department of Physical Education, Tsinghua University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Jingmin\",\"middleName\":\"\",\"lastName\":\"Liu\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-03-15 14:14:28\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-4108538/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-4108538/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1038/s41598-025-96440-6\",\"type\":\"published\",\"date\":\"2025-04-17T15:56:54+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":53881722,\"identity\":\"10a403a3-3a69-47c6-bc79-f274fbabdbb5\",\"added_by\":\"auto\",\"created_at\":\"2024-04-01 17:54:17\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":198341,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eFoot Pressure Regions\\u003c/p\\u003e\\n\\u003cp\\u003e(Note: HL = Lateral Heel, HM = Medial Heel, MF = Midfoot, M1-M5 correspond to the 1st to 5th Metatarsal regions, T2-5 = 2nd to 5th Toes, T1 = Hallux region)\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"floatimage1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4108538/v1/63a53ec69131a3a6150100e4.png\"},{\"id\":53881720,\"identity\":\"97ac4e3b-38e2-4f48-a778-4b5ca3963e5d\",\"added_by\":\"auto\",\"created_at\":\"2024-04-01 17:54:16\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":118026,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eDiagram of the Optimized Clustering Algorithm\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"floatimage2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4108538/v1/335097a593be7848ee2de3b4.png\"},{\"id\":53882269,\"identity\":\"09f6e4ed-a949-4a19-829e-f04799ba7cbf\",\"added_by\":\"auto\",\"created_at\":\"2024-04-01 18:02:17\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":93897,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eResults of Optimized Clustering\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"floatimage3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4108538/v1/a112e7e7854217c6fad59045.png\"},{\"id\":53881719,\"identity\":\"cf9542ad-1b28-4b54-8867-7bd387ca2a2a\",\"added_by\":\"auto\",\"created_at\":\"2024-04-01 17:54:16\",\"extension\":\"jpg\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":73914,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComparison Results of Each Classification\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"4.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4108538/v1/18feae4387c3d5faafafaefd.jpg\"},{\"id\":53881723,\"identity\":\"054f4a24-edb8-492b-a158-4411da2c68a2\",\"added_by\":\"auto\",\"created_at\":\"2024-04-01 17:54:17\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":253753,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eClassifications of Plantar Pressure Characteristics\\u003c/p\\u003e\\n\\u003cp\\u003e(Note: a represents the Thumb Extension Type, b represents the Midfoot-Lateral Forefoot Push-off Type, and c represents the Normal Type)\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"floatimage5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4108538/v1/71b81016521a91836a022e95.png\"},{\"id\":81050747,\"identity\":\"89c5dcdc-aa71-4e1d-b3b4-83446e31958d\",\"added_by\":\"auto\",\"created_at\":\"2025-04-21 16:03:14\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1573361,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4108538/v1/c2b53b49-1352-4751-8d3f-78572ebda7c2.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Foot Pressure Classification and Feature Extraction Based on Multiple Fusion Algorithms\",\"fulltext\":[{\"header\":\"Introduction\",\"content\":\"\\u003cp\\u003eWalking is the most common form of human locomotion, and the foot, as the organ in direct contact with the ground, interacts with the surface to generate plantar pressure during ambulation\\u003csup\\u003e1\\u0026ndash;3\\u003c/sup\\u003e. Research has revealed that during walking, different regions of the foot function as two distinct units: a buffering unit and a push-off unit. Each unit performs its role through the coordinated effort of various parts of the foot to execute dynamic foot functions\\u003csup\\u003e1\\u003c/sup\\u003e. During the cushioning process, the foot's regions bear the load, causing a continuous accumulation of force over time. This can be reflected by the impulse and pressure, which indicate the key areas for foot cushioning and those at greater risk of injury\\u003csup\\u003e2\\u0026ndash;4\\u003c/sup\\u003e. In the propelling phase, the impulse and maximum pressure of the foot's regions also evaluate the main supporting and key force points during foot push-off\\u003csup\\u003e2,5\\u003c/sup\\u003e. By examining the characteristics and distribution of plantar pressure, it is possible to diagnose foot conditions such as flatfoot, pes cavus, and hallux valgus, as well as to assess foot function in different populations\\u003csup\\u003e2,6,7\\u003c/sup\\u003e. Thus, the mechanical features of the foot's sole are crucial reference indicators for evaluating foot function and diagnosing diseases.\\u003c/p\\u003e \\u003cp\\u003eIn the analysis of abnormal foot types and foot diseases, existing research has developed relatively comprehensive testing methods and evaluation systems for plantar pressure\\u003csup\\u003e6\\u0026ndash;8\\u003c/sup\\u003e. However, for the general population, the complexity of foot types and postures, along with the variability in foot structure and morphology among individuals, leads to a diverse distribution of plantar pressure\\u003csup\\u003e2,9,10\\u003c/sup\\u003e. The complexity of foot structure also means that there may be redundancy in the pressure data, necessitating the extraction of data that have the most significant classification effects to ensure the accuracy and practicality of gait analysis. Although some studies have classified foot types based on morphological characteristics\\u003csup\\u003e11,12\\u003c/sup\\u003e, there remains a lack of systematic studies on the diversity of plantar pressure, which is the most intuitive reference for foot function. This limitation hampers our understanding of gait characteristics within the general population, and such understanding is crucial for both foot function evaluation and personalized diagnosis.\\u003c/p\\u003e \\u003cp\\u003eTo address the diversity of foot pressure during walking in the general population, this study first reduced the dimensionality of foot pressure data through principal component analysis. An optimized K-means clustering algorithm was then utilized to categorize foot pressure. Combined with correlation coefficient screening and Fisher's linear discriminant analysis, the optimal classification features were extracted to construct discriminant functions for foot pressure classification. By exploring differences in foot pressure distribution through multiple fusion algorithms, gait characteristics can be examined for varying foot types to provide a more comprehensive gait analysis toolkit. This will facilitate more personalized diagnosis and treatment suggestions regarding foot health issues.\\u003c/p\\u003e\"},{\"header\":\"Methods\",\"content\":\"\\u003cp\\u003e1.1 Participants\\u003c/p\\u003e\\n\\u003cp\\u003e292 young male participants were recruited (age 33.76\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;4.59 years, height 176.21\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;5.33cm, weight 68.44\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;5.23kg). Participants were required to be physically healthy, without lower limb surgery in the past 3 years, and have normal foot types (arch index between 0.21-0.26\\u003csup\\u003e13\\u003c/sup\\u003e). Prior to testing, participants were informed of the study details and signed an informed consent form. This study was approved by the Ethics Committee of Hebei Normal University (No. 2022LLSC026), and all procedures of this experiment were in accordance with the ethical standards laid out in the 1964 Declaration of Helsinki.\\u003c/p\\u003e\\n\\u003cp\\u003e1.2 Data Collection\\u003c/p\\u003e\\n\\u003cp\\u003eAfter familiarizing with the protocol and warming up, participants had their foot pressure data collected during walking using a high-frequency foot pressure plate (RSscan International, Belgium, sampling frequency 126Hz, minimum resolution 0.25N, measuring range 1-60N/cm\\u003csup\\u003e2\\u003c/sup\\u003e, plate length 2m with 1.5m extended runways at start and end). Three trials of foot pressure data were recorded for each participant at their self-selected walking speed. Data from trials with walking speeds between 1.1-1.3m/s and containing complete bilateral footprints were included for processing.\\u003c/p\\u003e\\n\\u003cp\\u003e1.3 Data Processing\\u003c/p\\u003e\\n\\u003cp\\u003e1.3.1 Data Preprocessing\\u003c/p\\u003e\\n\\u003cp\\u003eBased on the collected foot pressure data, the foot regions were adjusted in the instrument's built-in foot pressure analysis software (see Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e). The peak pressures and impulses of different regions were recorded for both feet of each participant. The foot with higher total impulse across 10 regions during the stance phase was identified as the primary force-producing foot. A total of 20 parameters including peak pressures and impulses from the 10 regions of the primary force-producing foot during stance were compiled for all participants. Z-scores were calculated to exclude outliers, with any foot pressure parameter having a Z-score greater than 3 considered an outlier\\u003csup\\u003e14,15\\u003c/sup\\u003e. Data without outliers were retained for further analysis, resulting in a final sample size of 243 participants.\\u003c/p\\u003e\\n\\u003cp\\u003e1.3.2 Principal Component Extraction\\u003c/p\\u003e\\n\\u003cp\\u003eThe preprocessed 20 parameters underwent the Kaiser-Meyer-Olkin (KMO) and Bartlett's tests of sphericity to assess correlations and multicollinearity among the parameters. Principal components with eigenvalues greater than 1 were extracted for dimensionality reduction. To enhance interpretability, the principal components were rotated using the maximum variance method. The scores of the extracted principal components were retained.\\u003c/p\\u003e\\n\\u003cp\\u003e1.3.3 Optimized Clustering Algorithm\\u003c/p\\u003e\\n\\u003cp\\u003eThe K-means\\u0026thinsp;+\\u0026thinsp;+\\u0026thinsp;clustering algorithm was applied to the scores of the extracted principal components. The number of clusters ranged from 2 to n (where n is the number of extracted principal components). Compared to traditional K-means, K-means\\u0026thinsp;+\\u0026thinsp;+\\u0026thinsp;optimizes the selection of initial cluster centers, thereby improving clustering quality\\u003csup\\u003e16\\u003c/sup\\u003e. In this study, the maximum number of iterations was set to 10,000. The silhouette coefficient was introduced to optimize the iteration quality (Eq.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e). The silhouette coefficient ranges from \\u0026minus;\\u0026thinsp;1 to 1, where values closer to 1 indicate better clustering and negative values suggest misclassification\\u003csup\\u003e17,18\\u003c/sup\\u003e. The number of misclassified samples (silhouette coefficient\\u0026thinsp;\\u0026lt;\\u0026thinsp;0) and the average silhouette coefficient (Eq.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e) in each cluster were calculated to optimize each iteration.\\u003c/p\\u003e\\n\\u003cp\\u003eThe Elbow Method is a technique to determine the optimal number of clusters by finding the \\\"elbow point\\\" of the sum of squared errors (SSE) curve. SSE represents the sum of squared distances between each sample and its nearest cluster centroid (Eq.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). As the number of clusters increases, SSE gradually decreases, but after the \\\"elbow point,\\\" the reduction in SSE becomes insignificant with additional clusters. This elbow point indicates the optimal number of clusters\\u003csup\\u003e19\\u003c/sup\\u003e. In this study, the optimal number of clusters was determined by combining the Elbow Method and silhouette coefficients. The process of the optimized clustering algorithm is shown in Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e.\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ1\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ1\\\" class=\\\"mathdisplay\\\"\\u003e$${s}_{i}=\\\\frac{({b}_{i}-{a}_{i})}{\\\\text{m}\\\\text{a}\\\\text{x}({a}_{i},{b}_{i})}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e1\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e(\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({s}_{i}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the silhouette coefficient of sample i, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({b}_{i}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the distance from i to its cluster centroid, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({a}_{i}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the distance from i to the nearest neighboring cluster centroid)\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ2\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ2\\\" class=\\\"mathdisplay\\\"\\u003e$${s}_{k}=\\\\sum _{i=1}^{n}{s}_{i}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e2\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e(Where n is the number of samples, k is the number of clusters. \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({s}_{k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the average silhouette coefficient for that number of clusters)\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ3\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ3\\\" class=\\\"mathdisplay\\\"\\u003e$$SSE=\\\\sum _{k=1}^{n}\\\\sum _{i\\\\in {C}_{k}}{\\\\left|i-{m}_{k}\\\\right|}^{2}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e3\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e(Where n is the number of clusters, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({C}_{k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the k-th cluster, i is a sample point in cluster \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({C}_{k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({m}_{k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the centroid of the kth cluster)\\u003c/p\\u003e\\n\\u003cp\\u003e1.3.4 Feature Index Selection\\u003c/p\\u003e\\n\\u003cp\\u003eIn this study, feature indexes are selected by combining correlation coefficients and the Fisher criterion\\u003csup\\u003e20,21\\u003c/sup\\u003e. For plantar pressure indices, Pearson's correlation analysis is used to categorize the similarity of indicators, as shown in Eq.\\u0026nbsp;(\\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e). If r\\u0026thinsp;\\u0026ge;\\u0026thinsp;0.60, it was considered that there was redundancy between the indicators, and the highly correlated indices are grouped accordingly.\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ4\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ4\\\" class=\\\"mathdisplay\\\"\\u003e$$r=\\\\frac{\\\\sum _{i=1}^{n}{(x}_{i}-\\\\stackrel{-}{x}\\\\left)\\\\right({y}_{i}-\\\\stackrel{-}{y})}{\\\\sqrt{\\\\sum _{i=1}^{n}{{(x}_{i}-\\\\stackrel{-}{x})}^{2}}\\\\sqrt{\\\\sum _{i=1}^{n}{{(y}_{i}-\\\\stackrel{-}{y})}^{2}}}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e4\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e(where \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\stackrel{-}{x}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\stackrel{-}{y}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e represent the mean values of the samples within the two feature sets, and the value of r ranges from [-1, 1]).\\u003c/p\\u003e\\n\\u003cp\\u003eFor indicators with high correlation, the Fisher criterion is used for feature selection in conjunction with the classification results mentioned above. The Fisher criterion extracts the optimal feature indicators for classification by calculating the ratio of between-class variance to within-class variance, achieving the best class discrimination\\u003csup\\u003e20,22\\u003c/sup\\u003e. The calculation method for the Fisher criterion is as follows:\\u003c/p\\u003e\\n\\u003cp\\u003eIf n samples belong to c categories, the calculation of the between-class distance \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({f}_{a}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is as shown in Eq.\\u0026nbsp;(\\u003cspan class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e). The calculation of the between-class distance \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({f}_{b}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e for different indicators is as shown in Eq.\\u0026nbsp;(\\u003cspan class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e). Finally, the Fisher value \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(F\\\\)\\u003c/span\\u003e\\u003c/span\\u003e for each indicator is obtained, as shown in Eq.\\u0026nbsp;(\\u003cspan class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ5\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ5\\\" class=\\\"mathdisplay\\\"\\u003e$${f}_{a}=\\\\frac{1}{n}\\\\sum _{i=1}^{c}{\\\\sum }_{x\\\\in {n}_{i}}{({x}_{i}^{\\\\left(k\\\\right)}-{m}_{i}^{\\\\left(k\\\\right)})}^{2}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e5\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e(where \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({x}_{i}^{\\\\left(k\\\\right)}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e denotes the value of the k-th feature for the i-th sample, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({m}_{i}^{\\\\left(k\\\\right)}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the mean value of the k-th feature for the i-th sample).\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ6\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ6\\\" class=\\\"mathdisplay\\\"\\u003e$${f}_{b}=\\\\sum _{i=1}^{c}\\\\frac{{n}_{i}}{n}{({m}_{i}^{\\\\left(k\\\\right)}-{m}^{\\\\left(k\\\\right)})}^{2}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e6\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e(where \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({n}_{i}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the number of samples in the i-th class, n is the total number of samples, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({m}^{\\\\left(k\\\\right)}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the mean value of the k-th feature across all samples).\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ7\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ7\\\" class=\\\"mathdisplay\\\"\\u003e$$F=\\\\frac{{f}_{b}}{{f}_{a}}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e7\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eHigher F values indicate better separability of features and higher classification performance for the system. Among highly similar indicators, the one with the highest F value, representing the optimal classification performance, is extracted while the remaining indicators are excluded. Under the premise of relative independence among indicators, this completes the extraction of optimal foot pressure feature indicators.\\u003c/p\\u003e\\n\\u003cp\\u003e1.3.5 Linear Discriminant Analysis\\u003c/p\\u003e\\n\\u003cp\\u003eThe principle of linear discriminant analysis is based on multivariate linear regression and discriminant analysis. In this study, stepwise selection was used to exclude redundant independent variables and construct an optimal predictive model\\u003csup\\u003e22,23\\u003c/sup\\u003e. At each step, the contribution of an indicator to classification performance was evaluated based on the change in its F value. If p\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.05, indicating a significant F statistic, the indicator was included in the discriminant function.\\u003c/p\\u003e\\n\\u003cp\\u003eBased on the foot pressure classification results, the extracted foot pressure feature indicators were used as independent variables for linear discriminant analysis to obtain the classification function coefficients and constants for each included indicator. Discriminant functions were constructed for each class. The class corresponding to the maximum value calculated from the discriminant functions determined the class membership of a given sample. This process established the discriminant functions for classifying walking foot pressure and identified the final set of feature indicators.\\u003c/p\\u003e\\n\\u003cp\\u003e1.4 Statistical Methods\\u003c/p\\u003e\\n\\u003cp\\u003eThe optimized K-means\\u0026thinsp;+\\u0026thinsp;+\\u0026thinsp;clustering algorithm was implemented using a custom script in MATLAB R2022b. Principal component analysis and linear discriminant analysis were performed using SPSS 25.0. For different foot pressure classification results, independent samples t-tests or Wilcoxon rank-sum tests were used for between-group comparisons if there were two classes, according to the data distribution characteristics. If there were more than two classes, one-way analysis of variance or Kruskal-Wallis H tests were used for between-group comparisons. The significance level was set at 0.05.\\u003c/p\\u003e\"},{\"header\":\"Results\",\"content\":\"\\u003cp\\u003e2.1 Principal Component Extraction Results\\u003c/p\\u003e\\n\\u003cp\\u003eThe KMO value for the 20 foot pressure parameters was 0.621, and Bartlett\\u0026apos;s test of sphericity yielded an approximate chi-square of 4950.62 (P\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.001), indicating correlations among the foot pressure parameters during the stance phase and allowing for principal component extraction.\\u003c/p\\u003e\\n\\u003cp\\u003eAs shown in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e, among the 20 foot pressure parameters, 6 principal components had eigenvalues greater than 1, accounting for 81.00% of the cumulative variance.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n \\u003ctable id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003ePrincipal Component Extraction Results\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth rowspan=\\\"2\\\" align=\\\"left\\\"\\u003e\\n \\u003cp\\u003ePrincipal Components\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth colspan=\\\"3\\\" align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eInitial Eigenvalues\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth colspan=\\\"3\\\" align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eSums of Squared Loadings\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth colspan=\\\"3\\\" align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eRotation Sums of Squared Loadings\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eEigenvalues\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eVariance%\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCumulative %\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eEigenvalues\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eVariance%\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCumulative %\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eEigenvalues\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eVariance%\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCumulative %\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e5.34\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e26.71\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e26.71\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e5.34\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e26.71\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e26.71\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3.43\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e17.15\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e17.15\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e4.22\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e21.10\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e47.80\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e4.22\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e21.10\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e47.80\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3.24\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e16.19\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e33.33\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.96\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e9.79\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e57.59\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.96\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e9.79\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e57.59\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e2.94\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e14.71\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e48.04\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.88\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e9.39\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e66.99\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.88\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e9.39\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e66.99\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e2.58\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e12.89\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e60.94\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.53\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e7.64\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e74.63\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.53\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e7.64\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e74.63\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e2.22\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e11.12\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e72.06\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.27\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e6.37\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e81.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.27\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e6.37\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e81.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.79\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e8.94\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e81.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.97\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e4.86\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e85.86\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.67\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3.34\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e89.19\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e9\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.61\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3.07\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e92.26\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e10\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.35\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.77\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e94.04\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e11\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.27\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.37\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e95.40\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e12\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.23\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1.16\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e96.56\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e13\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.17\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.83\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e97.39\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e14\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.13\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.66\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e98.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e15\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.11\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.54\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e98.59\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e16\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.09\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.46\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e99.05\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e17\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.08\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.39\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e99.44\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e18\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.07\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.37\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e99.80\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e19\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.11\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e99.92\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e20\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.02\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.09\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e100.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003cp\\u003e2.2 Foot Pressure Clustering Results\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eThe optimized clustering algorithm was executed in MATLAB using the 243\\u0026times;6 matrix of scores from the 6 principal components for each sample. The clustering results are shown in Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e\\n\\u003cp\\u003eFrom Fig.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, it can be seen that the number of misclassifications (samples with silhouette coefficient\\u0026thinsp;\\u0026lt;\\u0026thinsp;0) was 0 for 2 to 5 clusters, and 3 for 6 clusters. The average silhouette coefficients ranged from 0.20 to 0.25 for 2 to 6 clusters, showing no significant difference. However, the SSE results indicate that the largest slope (414.43) occurred between 2 and 3 clusters, suggesting a deceleration in the reduction of SSE after 3 clusters as the number of clusters increased further. Therefore, the optimal number of clusters was determined to be 3.\\u003c/p\\u003e\\n\\u003cp\\u003e2.3 Feature Selection Results\\u003c/p\\u003e\\n\\u003cp\\u003eBy integrating correlation coefficients and the Fisher criterion based on the clustering results of plantar pressure, a preliminary selection yields seven indicators: Toe 1 Impulse, Meta 1 Impulse, Meta 2 Impulse, Meta 5 Impulse, Midfoot Impulse, Heel Lateral Pressure, and Toe 2\\u0026ndash;5 Pressure. The correlation coefficient matrix among these seven indicators is presented in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e, indicating that the indicators are relatively independent of each other.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n \\u003ctable id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 2\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eCorrelation Coefficient Matrix of Screened Indicators\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eToe 1 Impulse\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 1 Impulse\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 2 Impulse\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 5 Impulse\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMidfoot Impulse\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eHeel Lateral Impulse\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eToe 2\\u0026ndash;5 Pressure\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eToe 1 Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003e1.00\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.42\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.19\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-0.23\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-0.16\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.08\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.38\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 1 Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003e1.00\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.17\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-0.26\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-0.09\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.08\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.11\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 2 Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003e1.00\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.07\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-0.03\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.15\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.14\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 5 Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003e1.00\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.37\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.16\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.00\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMidfoot Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003e1.00\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.13\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-0.07\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eHeel Lateral Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003e1.00\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.23\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eToe 2\\u0026ndash;5 Pressure\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e\\u003cstrong\\u003e1.00\\u003c/strong\\u003e\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003cp\\u003e2.4 Linear Discriminant Function Results\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eThe 7 indicators including Toe 1 impulse, Meta 1 impulse, Meta 2 impulse, Meta 5 impulse, Midfoot impulse, Heel Lateral impulse, and Toe 2\\u0026ndash;5 pressure underwent stepwise linear discriminant analysis. Finally, 4 indicators were retained: Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse. The classification function coefficients are shown in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n \\u003ctable id=\\\"Tab3\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eLinear Discriminant Function Classification Coefficients\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eIndicators\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eClass1\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eClass2\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eClass3\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eToe 1 Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.145\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.082\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.09\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 1 Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.27\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.12\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.092\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMeta 5 Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.115\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.047\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.088\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eMidfoot Impulse\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.091\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.348\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e0.066\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eConstant\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-13.789\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-12.973\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e-4.422\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003cp\\u003eAs showed in Table 3, the linear discriminant functions for the three classifications of plantar pressure are as follows:\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ8\\\" class=\\\"Equation\\\"\\u003e\\n \\u003cdiv id=\\\"FileID_Equ8\\\" class=\\\"mathdisplay\\\"\\u003e$$\\\\text{C}\\\\text{l}\\\\text{a}\\\\text{s}\\\\text{s}1=0.145\\\\times \\\\text{T}\\\\text{o}\\\\text{e} 1 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.27\\\\times \\\\text{M}\\\\text{e}\\\\text{t}\\\\text{a} 1 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.115\\\\times \\\\text{M}\\\\text{e}\\\\text{t}\\\\text{a}5 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.091\\\\times \\\\text{M}\\\\text{i}\\\\text{d}\\\\text{f}\\\\text{o}\\\\text{o}\\\\text{t} \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}-13.789$$\\u003c/div\\u003e\\n \\u003cdiv class=\\\"EquationNumber\\\"\\u003e8\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ9\\\" class=\\\"Equation\\\"\\u003e\\n \\u003cdiv id=\\\"FileID_Equ9\\\" class=\\\"mathdisplay\\\"\\u003e$$\\\\text{C}\\\\text{l}\\\\text{a}\\\\text{s}\\\\text{s}2=0.0082\\\\times \\\\text{T}\\\\text{o}\\\\text{e} 1 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.12\\\\times \\\\text{M}\\\\text{e}\\\\text{t}\\\\text{a} 1 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.047\\\\times \\\\text{M}\\\\text{e}\\\\text{t}\\\\text{a}5 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.348\\\\times \\\\text{M}\\\\text{i}\\\\text{d}\\\\text{f}\\\\text{o}\\\\text{o}\\\\text{t} \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}-12.973$$\\u003c/div\\u003e\\n \\u003cdiv class=\\\"EquationNumber\\\"\\u003e9\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ10\\\" class=\\\"Equation\\\"\\u003e\\n \\u003cdiv id=\\\"FileID_Equ10\\\" class=\\\"mathdisplay\\\"\\u003e$$\\\\text{C}\\\\text{l}\\\\text{a}\\\\text{s}\\\\text{s}3=0.09\\\\times \\\\text{T}\\\\text{o}\\\\text{e} 1 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.092\\\\times \\\\text{M}\\\\text{e}\\\\text{t}\\\\text{a} 1 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.088\\\\times \\\\text{M}\\\\text{e}\\\\text{t}\\\\text{a}5 \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}+0.066\\\\times \\\\text{M}\\\\text{i}\\\\text{d}\\\\text{f}\\\\text{o}\\\\text{o}\\\\text{t} \\\\text{I}\\\\text{m}\\\\text{p}\\\\text{u}\\\\text{l}\\\\text{s}\\\\text{e}-4.422$$\\u003c/div\\u003e\\n \\u003cdiv class=\\\"EquationNumber\\\"\\u003e10\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eThe classification of plantar pressure is judged according to the discriminant scores of Eq.\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e8\\u003c/span\\u003e\\u0026ndash;\\u003cspan class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e, and the accuracy of the discriminant is shown in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e. As shown in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e, the average evaluation accuracy of the original data of the three classifications is 89.70%, and the average accuracy of the three classifications after cross-verification is 88.5%, indicating a high linear discriminant accuracy.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n \\u003ctable id=\\\"Tab4\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 4\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eResults of Linear Discriminant Classification\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n \\u003cth colspan=\\\"3\\\" align=\\\"left\\\"\\u003e\\n \\u003cp\\u003ePredicted Group Membership Information\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eLabel\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eAccuracy\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eOriginal data\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCount\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e55\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e7\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e85.9%\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e42\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e82.4%\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e4\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e121\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e94.5%\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCross-verification\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eCount\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e1\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e53\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e8\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e82.8%\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e2\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e42\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e6\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e82.4%\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e3\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e5\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"char\\\"\\u003e\\n \\u003cp\\u003e120\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e93.8%\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n \\u003cp\\u003e2.5 Foot Pressure Classification Characteristics\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eFrom Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e, it can be observed that Class 1 had higher Toe1 impulse and Meta1 impulse compared to Class 2 and 3 (P\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.05). Class 2 exhibited higher Midfoot impulse than Class 1 and 3 (P\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.05), and higher Meta5 impulse than Class 1 (P\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.05).\\u003c/p\\u003e\\n\\u003cp\\u003eBased on the characteristics of the indices for each classification, it can be determined that individuals in Class 1 primarily bear weight on the thumb and first metatarsal during walking, hence named the \\u0026quot;Thumb Extension Type\\u0026quot;; those in Class 2 mainly exert force on the midfoot and fifth metatarsal, and are termed the \\u0026quot;Midfoot-Lateral Forefoot Push-off Type\\u0026quot;; Class 3 individuals do not exhibit distinct features compared to the first two classes and are thus named the \\u0026quot;Normal Type\\u0026quot;. The plantar pressure characteristics for the three types of walking are depicted in Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e.\\u003c/p\\u003e\"},{\"header\":\"Discussion\",\"content\":\"\\u003cp\\u003eThrough multiple fusion algorithms, this study classified and extracted features from the peak pressures and impulses of 10 foot regions during the stance phase of walking in 243 participants. By combining principal component analysis with a clustering algorithm optimized based on silhouette coefficients, walking foot pressure characteristics were categorized into three classes. Subsequently, redundant indicators were excluded through correlation coefficient screening and Fisher's criterion. Linear discriminant functions were constructed for the three classifications. The results revealed that Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse, effectively distinguished foot pressure characteristics during walking. Based on these features, an analysis of foot pressure differences during the stance phase of different gait patterns was conducted, providing methodological support and theoretical references for the study of foot pressure distribution characteristics and dynamic foot function analysis during walking.\\u003c/p\\u003e\\n\\u003cp\\u003e3.1 Analysis of Optimized Clustering and Feature Extraction Algorithms\\u003c/p\\u003e\\n\\u003cp\\u003eFoot pressure is an important dynamic indicator for investigating the biomechanical characteristics of the lower limbs, and it holds significant reference value for the diagnosis of foot diseases and the analysis of lower limb force lines\\u003csup\\u003e2,6,8\\u003c/sup\\u003e. During physical activity, the dynamic indicators of certain foot regions exhibit coordinated characteristics to perform foot functions\\u003csup\\u003e1\\u003c/sup\\u003e, suggesting potential redundancy among the dynamic indicators of different foot regions in foot pressure analysis. Therefore, when classifying foot pressure, it is necessary to reduce the dimensionality of the complex dynamic information to extract effective principal components for analysis. In this study, principal component analysis was performed on 20 foot pressure parameters, and the principal components were rotated using the maximum variance method to enhance their interpretability. Ultimately, 6 principal components accounting for 81% of the cumulative variance were extracted, preserving a significant amount of the original data information.\\u003c/p\\u003e\\n\\u003cp\\u003eK-means is a common clustering analysis method, however, it is highly sensitive to the selection of initial cluster centers, which can lead the algorithm to converge to local optima\\u003csup\\u003e24\\u003c/sup\\u003e. To address this issue, K-means\\u0026thinsp;+\\u0026thinsp;+\\u0026thinsp;optimizes the selection of initial cluster centers in the K-means algorithm to improve clustering quality. By choosing the point farthest from existing cluster centers as the new cluster center, the initial cluster centers are distributed more evenly in the data space, avoiding convergence to local optima\\u003csup\\u003e16\\u003c/sup\\u003e. In this study, based on the K-means\\u0026thinsp;+\\u0026thinsp;+\\u0026thinsp;algorithm, the silhouette coefficient was used to optimize the iterations\\u003csup\\u003e17,18\\u003c/sup\\u003e. By minimizing the number of misclassified samples (those with negative silhouette coefficients) for different numbers of clusters and combining the average silhouette coefficient across samples for each number of clusters, clustering quality was improved. The elbow method was then applied to determine the optimal number of clusters\\u003csup\\u003e19\\u003c/sup\\u003e, resulting in three classifications of foot pressure characteristics during walking in the general population.\\u003c/p\\u003e\\n\\u003cp\\u003eFor the three classified feature sets, this study performed an initial feature screening by combining correlation coefficient selection and Fisher's criterion\\u003csup\\u003e21,22\\u003c/sup\\u003e. For indicators with high Pearson correlation coefficients (threshold set at 0.60 in this study), the indicator with the maximum between-class difference and minimum within-class difference, as indicated by the Fisher value, was selected, while redundant indicators were excluded. This allowed the removal of redundant indicators while preserving complete information. Seven relatively independent pre-screened indicators were obtained: Toe 1 impulse, Meta 1 impulse, Meta 2 impulse, Meta 5 impulse, Midfoot impulse, Heel Lateral impulse, and Toe 2\\u0026ndash;5 pressure. However, although this method eliminated redundant indicators, it included indicators with minor classification impact to retain complete information. Therefore, this study employed stepwise linear discriminant analysis for the final screening, ultimately identifying four indicators: Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse. The three classifications based on linear discriminant analysis achieved an accuracy of 89.70% for the original data and 88.5% for cross-validation, both demonstrating satisfactory classification performance. This indicates that the multiple fusion algorithms used in this study maximized feature simplification while maintaining optimal classification performance.\\u003c/p\\u003e\\n\\u003cp\\u003e3.2 Analysis of Different Types of Foot Pressure Characteristics\\u003c/p\\u003e\\n\\u003cp\\u003eBy combining multiple fusion algorithms, this study screened out four indicators, Toe 1 impulse, Meta 1 impulse, Meta 5 impulse, and Midfoot impulse, from the initial 20 foot pressure parameters. However, no peak pressure indicators demonstrated satisfactory classification performance among the selected indicators. Combined with previous research, peak pressures are typically associated with foot comfort or foot injuries, suggesting that peak pressures may exhibit strong individual differences and thus may not be suitable as classification references for normative data.\\u003c/p\\u003e\\n\\u003cp\\u003eThe 1st metatarsophalangeal joint and the hallux are crucial areas for energy absorption and propulsion during foot movement\\u003csup\\u003e25\\u0026ndash;27\\u003c/sup\\u003e. The Toe1 and Meta1 impulse, as derived from this study, predominantly reflect the activity of the first metatarsophalangeal joint. During the push-off phase of walking, the load is transferred medially and the foot is propelled off the ground along the axes of the metatarsophalangeal joint and the hallux\\u003csup\\u003e1,8\\u003c/sup\\u003e. It can be inferred that Class 1 exhibits a strong function of toe extension, hence the naming of the \\\"Thumb Extension Type\\\". During the stance phase of walking, the foot arch compresses to bear the body's weight, causing the soft tissues on the sole to lengthen and store elastic potential energy. In the push-off phase, the extension of the metatarsophalangeal joint further lengthens the plantar fascia. As the toes gradually lift off the ground, the elastic potential energy stored in the plantar fascia is released, which helps to improve the economy of movement during walking\\u003csup\\u003e28\\u003c/sup\\u003e. Research has found that the stiffness of the metatarsophalangeal joint is also an important indicator for evaluating symptoms of plantar fasciitis\\u003csup\\u003e29\\u003c/sup\\u003e. This suggests that the \\\"Thumb Extension Type\\\" gait can make full use of the function of the metatarsophalangeal joint, thereby may exhibit better gait economy.\\u003c/p\\u003e\\n\\u003cp\\u003eDuring the gait cycle, the center of pressure on the foot begins at the heel, transitions to the medial side of the forefoot, and is ultimately propelled off the ground by the hallux\\u003csup\\u003e30\\u003c/sup\\u003e. Research on foot function indicates that during the stance and push-off phase of walking, the forefoot primarily bears load between the second and third metatarsals\\u003csup\\u003e1\\u003c/sup\\u003e. This study observed that for Class 2, the gait characteristics show a significantly larger impulse in the lateral forefoot area compared to the other two classes, indicating a lateral bias in force distribution on the forefoot. Based on the above characteristics, Class 2 is named \\u0026ldquo;Midfoot-Lateral Forefoot Push-off Type\\u0026rdquo;. Regarding the arch of the foot, it descends to cushion the impact during weight-bearing and works in conjunction with the transverse arch to act as a rigid lever during extension\\u003csup\\u003e28,31\\u003c/sup\\u003e. The findings suggest that individuals with the \\\"Midfoot-Lateral Forefoot Push-off Type\\\" gait exhibit a larger impulse in the midfoot area, which may be due to lower arch stiffness in this population, leading to poorer adaptability to weight-bearing and thus a larger impulse in the midfoot region. However, since all subjects in this study had normal foot types, whether this gait pattern, which shows weaker arch function, would lead to foot injuries remains to be further confirmed with prospective studies.\\u003c/p\\u003e\\n\\u003cp\\u003eThis study has achieved classification and feature extraction of plantar pressure based on a healthy population, and has obtained satisfactory results in classification discrimination. However, there are still some shortcomings. The linear discriminant function was used for classification prediction at the end of this paper. It is suggested that future research could construct Support Vector Machines (SVM) or Convolutional Neural Networks (CNN) to improve the accuracy of classification prediction. Additionally, this study only classified plantar pressure features in a healthy population, and the potential injury risks associated with the three gait characteristics identified need further investigation. It is recommended that future studies could expand the sample size and combine different foot conditions and lower limb injuries for prospective research to explore the relationship between different gait characteristics and sports injuries.\\u003c/p\\u003e\"},{\"header\":\"Conclusion \",\"content\":\"\\u003cp\\u003eThe plantar pressure among healthy individuals during walking can be categorized into three types: Thumb Extension Type, Midfoot-Lateral Forefoot Push-off Type, and Normal Type. Among these, the impulse in the areas around the 1st metatarsophalangeal joint, the 5th metatarsal, and the midfoot region exhibit satisfactory classification performance. It is recommended that future research should combine the results of this study and, through prospective studies, further analyze the relationship between different gait characteristics and sports injuries.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003ch2\\u003eAuthor Contribution\\u003c/h2\\u003e\\u003cp\\u003eXB and HH were in charge of designing the experiment. YS and ZT completed the data processing for this research.XB wrote the main manuscript. XH and JL revised the manuscript. All authors reviewed the manuscript.\\u003c/p\\u003e\\u003ch2\\u003eData Availability\\u003c/h2\\u003e\\n\\u003cp\\u003eThe data supporting the findings of this study are available from the author Xiaotian Bai. However, due to the personal gait information of the subjects involved, the data from this study is not made publicly available.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n\\u003cli\\u003eBai, X., Huo, H. \\u0026amp; Liu, J. Analysis of Mechanical Characteristics of Walking and Running Foot Functional Units Based On Non-Negative Matrix Factorization. \\u003cem\\u003eFront. Bioeng. Biotechnol.\\u003c/em\\u003e \\u003cstrong\\u003e11\\u003c/strong\\u003e, 1201421 (2023).\\u003c/li\\u003e\\n\\u003cli\\u003eHillstrom, H. J. et al. Foot Type Biomechanics Part 1: Structure and Function of the Asymptomatic Foot. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e37\\u003c/strong\\u003e, 445-451 (2013).\\u003c/li\\u003e\\n\\u003cli\\u003eHinz, P. et al. Analysis of Pressure Distribution Below the Metatarsals with Different Insoles in Combat Boots of the German Army for Prevention of March Fractures. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e27\\u003c/strong\\u003e, 535-538 (2008).\\u003c/li\\u003e\\n\\u003cli\\u003eSchepers, T., Van der Stoep, A., Van der Avert, H., Van Lieshout, E. M. \\u0026amp; Patka, P. Plantar Pressure Analysis After Percutaneous Repair of Displaced Intra-Articular Calcaneal Fractures. \\u003cem\\u003eFoot Ankle Int.\\u003c/em\\u003e \\u003cstrong\\u003e29\\u003c/strong\\u003e, 128-135 (2008).\\u003c/li\\u003e\\n\\u003cli\\u003eDe Cock, A., De Clercq, D., Willems, T. \\u0026amp; Witvrouw, E. Temporal Characteristics of Foot Roll-Over During Barefoot Jogging: Reference Data for Young Adults. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e21\\u003c/strong\\u003e, 432-439 (2005).\\u003c/li\\u003e\\n\\u003cli\\u003eFernandez-Seguin, L. M. et al. Comparison of Plantar Pressures and Contact Area Between Normal and Cavus Foot. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e39\\u003c/strong\\u003e, 789-792 (2014).\\u003c/li\\u003e\\n\\u003cli\\u003eLedoux, W. R. \\u0026amp; Hillstrom, H. J. The Distributed Plantar Vertical Force of Neutrally Aligned and Pes Planus Feet. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e15\\u003c/strong\\u003e, 1-9 (2002).\\u003c/li\\u003e\\n\\u003cli\\u003eHofmann, U. K. et al. Transfer of Plantar Pressure From the Medial to the Central Forefoot in Patients with Hallux Valgus. \\u003cem\\u003eBmc Musculoskelet. Disord.\\u003c/em\\u003e \\u003cstrong\\u003e20\\u003c/strong\\u003e, (2019).\\u003c/li\\u003e\\n\\u003cli\\u003eArin-Bal, G., Livanelioglu, A., Leardini, A. \\u0026amp; Belvedere, C. Correlations Between Plantar Pressure and Postural Balance in Healthy Subjects and their Comparison According to Gender and Limb Dominance: A Cross-Sectional Descriptive Study. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e108\\u003c/strong\\u003e, 124-131 (2024).\\u003c/li\\u003e\\n\\u003cli\\u003eBuldt, A. K., Allan, J. J., Landorf, K. B. \\u0026amp; Menz, H. B. The Relationship Between Foot Posture and Plantar Pressure During Walking in Adults: A Systematic Review. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e62\\u003c/strong\\u003e, 56-67 (2018).\\u003c/li\\u003e\\n\\u003cli\\u003eLee, Y. C. \\u0026amp; Wang, M. J. Taiwanese Adult Foot Shape Classification Using 3D Scanning Data. \\u003cem\\u003eErgonomics\\u003c/em\\u003e. \\u003cstrong\\u003e58\\u003c/strong\\u003e, 513-523 (2015).\\u003c/li\\u003e\\n\\u003cli\\u003eXu, M., Li, J. X., Hong, Y. \\u0026amp; Wang, L. Foot Type Classification for Chinese Children and Adolescents. \\u003cem\\u003eKinesiology\\u003c/em\\u003e. (2019).\\u003c/li\\u003e\\n\\u003cli\\u003eCavanagh, P. R. \\u0026amp; Rodgers, M. M. The Arch Index: A Useful Measure From Footprints. \\u003cem\\u003eJ. Biomech.\\u003c/em\\u003e \\u003cstrong\\u003e20\\u003c/strong\\u003e, 547-551 (1987).\\u003c/li\\u003e\\n\\u003cli\\u003eBerger, A. \\u0026amp; Kiefer, M. Comparison of Different Response Time Outlier Exclusion Methods: A Simulation Study. \\u003cem\\u003eFront. Psychol.\\u003c/em\\u003e \\u003cstrong\\u003e12\\u003c/strong\\u003e, 675558 (2021).\\u003c/li\\u003e\\n\\u003cli\\u003eSHIFFLER, R. Maximum Z-Scores and Outliers. \\u003cem\\u003eAm. Stat.\\u003c/em\\u003e \\u003cstrong\\u003e42\\u003c/strong\\u003e, 79-80 (1988).\\u003c/li\\u003e\\n\\u003cli\\u003eArthur, D. \\u0026amp; Vassilvitskii, S. K-Means++: The Advantages of Careful Seeding. \\u003cem\\u003eProceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, USA, January 7-9, 2007\\u003c/em\\u003e, 2007.\\u003c/li\\u003e\\n\\u003cli\\u003eRousseeuwPeter. Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis. \\u003cem\\u003eJ. Comput. Appl. Math.\\u003c/em\\u003e (1987).\\u003c/li\\u003e\\n\\u003cli\\u003eArbelaitz, O., Gurrutxaga, I., Muguerza, J., P\\u0026eacute;rez, J. M. \\u0026amp; Perona, I. An Extensive Comparative Study of Cluster Validity Indices. \\u003cem\\u003ePattern Recognit.\\u003c/em\\u003e \\u003cstrong\\u003e46\\u003c/strong\\u003e, 243-256 (2013).\\u003c/li\\u003e\\n\\u003cli\\u003eNainggolan, R., Perangin-Angin, R., Simarmata, E. \\u0026amp; Tarigan, A. F. Improved the Performance of the K-Means Cluster Using the Sum of Squared Error (Sse) Optimized by Using the Elbow Method. \\u003cem\\u003eIOP Publishing Ltd\\u003c/em\\u003e, 2019:12015-12016.\\u003c/li\\u003e\\n\\u003cli\\u003eWang, Y., Ji, J., Liang, P. \\u0026amp; Wong, K. Feature Selection of Fmri Data Based On Normalized Mutual Information and Fisher Discriminant Ratio. \\u003cem\\u003eJ. X-Ray Sci. Technol.\\u003c/em\\u003e \\u003cstrong\\u003e24\\u003c/strong\\u003e, 467-475 (2016).\\u003c/li\\u003e\\n\\u003cli\\u003eAdler, J. \\u0026amp; Parmryd, I. Quantifying Colocalization by Correlation: The Pearson Correlation Coefficient is Superior to the Mander\\u0026apos;s Overlap Coefficient. \\u003cem\\u003eCytom. Part A\\u003c/em\\u003e. \\u003cstrong\\u003e77a\\u003c/strong\\u003e, 733-742 (2010).\\u003c/li\\u003e\\n\\u003cli\\u003eFisher, R. A. The Use of Multiple Measurements in Taxonomic Problems. \\u003cem\\u003eAnnals of Eugenics\\u003c/em\\u003e. \\u003cstrong\\u003e7\\u003c/strong\\u003e, 179-188 (1936).\\u003c/li\\u003e\\n\\u003cli\\u003eCarolyn, R., Virgina, F. \\u0026amp; Peter, L. Bias in Error Rate Estimates in Discriminant Analysis When Stepwise Variable Selection is Employed. \\u003cem\\u003eCommun. Stat.-Simul. Comput.\\u003c/em\\u003e \\u003cstrong\\u003e20\\u003c/strong\\u003e, 1-22 (1991).\\u003c/li\\u003e\\n\\u003cli\\u003eIkotun, A. M., Ezugwu, A. E., Abualigah, L., Abuhaija, B. \\u0026amp; Heming, J. K-Means Clustering Algorithms : A Comprehensive Review , Variants Analysis , and Advances in the Era of Big Data. \\u003cem\\u003eInf. Sci.\\u003c/em\\u003e \\u003cstrong\\u003e622\\u003c/strong\\u003e, 178-210 (2023).\\u003c/li\\u003e\\n\\u003cli\\u003eOleson, M., Adler, D. \\u0026amp; Goldsmith, P. A Comparison of Forefoot Stiffness in Running and Running Shoe Bending Stiffness. \\u003cem\\u003eJ. Biomech.\\u003c/em\\u003e \\u003cstrong\\u003e38\\u003c/strong\\u003e, 1886-1894 (2005).\\u003c/li\\u003e\\n\\u003cli\\u003eStefanyshyn, D. J. \\u0026amp; Nigg, B. M. Mechanical Energy Contribution of the Metatarsophalangeal Joint to Running and Sprinting. \\u003cem\\u003eJ. Biomech.\\u003c/em\\u003e \\u003cstrong\\u003e30\\u003c/strong\\u003e, 1081-1085 (1997).\\u003c/li\\u003e\\n\\u003cli\\u003eStefanyshyn, D. J. \\u0026amp; Nigg, B. M. Contribution of the Lower Extremity Joints to Mechanical Energy in Running Vertical Jumps and Running Long Jumps. \\u003cem\\u003eJ. Sports Sci.\\u003c/em\\u003e \\u003cstrong\\u003e16\\u003c/strong\\u003e, 177-186 (1998).\\u003c/li\\u003e\\n\\u003cli\\u003eKelly, L. A., Cresswell, A. G., Racinais, S., Whiteley, R. \\u0026amp; Lichtwark, G. Intrinsic Foot Muscles Have the Capacity to Control Deformation of the Longitudinal Arch. \\u003cem\\u003eJ. R. Soc. Interface\\u003c/em\\u003e. \\u003cstrong\\u003e11\\u003c/strong\\u003e, 20131188 (2014).\\u003c/li\\u003e\\n\\u003cli\\u003eKim, Y., Bhatia, D., Lee, Y., Ryu, Y. \\u0026amp; Park, H. Development and Clinical Evaluation of a Novel Foot Stretching Robot that Simultaneously Stretches Plantar Fascia and Achilles Tendon for Treatment of Plantar Fasciitis. \\u003cem\\u003eIeee Trans. Biomed. Eng.\\u003c/em\\u003e \\u003cstrong\\u003e69\\u003c/strong\\u003e, 2628-2637 (2022).\\u003c/li\\u003e\\n\\u003cli\\u003ePataky, T. C. et al. Vector Field Statistics for Objective Center-of-Pressure Trajectory Analysis During Gait, with Evidence of Scalar Sensitivity to Small Coordinate System Rotations. \\u003cem\\u003eGait Posture\\u003c/em\\u003e. \\u003cstrong\\u003e40\\u003c/strong\\u003e, 255-258 (2014).\\u003c/li\\u003e\\n\\u003cli\\u003eLichtwark, G. A. \\u0026amp; Kelly, L. A. Ahead of the Curve in the Evolution of Human Feet. \\u003cem\\u003eNature\\u003c/em\\u003e. \\u003cstrong\\u003e579\\u003c/strong\\u003e, 31-32 (2020).\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Gait, Plantar Pressure, Cluster Analysis, Feature Extraction\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-4108538/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-4108538/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003ch2\\u003eObjective\\u003c/h2\\u003e \\u003cp\\u003eUsing multiple fusion algorithms to optimize the classification and feature extraction of foot pressure during walking stance phase in healthy people, and explore the diversity of foot pressure distribution.\\u003c/p\\u003e\\u003ch2\\u003eMethods\\u003c/h2\\u003e \\u003cp\\u003e243 healthy young male individuals was studied to collect data on plantar impulse and maximum pressure indices from ten distinct regions of the foot during walking. Principal component analysis was utilized to reduce the dimensionality of the data. Optimized clustering and feature extraction algorithms categorized the foot pressure characteristics and extracted key indicators. Classification discriminant functions were developed using linear discriminant analysis. Analysis of variance compared the differences in features between various foot pressure distribution patterns.\\u003c/p\\u003e\\u003ch2\\u003eResults\\u003c/h2\\u003e \\u003cp\\u003eThree types of foot pressure distribution were identified by multiple fusion algorithms, and four indicators were extracted, including impulses of Toe1, Meta1, Meta5 and Midfoot. The average accuracy rates of original data and cross-validation were 89.70% and 88.50%. Based on one-way analysis of variance, the distribution types were ultimately determined as Thumb Extension Type, Midfoot-Lateral Forefoot Push-off Type, and Normal Type.\\u003c/p\\u003e\\u003ch2\\u003eConclusion\\u003c/h2\\u003e \\u003cp\\u003eFoot pressure distribution during walking in healthy people can be categorized into Thumb Extension Type, Midfoot-Lateral Forefoot Push-off Type, and Normal Type. Among them, the impulses around the first metatarsophalangeal joint region, fifth metatarsal bone region and midfoot region showed better classification performance. It is recommended that future studies combine the current findings and use prospective studies to further analyze the relationship between gait characteristics and sports injuries.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Foot Pressure Classification and Feature Extraction Based on Multiple Fusion Algorithms\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2024-04-01 17:54:12\",\"doi\":\"10.21203/rs.3.rs-4108538/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2024-09-23T10:45:58+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2024-07-28T15:20:31+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2024-07-13T07:22:57+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2024-07-06T23:52:03+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"337085870402521488071556628608602257345\",\"date\":\"2024-07-04T14:31:23+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"70750647407434396541432497064294776381\",\"date\":\"2024-06-28T07:13:15+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"108832595468249228364200376883279807186\",\"date\":\"2024-06-28T05:26:51+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"303357009145978294929927893913808076982\",\"date\":\"2024-06-21T12:44:45+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2024-06-21T11:14:46+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2024-06-19T10:08:15+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvited\",\"content\":\"\",\"date\":\"2024-04-01T11:10:23+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2024-03-27T10:51:59+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Scientific Reports\",\"date\":\"2024-03-15T14:13:16+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"af5b2427-651a-4194-a500-26363550a19f\",\"owner\":[],\"postedDate\":\"April 1st, 2024\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[{\"id\":29948407,\"name\":\"Biological sciences/Biophysics\"},{\"id\":29948408,\"name\":\"Health sciences/Signs and symptoms\"},{\"id\":29948409,\"name\":\"Physical sciences/Engineering/Biomedical engineering\"}],\"tags\":[],\"updatedAt\":\"2025-04-21T15:58:44+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-4108538\",\"link\":\"https://doi.org/10.1038/s41598-025-96440-6\",\"journal\":{\"identity\":\"scientific-reports\",\"isVorOnly\":false,\"title\":\"Scientific Reports\"},\"publishedOn\":\"2025-04-17 15:56:54\",\"publishedOnDateReadable\":\"April 17th, 2025\"},\"versionCreatedAt\":\"2024-04-01 17:54:12\",\"video\":\"\",\"vorDoi\":\"10.1038/s41598-025-96440-6\",\"vorDoiUrl\":\"https://doi.org/10.1038/s41598-025-96440-6\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-4108538\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-4108538\",\"identity\":\"rs-4108538\",\"version\":[\"v1\"]},\"buildId\":\"qtupq5eGEP_6zYnWcrvyt\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}