Unsupervised machine learning and image recognition model application in English part-of-speech feature learning Under the open platform environment

Unsupervised machine learning and image recognition model application in English part-of-speech feature learning Under the open platform environment | 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 Research Article Unsupervised machine learning and image recognition model application in English part-of-speech feature learning Under the open platform environment Liu Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2575502/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Apr, 2023 Read the published version in Soft Computing → Version 1 posted 3 You are reading this latest preprint version Abstract The traditional English part-of-speech analysis model fails to meet people’s actual needs due to the fact that the accuracy and other parameters are not up to standard. Facing large-scale English text data, quickly and accurately obtaining the key information needed and improv-ing the efficiency and accuracy of clustering have always been the focus of attention. However, the inherent characteristics of English text make it impossible to accurately calculate the traditional feature weight calculation method, and it’s part of speech is difficult to recognize. Moreover, in order to obtain a structure closer to the real data, this paper fuses the norm graph and the k-nearest neighbor graph, proposes a new composition framework, and combines it with two common propagation algorithms to complete the classification task. In addition, in order to obtain the improvement effect of the algorithm, the algorithm is tested on the English text classification corpus data set of the natural language processing open platform, and a control experiment is set to analyze the model performance. Finally, this article combines mathematical statistics to process data and draw corresponding charts. Unsupervised learning machine learning image recognition part-of-speech recognition Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Part-of-speech tagging refers to the process of labeling reasonable parts of speech for each word in a sentence based on the contextual relationship. Part-of-speech tagging is one of the important pre-processing tasks of natural language processing, and it is also the basis of information extraction, lexical analysis, grammatical analysis, and semantic analysis. The accuracy of part-of-speech tagging will directly affect the effect of research on text retrieval, text classification, and machine translation. Part-of-speech tagging itself is a more difficult problem, because many words usually have multiple parts of speech. However, considering the context of the words, the parts of speech of these words are unique, and specific parts of speech tags such as nouns, verbs, and adjectives can be clearly attached. Part-of-speech tagging is a very important research content in the field of Chinese information processing. After the input text is segmented in Chinese, combined with the context of the word, part-of-speech tagging marks each word with the appropriate part of speech. The traditional transfer learning text feature alignment method considers the characteristics of words in sentence structure. For example, the structural consistency learning algorithm and the spectral feature alignment algorithm use the word co-occurrence matrix of the entire corpus to perform matrix operations to obtain words that are similar in frequency or probability, but ignore the connection between the text classification information and the features in the text. 2. Related Work In the face of large-scale short text data, quickly and accurately obtaining the required key information and improving the efficiency and accuracy of clustering have always been the focus of attention. However, the inherent characteristics of short texts make it impossible to calculate the traditional feature weights accurately. Therefore, scholars use different methods to solve this defect, which is generally divided into three aspects. One aspect is to use feature subset evaluation methods to improve the feature space, including information gain, chi-square test (CHI-sqare, CHI), expected cross entropy (Expected Cross Entropy, ECE), etc. The literature proposes an improved feature weight calculation method, which introduces the concept of information gain in information theory to realize the comprehensive consideration of the specific dimensions of short text feature distribution and overcome the shortcomings of traditional formulas [ 1 ]. The experimental results show that the improved feature weight calculation algorithm is more effective in calculating feature weights. The second is to improve the search space strategy, including sequential selection algorithm, genetic algorithm, particle swarm algorithm, etc. These algorithms use search and superposition to reduce the dimensionality of the feature space while improving the accuracy of the algorithm itself. When generating a single-document summary, it can be achieved through deep learning, that is, using a large-scale data set to train a neural network in a data-driven manner to learn the shallow semantics of the original text and generate a summary. In related work, the literature used the Seq2Seq framework to give input sentences on the encoder side, output each word of the abstract on the decoder side, and use a local attention mechanism to improve the effect [ 2 ]. The literature incorporated traditional TF-IDF, POS, named entity and other features to improve the effect, and introduces Pointer to solve unknown words and low-frequency words [ 3 ]. The literature provided a new Chinese short text abstract data set (data source is Sina Weibo), and manually scored it according to the correlation between the text and abstract [ 4 ]. The literature summarized the new methods in the field of text summarization in recent years, and evaluated them from extractive and generative, single-document and multi-document aspects, including data sets and evaluation methods [ 5 ]. The literature proposed an internal attention mechanism to solve the problem of repeated words, and the training method combines supervised learning and reinforcement learning to improve the effect [ 8 ]. Based on convolutional sequence to sequence (ConvS2S), the literature incorporated the subject information into it, and used reinforcement learning training methods to optimize it. FAN et al. generated abstracts based on the user's style of writing abstracts, including abstract length, words used and other characteristics. The literature proposed the task of generating abstracts based on reader perception, and designed an adversarial learning model called Reader Perception Summarizer (RASG), which incorporates readers’ comments into generative abstracts [ 9 ]. For the task of PECH (Product Perception Answer Generation), the literature designed a model PAAG based on adversarial learning, and proposed a reading review method based on attention mechanism to capture the most relevant words in a given question [ 10 ]. The literature proposed to extract nouns and verbs with strong category characteristics as the first-level part of speech of the text, which improves the efficiency of feature extraction and reduces the dimension of feature vectors, so it is a simple and efficient feature extraction method [ 11 ]. When using semantic-based short text similarity for text classification, the literature assigned different weight coefficients to the extracted keywords of different parts of speech to distinguish the importance of various contribution terms in the calculation of short text similarity, which effectively improves the accuracy of short text classification [ 12 ]. In these methods, part-of-speech features are considered, and different parts of speech contain different information. Words with strong classification characteristics are given higher weights or the words with strong classification characteristics are directly used as first-level feature words for feature selection, which lacks further research and comparison. When considering the important factors that affect the classification category, the literature found through manual observation and comparison that the word that contains the most category information is noun, while verbs, adjectives, pronouns, quantifiers, etc. contain less category distinguishing features [ 13 ]. The literature proposed an English phrase extraction algorithm based on statistical methods, and used the support vector machine (SVM) algorithm for classification experiments. The literature proposed an English keyword extraction method based on TextRank algorithm and mutual information similarity [ 14 ]. Then, it calculated the similarity between the input text keyword set and various keyword sets according to the mutual information similarity measure, and realized text classification. The literature studied an n-ary incremental algorithm to extract semantic strings expressing key information in Uyghur texts, and proposed a similarity measurement method for text and topic similarity similar to Jaccard to implement an English classification algorithm [ 15 ]. 3. Graph-based Semi-supervised Learning Figure 1 shows the general framework of graph-based semi-supervised learning. Most graph-based methods are directly based on sample sets. The labeled and unlabeled samples are represented by vertices, and the similarity is represented by the weight of the edge connecting the two vertices. The similarity is generally obtained through a certain distance measurement method. The common distance measurement methods include Euclidean distance, Gaussian distance, angle cosine distance, Chebyshev distance, correlation coefficient, weighted S-order Minkowski distance and so on. For different graph-based semi-supervised learning methods, its composition method is also different. No matter how to construct the graph, their purpose is to make the constructed graph represent the real data structure of the data, thereby improving the learning performance of the classifier. As shown in Fig. 2 , the graph is constructed by the similarity between samples and samples. The sample set \(X=\left\{ {{X_i},{X_u}} \right\}=\left\{ {{x_1}, \cdots ,{x_l},{x_{l+1}}, \cdots ,{x_{l+u}}} \right\}\) and \(Y={\left\{ {{Y_l},{Y_u}} \right\}^T} \in {R^{\left| V \right| \times c}}\) are the class mark matrix. The class mark matrix is \(L=\left\{ {1, \cdots ,c} \right\}\) , and c is the number of classes. If sample \({x_i}\) belongs to class \(j \in L,{Y_{ij}}=1\) , otherwise \({Y_{ij}}=0\) . \(n=l+u\) is the total number of samples in the data set. Among them, l represents the number of labeled samples \({x_i}\left( {i \leqslant l} \right)\) , the corresponding labeled value is \(y \in L\) , and u is the number of unlabeled samples \({x_j}\left( {l<j \leqslant l+u} \right)\) . \(G=\left( {V,E} \right)\) represents an undirected weighted graph. Among them, V represents the vertex set, E represents the edge set, and \({w_{ij}}\) is the weight of the edge \(e=\left( {i,j} \right)\) , which represents the similarity between nodes i and j. Since the constructed graph is an undirected graph, \({w_{ij}}={w_{ji}}\) . The weight matrix W of G is: $${W_{ij}}=\left\{ {\begin{array}{*{20}{c}} {{w_{ij}}}&{if\left( {e\left( {i,j} \right) \in E} \right)} \\ 0&{otherwise} \end{array}} \right.$$ 1 \({D_{ii}}=\sum {_{j}} {W_{ij}}\) is the sum of the weights of all edges connected to the node. From the diagonal matrix D, the Laplacian matrix can be obtained. There are usually two ways to obtain the graph Laplacian matrix: One is the non-normalized graph Laplacian: $$\Delta {\text{=}}D - W$$ 2 The other is the normalized Tulaplas: $$S={D^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}}\Delta {D^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}}=I - {D^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}}W{D^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}}$$ 3 I is the identity matrix. 4. Graph Construction Method According to the way of picture construction, we roughly divide the types of existing pictures into two categories, that is, traditional composition and non-traditional composition. 1. Traditional Composition Method Sometimes, we cannot predict the type of structure of a certain data. In this case, we can only use some traditional methods to construct the graph. Traditional graphs include exponential weighted graphs, k nearest neighbor graphs (kNN graphs), \(\varepsilon\) nearest neighbor graphs ( \(\varepsilon NN\) graphs), and local linear embedding graphs (LLE graphs). Traditional composition is usually composed of two parts: the choice of graph structure and the weight of edges. 1) exp-weighted graph The exp-weighted picture is the simplest way of composition. It uses the Gaussian kernel function to set the weights of the edges in the graph. The specific composition method is as follows: $${W_{ij}}=\left\{ {\begin{array}{*{20}{c}} {\exp \left( { - \frac{1}{2}{d_{ij}}{\sigma ^{ - 2}}} \right)}&{if\left( {i \ne j} \right)} \\ 0&{otherwise} \end{array}} \right.$$ 4 2) kNN graph Since the k-nearest neighbor relationship is asymmetric, in the k-nearest neighbor graph, if node i is the k-nearest neighbor of node j, there is an arc connection between nodes i and j instead of an edge connection. The arc starts at j and ends at i. In order to get an undirected graph, the direction of the arc can be ignored. To construct a kNN graph, a distance metric is usually selected first, and then the distance between the data sample and other data samples is calculated through the distance metric, and the distance between the two samples is used as the weight of the two samples on the corresponding edges of the graph. In this way, a kNN graph can be obtained for the convenience of description. This section takes Euclidean distance \({d_{ij}}=\sum\limits_{{k=1}}^{n} {{{\left( {{x_{ik}} - {x_{ik}}} \right)}^2}}\) as an example. The specific composition method is as follows: $${W_{ij}}=\left\{ {\begin{array}{*{20}{c}} {\exp \left( { - \frac{1}{2}{d_{ij}}{\sigma ^{ - 2}}} \right)}&{if\left( {{x_j} \in {K_j}} \right)} \\ 0&{otherwise} \end{array}} \right.$$ 5 For any sample \({x_i}\) , \({K_j}\) represents the set of k-nearest neighbor nodes of sample \({x_i}\) . 3) Graphs \(\varepsilon NN\) In graphs \(\varepsilon NN\) , a threshold is set for the distance between the data sample points, and the threshold must be less than or equal to parameter \(\varepsilon\) . If the distance between sample \({x_i}\) and sample \({x_j}\) is \({d_{ij}} \leqslant \varepsilon\) , then there is an edge connection, otherwise there is no edge connection. The specific diagram is constructed as follows: $${W_{ij}}=\left\{ {\begin{array}{*{20}{c}} {\exp \left( { - \frac{1}{2}{d_{ij}}{\sigma ^{ - 2}}} \right)}&{if\left( {{d_{ij}} \leqslant \varepsilon } \right)} \\ 0&{otherwise} \end{array}} \right.$$ 6 4) LLE diagram Roweis et al. first proposed local linear embedding. The basic idea is: First, the neighbors of the sample are determined. If there is no neighbor relationship between sample \({x_i}\) and sample \({x_j}\) , and there is \({\omega _{ij}}=0\) . The local linear reconstruction coefficient is solved by the following formula, and the coefficient is used as the weight of the connection. $$\left\{ {\begin{array}{*{20}{c}} {\hbox{min} \sum\limits_{i} {{{\left\| {{x_i} - \sum\limits_{j} {{w_{ij}}{x_j}} } \right\|}^2}} } \\ {s.t.\sum\limits_{j} {{w_{ij}}} =1} \end{array}} \right.$$ 7 $${W_{ij}}=\left\{ {\begin{array}{*{20}{c}} {{w_{ij}}}&{if\left( {if\left( {{x_j} \in {K_j}} \right)} \right)} \\ 0&{otherwise} \end{array}} \right.$$ 8 2. Non-traditional Composition Method 1) \({\ell ^1}\) norm graph For any sample \({x_i}\) in the sample set \(X=\left\{ {{x_1},{x_2}, \cdots ,{x_n}} \right\} \in {R^{m \times n}}\) , since the \({\ell ^0}\) norm is an NP-hard problem, its sparse coding can be achieved by solving the following \({\ell ^1}\) norm optimization problem: $$\begin{gathered} \mathop {\hbox{min} }\limits_{{{\alpha ^i}}} {\left\| {{\alpha ^i}} \right\|_1} \hfill \\ s.t.{x_i}={D^i}{\alpha ^i}=\sum\limits_{{j \ne i}} {{x_j}\alpha _{j}^{i},{\alpha ^i} \geqslant 0} \hfill \\ \end{gathered}$$ 9 Among them, the dictionary is \({D^i}=\left[ {{x_1}, \cdots ,{x_{i - 1}},{x_{i+1}}, \cdots ,{x_n}} \right] \in {R^{m \times \left( {m+n - 1} \right)}}\) and the coefficient matrix is \({\alpha ^i} \in {R^{m \times \left( {n - 1} \right)}};j=1,2, \cdots ,n,j \ne i\) . W is used as the weight matrix of the graph. If \(i>j,{W_{ij}}=\alpha _{j}^{i}\) , if \(ij} \\ {\alpha _{{j - 1}}^{i}}&{i{f_{}}i<j} \end{array}} \right.$$ 10 2) Low rank representation graph (LRR graph) For any sample \({x_i}\) in the sample set \(X=\left[ {{x_1},{x_2}, \cdots ,{x_n}} \right] \in {R^{m \times n}}\) , its low-rank coding can be achieved by solving the following kernel norm optimization problem: $$\begin{gathered} \mathop {\hbox{min} }\limits_{{{Z^i}}} {\left\| {{Z^i}} \right\|_*} \hfill \\ s.t.{x_i}={D^i}{Z^i}=\sum\limits_{{j \ne i}} {{x_j}\alpha _{j}^{i},{\alpha ^i} \geqslant 0} \hfill \\ \end{gathered}$$ 11 Among them, $${D^i}=\left[ {{x_1},{x_2}, \cdots ,{x_n}} \right] \in {R^{m \times \left( {m+n} \right)}}$$ , \({Z^i}=\left[ {{z_1},{z_2}, \cdots ,{z_n}} \right] \in {R^{m \times n}}\) is the low-rank representation coefficient matrix, and the calculation formula of the low-rank representation matrix W is as follows: $${W_{ij}}=Z_{j}^{i}$$ 12 5. Graph-based Semi-supervised Learning Method The graph method is a method based on the manifold assumption. Its goal is to find a classification function \(f:V \to R\) in the graph, and the classification function f needs to meet two basic conditions. (1) For labeled samples, the classification value should be as close as possible to the target value; (2) The classification function should be as smooth as possible on the entire graph. An energy function framework can be represented by these two conditions, the first part is the loss term, and the second part is the regularizer. $$E\left( f \right)=Loss{\text{ }}item+Regular{\text{ }}term$$ 13 With the energy function framework, we can obtain the classification function by optimizing the energy function. Currently, most graph-based semi-supervised learning uses this energy function framework. Their loss items and regular items may be different, and they belong to the same type of method. Next, a few more popular graph-based semi-supervised learning methods are introduced. (1) Minimum cut method The purpose of learning is to find a minimum cut set, which cuts all the connections between the "source" and the "well" of the entire graph, so that the samples are "cut" into two categories. The "+" sample is connected to the "source", and the "-" sample is connected to all the "wells", as shown in Fig. 4 . The objective function is composed of two parts. The first part is the loss term, which is used to punish the mislabeled samples. The loss term can be obtained by adding the infinite coefficient \(\infty\) to the square loss function, which can fix the class label of the marked sample. The loss term can be expressed as: $$\infty \sum\limits_{{i=1}}^{l} {{{\left( {{y_i} - f\left( {{x_i}} \right)} \right)}^2}}$$ 14 The other part is the regular term, which is to make the adjacent sample labels as similar as possible, so that the labels distributed on the graph are smooth. The regular term is defined: $$\frac{1}{2}\sum\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\left( {f\left( {{x_j}} \right) - f\left( {{x_i}} \right)} \right)}^2}}$$ 15 The energy function is: $$E\left( f \right)=\infty \sum\limits_{{i=1}}^{l} {{{\left( {{y_i} - f\left( {{x_i}} \right)} \right)}^2}} {\text{+}}\frac{1}{2}\sum\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\left( {f\left( {{x_j}} \right) - f\left( {{x_i}} \right)} \right)}^2}}$$ 16 Since the loss term \(\infty \sum\limits_{{i=1}}^{l} {{{\left( {{y_i} - f\left( {{x_i}} \right)} \right)}^2}}\) is 0, the energy function can be converted to: $$E\left( f \right)=\frac{1}{2}\sum\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\left( {f\left( {{x_j}} \right) - f\left( {{x_i}} \right)} \right)}^2}}$$ 17 Because of \({y_i} \in \left\{ {0,1} \right\}\) , the energy function can be transformed into: $$E\left( f \right)=\sum\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}}$$ 18 In this way, the solution of semi-supervised learning can be transformed into a minimization problem, $$F=\arg {\hbox{min} _{f\left( x \right) \in \left\{ { - 1,1} \right\}}}E\left( f \right)$$ 19 (2) Method based on Gaussian field and harmonic function The loss term uses the same loss term as the minimum cut method. In order to keep the target value of the labeled sample unchanged, the loss item sets an infinite weight. The regular term is different from the minimum cut method, and its classification range is relaxed to the real number domain R. Energy function definition: $$E\left( f \right)=\infty \sum\limits_{{i=1}}^{l} {{{\left( {{y_i} - f\left( {{x_i}} \right)} \right)}^2}} {\text{+}}\frac{1}{2}\sum\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\left( {f\left( {{x_j}} \right) - f\left( {{x_i}} \right)} \right)}^2}}$$ 20 Among them, there is \(f\left( x \right) \in R\) , and the energy function is represented by Laplacian \(\Delta\) of the denormalized graph: $$E\left( f \right)=\infty \sum\limits_{{i=1}}^{l} {{{\left( {{y_i} - f\left( {{x_i}} \right)} \right)}^2}} +{f^T}\Delta f={f^T}\Delta f$$ 21 The optimal solution of the above formula is \(F=\arg {\hbox{min} _{f\left| {{f_l}={X_l}} \right.}}E\left( f \right)\) , and its solution satisfies \(\Delta f=0\) on \({X_u}\) . (Satisfying \(\Delta f=0\) function becomes a harmonic function), the harmonic function can be transformed into: $$E\left( j \right)=\frac{1}{{{d_j}}}\sum\limits_{{i\sim j}} {{w_{ij}}} F\left( j \right),j=l+1,l+2, \cdots ,l+u$$ 22 Among them, there is \(D=dia\left( {{d_i}} \right),{d_i}=\sum\limits_{j} {{w_{ij}}}\) . The above equation is equivalent to \(F=PF\) , among them, there is \(P={D^{ - 1}}W\) . In order to calculate the harmonic solution, the weight matrix W is divided into four blocks: $$\begin{gathered} W=\left[ {\begin{array}{*{20}{c}} {{W_{ll}}}&{{W_{ll}}} \\ {{W_{ul}}}&{{W_{uu}}} \end{array}} \right] \hfill \\ f=\left[ {\begin{array}{*{20}{c}} {{F_l}} \\ {{F_u}} \end{array}} \right] \hfill \\ \end{gathered}$$ 23 From \(\Delta f=0,{f_l}={Y_l}\) , we can get: $${F_u}={P_{uu}}{F_u}+{P_{ul}}{Y_l}$$ 24 \({F^*}\) is recorded as the limit of \({F_u}\) , \({F^*}{\text{=}}\mathop {\lim }\limits_{{n \to \infty }} {F_u}={\left( {I - {P_{uu}}} \right)^{ - 1}}{P_{ul}}{Y_l}\) The specific algorithm steps are as follows: Step 1: the weight matrix W is constructed. Step 2: The non-standardized graph Laplacian matrix \(\Delta\) is calculated. Step 3: Calculate \({F_u}={P_{uu}}{F_u}+{P_{ul}}{Y_l}\) Step 4: The limit \({F^*}\) of \({F_u}\) is sought, \({F^*}{\text{=}}\mathop {\lim }\limits_{{n \to \infty }} {F_u}={\left( {I - {P_{uu}}} \right)^{ - 1}}{P_{ul}}{Y_l}\) Step 5: Each unlabeled sample label is predicted \({y_i}=\arg \mathop {max}\limits_{{j \leqslant c}} F_{{ij}}^{*}\left( {l \leqslant i \leqslant l+u} \right)\) (3) A method based on local consistency and global consistency Most current semi-supervised learning methods based on graphs are local learning methods. From this perspective, a method based on local and global consistency is proposed. Similar to other graph-based semi-supervised learning methods, it makes the label information of each sample propagate to neighboring samples in an iterative manner (locality). The difference from other graph-based semi-supervised learning is that it adds a constraint. The condition requires the iteration to reach a global stable state before stopping propagation, which reflects the globality. Energy function definition: $$E\left( f \right)=\frac{1}{2}\left( \begin{gathered} \mu \sum\limits_{{i=1}}^{n} {{{\left\| {{y_i} - f\left( {{x_i}} \right)} \right\|}^2}+} \hfill \\ \sum\limits_{{i,j=1}}^{n} {{w_{ij}}{{\left\| {\frac{1}{{\sqrt {{d_{ii}}} }}f\left( {{x_i}} \right) - \frac{1}{{\sqrt {{d_{jj}}} }}f\left( {{x_i}} \right)} \right\|}^2}} \hfill \\ \end{gathered} \right)$$ 25 Among them, \(\mu >0\) is a regular parameter. The energy function is represented by the Laplacian S of the normalized graph: $$E\left( f \right)=\frac{1}{2}\left( {\mu \sum\limits_{{i=1}}^{n} {{{\left\| {{y_i} - f\left( {{x_i}} \right)} \right\|}^2}+} {f^T}Sf} \right)$$ 26 Unlike the Gaussian field, the locally consistent and global consistent methods have an additional loss term \(\mu \sum\limits_{{i=1}}^{n} {{{\left\| {{y_i} - f\left( {{x_i}} \right)} \right\|}^2}}\) . If there is an error in the marking of the marked sample, it will be punished. When \(\mu {\text{=}}\infty\) , its energy function is the same as the high random field. The optimal solution is \(F=\arg \hbox{min} E\left( f \right)\) . The iterative equation is: $$F\left( t \right)=\alpha SF\left( {t - 1} \right)+\left( {I - \alpha } \right)Y,\alpha \in \left( {0,1} \right)$$ 27 6. Case Study In order to get the effect of the algorithm improvement, this paper experimented with the English text classification corpus data set of the natural language processing open platform to test the algorithm constructed in this paper. This paper respectively selects 20 documents from the data set in traffic, computer, sports, and economy to form a test data set. The experimental results are tested in the following two ways: fuzzy clustering considering the semantic contribution of feature items and fuzzy clustering without considering the semantic contribution of feature items. The comparison results are shown in Table 1 . The corresponding statistical diagrams are shown in Fig. 5 and Fig. 6 . Table 1 Comparison of the effect of fuzzy clustering considering the semantic contribution of feature items and fuzzy clustering without considering the semantic contribution of feature items Project traffic computer physical education economic Fuzzy clustering without considering semantic relations Number of clustered text 18 19 20 23 Number of correct texts 14 15 15 16 Accuracy 0.78 0.80 0.76 0.70 Recall rate 0.71 0.76 0.76 0.81 Fuzzy clustering considering semantic relations Number of clustered text 19 19 20 22 Number of correct texts 15 16 16 17 Accuracy 0.80 0.85 0.81 0.78 Recall rate 0.76 0.81 0.81 0.86 7. Conclusion Many problems in the field of machine learning, such as classification, dimensionality reduction, clustering, etc., are closely related to graphs. It can be considered that the performance of these algorithms for different applications depends to a large extent on the constructed graph and the optimization on the graph. At present, most of the existing graph-based methods often rely on local nearest neighbor composition, or maintain a certain global property composition. However, how to construct a good graph has not been well studied. In response to this problem, after careful study of the existing image construction methods, we propose a new composition framework. First, we construct a 1-norm graph as the main graph, and then construct a k-nearest neighbor graph as the auxiliary graph, and finally superimpose the two in a certain proportion to obtain a norm and nearest neighbor superposition (LNKNNS) graph. Finally, the performance of the model constructed in this paper is analyzed through experimental research. From the research results, it can be seen that the model constructed in this paper is relatively effective. 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LI, et al., “Text keyword extraction method based on word frequency statistics,” Journal of computer applications, vol. 36, no. 3, p. 718, 2016. V. N. Phu, and T. N. T. Vo, “K-Medoids algorithm used for english sentiment classification in a distributed system,” Computer Modelling and New Technologies, vol. 22, no. 1, pp. 20-39, 2018. Cite Share Download PDF Status: Published Journal Publication published 26 Apr, 2023 Read the published version in Soft Computing → Version 1 posted Reviewers agreed at journal 22 Feb, 2023 Editor assigned by journal 15 Feb, 2023 First submitted to journal 10 Feb, 2023 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. 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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-2575502","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":178062270,"identity":"78eedab6-378f-4ea1-b6eb-8b549207b2c9","order_by":0,"name":"Liu Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIie2QsQrCMBCGrxTSJTi3SOkrpBR0EZ/litDJQRDEqRSEdhHnCj5EHyHQwUV8hkydHHwAQXMWN4kdHfJNP+G+y90BWCx/iFMACqUD8woU/cMQBUnhcqDyhhTw8dPjB26NapWWeTQKlFpzmIWNdDtlHGyv50nLNi7HiAmHLGkkmwqjUhWkSGS90qaN5Mw3KjsgJUcWSFKeA5T+Fxd1GSlygEK74FXvwhHjk1gkx5ZNjEpcLzNx3+RRVF0ycdvOw8N515mVgmfCYRR1ADqVa6rXROC1Ch4UKVgsFovlCy/wz0iXUsb/SgAAAABJRU5ErkJggg==","orcid":"","institution":"Jiujiang University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Liu","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2023-02-11 08:11:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2575502/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2575502/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00500-023-08206-9","type":"published","date":"2023-04-26T20:35:28+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":33365263,"identity":"373ace45-23b3-42df-861d-ce821ce0754f","added_by":"auto","created_at":"2023-02-23 19:17:42","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":37598,"visible":true,"origin":"","legend":"\u003cp\u003eGeneral framework of graph-based semi-supervised learning\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2575502/v1/6ac4b10c08c52776a174b6d0.png"},{"id":33365264,"identity":"baaad75d-c49b-4b91-b598-a166345af28f","added_by":"auto","created_at":"2023-02-23 19:17:42","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":53053,"visible":true,"origin":"","legend":"\u003cp\u003eConstructed by the similarity between samples and samples\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2575502/v1/056bf693243cd65b6c9d6c75.png"},{"id":33365363,"identity":"bf8f968f-e00d-4ecb-aac0-55fe92e80793","added_by":"auto","created_at":"2023-02-23 19:25:42","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":70395,"visible":true,"origin":"","legend":"\u003cp\u003eHandwritten digital structure diagram\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2575502/v1/c5a31198a00ff8ecf0e755c0.png"},{"id":33365265,"identity":"1a449695-852e-489d-8ae5-4f22a4404883","added_by":"auto","created_at":"2023-02-23 19:17:42","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":39645,"visible":true,"origin":"","legend":"\u003cp\u003eMinimum cut set\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2575502/v1/bbede476fe9ee3ae16c92304.png"},{"id":33365690,"identity":"6c8291b0-6560-42d1-a24e-c83db7e6f778","added_by":"auto","created_at":"2023-02-23 19:33:42","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":120368,"visible":true,"origin":"","legend":"\u003cp\u003eFuzzy clustering effects without considering the semantic contribution of feature items\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2575502/v1/2dfeab96533d2b12fd6efac7.jpg"},{"id":33365365,"identity":"912e1d3c-064b-4e85-8cfb-0b2d38da9778","added_by":"auto","created_at":"2023-02-23 19:25:42","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":123794,"visible":true,"origin":"","legend":"\u003cp\u003eFuzzy clustering effects considering the semantic contribution of feature items\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2575502/v1/e95391247e050c8fce9d2588.jpg"},{"id":44727384,"identity":"196738fe-3a0e-4ccc-bac9-ac3568878e88","added_by":"auto","created_at":"2023-10-16 20:52:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":640798,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2575502/v1/61e890be-d8dd-41ab-895b-0b8b626a6710.pdf"}],"financialInterests":"","formattedTitle":"Unsupervised machine learning and image recognition model application in English part-of-speech feature learning Under the open platform environment","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003ePart-of-speech tagging refers to the process of labeling reasonable parts of speech for each word in a sentence based on the contextual relationship. Part-of-speech tagging is one of the important pre-processing tasks of natural language processing, and it is also the basis of information extraction, lexical analysis, grammatical analysis, and semantic analysis. The accuracy of part-of-speech tagging will directly affect the effect of research on text retrieval, text classification, and machine translation. Part-of-speech tagging itself is a more difficult problem, because many words usually have multiple parts of speech. However, considering the context of the words, the parts of speech of these words are unique, and specific parts of speech tags such as nouns, verbs, and adjectives can be clearly attached. Part-of-speech tagging is a very important research content in the field of Chinese information processing. After the input text is segmented in Chinese, combined with the context of the word, part-of-speech tagging marks each word with the appropriate part of speech. The traditional transfer learning text feature alignment method considers the characteristics of words in sentence structure. For example, the structural consistency learning algorithm and the spectral feature alignment algorithm use the word co-occurrence matrix of the entire corpus to perform matrix operations to obtain words that are similar in frequency or probability, but ignore the connection between the text classification information and the features in the text.\u003c/p\u003e"},{"header":"2. Related Work","content":"\u003cp\u003eIn the face of large-scale short text data, quickly and accurately obtaining the required key information and improving the efficiency and accuracy of clustering have always been the focus of attention. However, the inherent characteristics of short texts make it impossible to calculate the traditional feature weights accurately. Therefore, scholars use different methods to solve this defect, which is generally divided into three aspects. One aspect is to use feature subset evaluation methods to improve the feature space, including information gain, chi-square test (CHI-sqare, CHI), expected cross entropy (Expected Cross Entropy, ECE), etc. The literature proposes an improved feature weight calculation method, which introduces the concept of information gain in information theory to realize the comprehensive consideration of the specific dimensions of short text feature distribution and overcome the shortcomings of traditional formulas [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The experimental results show that the improved feature weight calculation algorithm is more effective in calculating feature weights. The second is to improve the search space strategy, including sequential selection algorithm, genetic algorithm, particle swarm algorithm, etc. These algorithms use search and superposition to reduce the dimensionality of the feature space while improving the accuracy of the algorithm itself.\u003c/p\u003e \u003cp\u003eWhen generating a single-document summary, it can be achieved through deep learning, that is, using a large-scale data set to train a neural network in a data-driven manner to learn the shallow semantics of the original text and generate a summary. In related work, the literature used the Seq2Seq framework to give input sentences on the encoder side, output each word of the abstract on the decoder side, and use a local attention mechanism to improve the effect [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. The literature incorporated traditional TF-IDF, POS, named entity and other features to improve the effect, and introduces Pointer to solve unknown words and low-frequency words [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The literature provided a new Chinese short text abstract data set (data source is Sina Weibo), and manually scored it according to the correlation between the text and abstract [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The literature summarized the new methods in the field of text summarization in recent years, and evaluated them from extractive and generative, single-document and multi-document aspects, including data sets and evaluation methods [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The literature proposed an internal attention mechanism to solve the problem of repeated words, and the training method combines supervised learning and reinforcement learning to improve the effect [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Based on convolutional sequence to sequence (ConvS2S), the literature incorporated the subject information into it, and used reinforcement learning training methods to optimize it. FAN et al. generated abstracts based on the user's style of writing abstracts, including abstract length, words used and other characteristics. The literature proposed the task of generating abstracts based on reader perception, and designed an adversarial learning model called Reader Perception Summarizer (RASG), which incorporates readers\u0026rsquo; comments into generative abstracts [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. For the task of PECH (Product Perception Answer Generation), the literature designed a model PAAG based on adversarial learning, and proposed a reading review method based on attention mechanism to capture the most relevant words in a given question [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe literature proposed to extract nouns and verbs with strong category characteristics as the first-level part of speech of the text, which improves the efficiency of feature extraction and reduces the dimension of feature vectors, so it is a simple and efficient feature extraction method [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. When using semantic-based short text similarity for text classification, the literature assigned different weight coefficients to the extracted keywords of different parts of speech to distinguish the importance of various contribution terms in the calculation of short text similarity, which effectively improves the accuracy of short text classification [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. In these methods, part-of-speech features are considered, and different parts of speech contain different information. Words with strong classification characteristics are given higher weights or the words with strong classification characteristics are directly used as first-level feature words for feature selection, which lacks further research and comparison. When considering the important factors that affect the classification category, the literature found through manual observation and comparison that the word that contains the most category information is noun, while verbs, adjectives, pronouns, quantifiers, etc. contain less category distinguishing features [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The literature proposed an English phrase extraction algorithm based on statistical methods, and used the support vector machine (SVM) algorithm for classification experiments. The literature proposed an English keyword extraction method based on TextRank algorithm and mutual information similarity [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Then, it calculated the similarity between the input text keyword set and various keyword sets according to the mutual information similarity measure, and realized text classification. The literature studied an n-ary incremental algorithm to extract semantic strings expressing key information in Uyghur texts, and proposed a similarity measurement method for text and topic similarity similar to Jaccard to implement an English classification algorithm [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e"},{"header":"3. Graph-based Semi-supervised Learning","content":"\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the general framework of graph-based semi-supervised learning. Most graph-based methods are directly based on sample sets. The labeled and unlabeled samples are represented by vertices, and the similarity is represented by the weight of the edge connecting the two vertices. The similarity is generally obtained through a certain distance measurement method. The common distance measurement methods include Euclidean distance, Gaussian distance, angle cosine distance, Chebyshev distance, correlation coefficient, weighted S-order Minkowski distance and so on. For different graph-based semi-supervised learning methods, its composition method is also different. No matter how to construct the graph, their purpose is to make the constructed graph represent the real data structure of the data, thereby improving the learning performance of the classifier. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the graph is constructed by the similarity between samples and samples.\u003c/p\u003e\n\u003cp\u003eThe sample set \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X=\\left\\{ {{X_i},{X_u}} \\right\\}=\\left\\{ {{x_1}, \\cdots ,{x_l},{x_{l+1}}, \\cdots ,{x_{l+u}}} \\right\\}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(Y={\\left\\{ {{Y_l},{Y_u}} \\right\\}^T} \\in {R^{\\left| V \\right| \\times c}}\\)\u003c/span\u003e\u003c/span\u003e are the class mark matrix. The class mark matrix is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(L=\\left\\{ {1, \\cdots ,c} \\right\\}\\)\u003c/span\u003e\u003c/span\u003e, and c is the number of classes. If sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e belongs to class \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(j \\in L,{Y_{ij}}=1\\)\u003c/span\u003e\u003c/span\u003e, otherwise \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y_{ij}}=0\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=l+u\\)\u003c/span\u003e\u003c/span\u003e is the total number of samples in the data set. Among them, l represents the number of labeled samples \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\left( {i \\leqslant l} \\right)\\)\u003c/span\u003e\u003c/span\u003e, the corresponding labeled value is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(y \\in L\\)\u003c/span\u003e\u003c/span\u003e, and u is the number of unlabeled samples \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_j}\\left( {l\u0026lt;j \\leqslant l+u} \\right)\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=\\left( {V,E} \\right)\\)\u003c/span\u003e\u003c/span\u003e represents an undirected weighted graph. Among them, V represents the vertex set, E represents the edge set, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w_{ij}}\\)\u003c/span\u003e\u003c/span\u003e is the weight of the edge \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(e=\\left( {i,j} \\right)\\)\u003c/span\u003e\u003c/span\u003e, which represents the similarity between nodes i and j. Since the constructed graph is an undirected graph, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w_{ij}}={w_{ji}}\\)\u003c/span\u003e\u003c/span\u003e. The weight matrix W of G is:\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$${W_{ij}}=\\left\\{ {\\begin{array}{*{20}{c}} {{w_{ij}}}\u0026amp;{if\\left( {e\\left( {i,j} \\right) \\in E} \\right)} \\\\ 0\u0026amp;{otherwise} \\end{array}} \\right.$$\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\\({D_{ii}}=\\sum {_{j}} {W_{ij}}\\)\u003c/span\u003e \u003c/span\u003e is the sum of the weights of all edges connected to the node. From the diagonal matrix D, the Laplacian matrix can be obtained. There are usually two ways to obtain the graph Laplacian matrix: One is the non-normalized graph Laplacian:\u003c/p\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$$\\Delta {\\text{=}}D - W$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe other is the normalized Tulaplas:\u003c/p\u003e\n\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ3\" class=\"mathdisplay\"\u003e$$S={D^{ - {1 \\mathord{\\left/ {\\vphantom {1 2}} \\right. \\kern-0pt} 2}}}\\Delta {D^{ - {1 \\mathord{\\left/ {\\vphantom {1 2}} \\right. \\kern-0pt} 2}}}=I - {D^{ - {1 \\mathord{\\left/ {\\vphantom {1 2}} \\right. \\kern-0pt} 2}}}W{D^{ - {1 \\mathord{\\left/ {\\vphantom {1 2}} \\right. \\kern-0pt} 2}}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eI is the identity matrix.\u003c/p\u003e"},{"header":"4. Graph Construction Method","content":"\u003cp\u003eAccording to the way of picture construction, we roughly divide the types of existing pictures into two categories, that is, traditional composition and non-traditional composition.\u003c/p\u003e\n\u003ch3\u003e1. Traditional Composition Method\u003c/h3\u003e\n\u003cp\u003eSometimes, we cannot predict the type of structure of a certain data. In this case, we can only use some traditional methods to construct the graph. Traditional graphs include exponential weighted graphs, k nearest neighbor graphs (kNN graphs), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varepsilon\\)\u003c/span\u003e\u003c/span\u003e nearest neighbor graphs (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varepsilon NN\\)\u003c/span\u003e\u003c/span\u003e graphs), and local linear embedding graphs (LLE graphs). Traditional composition is usually composed of two parts: the choice of graph structure and the weight of edges.\u003c/p\u003e\n\u003cp\u003e1) exp-weighted graph\u003c/p\u003e\n\u003cp\u003eThe exp-weighted picture is the simplest way of composition. It uses the Gaussian kernel function to set the weights of the edges in the graph. The specific composition method is as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ4\" class=\"mathdisplay\"\u003e$${W_{ij}}=\\left\\{ {\\begin{array}{*{20}{c}} {\\exp \\left( { - \\frac{1}{2}{d_{ij}}{\\sigma ^{ - 2}}} \\right)}\u0026amp;{if\\left( {i \\ne j} \\right)} \\\\ 0\u0026amp;{otherwise} \\end{array}} \\right.$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e2) kNN graph\u003c/p\u003e\n\u003cp\u003eSince the k-nearest neighbor relationship is asymmetric, in the k-nearest neighbor graph, if node i is the k-nearest neighbor of node j, there is an arc connection between nodes i and j instead of an edge connection. The arc starts at j and ends at i. In order to get an undirected graph, the direction of the arc can be ignored. To construct a kNN graph, a distance metric is usually selected first, and then the distance between the data sample and other data samples is calculated through the distance metric, and the distance between the two samples is used as the weight of the two samples on the corresponding edges of the graph. In this way, a kNN graph can be obtained for the convenience of description. This section takes Euclidean distance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({d_{ij}}=\\sum\\limits_{{k=1}}^{n} {{{\\left( {{x_{ik}} - {x_{ik}}} \\right)}^2}}\\)\u003c/span\u003e\u003c/span\u003e as an example. The specific composition method is as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ5\" class=\"mathdisplay\"\u003e$${W_{ij}}=\\left\\{ {\\begin{array}{*{20}{c}} {\\exp \\left( { - \\frac{1}{2}{d_{ij}}{\\sigma ^{ - 2}}} \\right)}\u0026amp;{if\\left( {{x_j} \\in {K_j}} \\right)} \\\\ 0\u0026amp;{otherwise} \\end{array}} \\right.$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eFor any sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({K_j}\\)\u003c/span\u003e\u003c/span\u003e represents the set of k-nearest neighbor nodes of sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003e3) Graphs \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varepsilon NN\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eIn graphs \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varepsilon NN\\)\u003c/span\u003e\u003c/span\u003e, a threshold is set for the distance between the data sample points, and the threshold must be less than or equal to parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varepsilon\\)\u003c/span\u003e\u003c/span\u003e. If the distance between sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e and sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_j}\\)\u003c/span\u003e\u003c/span\u003e is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({d_{ij}} \\leqslant \\varepsilon\\)\u003c/span\u003e\u003c/span\u003e, then there is an edge connection, otherwise there is no edge connection. The specific diagram is constructed as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ6\" class=\"mathdisplay\"\u003e$${W_{ij}}=\\left\\{ {\\begin{array}{*{20}{c}} {\\exp \\left( { - \\frac{1}{2}{d_{ij}}{\\sigma ^{ - 2}}} \\right)}\u0026amp;{if\\left( {{d_{ij}} \\leqslant \\varepsilon } \\right)} \\\\ 0\u0026amp;{otherwise} \\end{array}} \\right.$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e4) LLE diagram\u003c/p\u003e\n\u003cp\u003eRoweis et al. first proposed local linear embedding. The basic idea is: First, the neighbors of the sample are determined. If there is no neighbor relationship between sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e and sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_j}\\)\u003c/span\u003e\u003c/span\u003e, and there is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega _{ij}}=0\\)\u003c/span\u003e\u003c/span\u003e. The local linear reconstruction coefficient is solved by the following formula, and the coefficient is used as the weight of the connection.\u003c/p\u003e\n\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ7\" class=\"mathdisplay\"\u003e$$\\left\\{ {\\begin{array}{*{20}{c}} {\\hbox{min} \\sum\\limits_{i} {{{\\left\\| {{x_i} - \\sum\\limits_{j} {{w_{ij}}{x_j}} } \\right\\|}^2}} } \\\\ {s.t.\\sum\\limits_{j} {{w_{ij}}} =1} \\end{array}} \\right.$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ8\" class=\"mathdisplay\"\u003e$${W_{ij}}=\\left\\{ {\\begin{array}{*{20}{c}} {{w_{ij}}}\u0026amp;{if\\left( {if\\left( {{x_j} \\in {K_j}} \\right)} \\right)} \\\\ 0\u0026amp;{otherwise} \\end{array}} \\right.$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\n\u003c/div\u003e\n\u003ch3\u003e2. Non-traditional Composition Method\u003c/h3\u003e\n\u003cp\u003e1) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\ell ^1}\\)\u003c/span\u003e\u003c/span\u003e norm graph\u003c/p\u003e\n\u003cp\u003eFor any sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e in the sample set \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X=\\left\\{ {{x_1},{x_2}, \\cdots ,{x_n}} \\right\\} \\in {R^{m \\times n}}\\)\u003c/span\u003e\u003c/span\u003e, since the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\ell ^0}\\)\u003c/span\u003e\u003c/span\u003e norm is an NP-hard problem, its sparse coding can be achieved by solving the following \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\ell ^1}\\)\u003c/span\u003e\u003c/span\u003e norm optimization problem:\u003c/p\u003e\n\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ9\" class=\"mathdisplay\"\u003e$$\\begin{gathered} \\mathop {\\hbox{min} }\\limits_{{{\\alpha ^i}}} {\\left\\| {{\\alpha ^i}} \\right\\|_1} \\hfill \\\\ s.t.{x_i}={D^i}{\\alpha ^i}=\\sum\\limits_{{j \\ne i}} {{x_j}\\alpha _{j}^{i},{\\alpha ^i} \\geqslant 0} \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAmong them, the dictionary is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({D^i}=\\left[ {{x_1}, \\cdots ,{x_{i - 1}},{x_{i+1}}, \\cdots ,{x_n}} \\right] \\in {R^{m \\times \\left( {m+n - 1} \\right)}}\\)\u003c/span\u003e\u003c/span\u003e and the coefficient matrix is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha ^i} \\in {R^{m \\times \\left( {n - 1} \\right)}};j=1,2, \\cdots ,n,j \\ne i\\)\u003c/span\u003e\u003c/span\u003e. W is used as the weight matrix of the graph. If \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\u0026gt;j,{W_{ij}}=\\alpha _{j}^{i}\\)\u003c/span\u003e\u003c/span\u003e, if \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\u0026lt;j,{W_{ij}}=\\alpha _{{j - 1}}^{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\ell ^1}\\)\u003c/span\u003e\u003c/span\u003e norm matrix W is calculated as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ10\" class=\"mathdisplay\"\u003e$${W_{ij}}=\\left\\{ {\\begin{array}{*{20}{c}} {\\alpha _{j}^{i}}\u0026amp;{i{f_{}}i\u0026gt;j} \\\\ {\\alpha _{{j - 1}}^{i}}\u0026amp;{i{f_{}}i\u0026lt;j} \\end{array}} \\right.$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e2) Low rank representation graph (LRR graph)\u003c/p\u003e\n\u003cp\u003eFor any sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e in the sample set \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X=\\left[ {{x_1},{x_2}, \\cdots ,{x_n}} \\right] \\in {R^{m \\times n}}\\)\u003c/span\u003e\u003c/span\u003e, its low-rank coding can be achieved by solving the following kernel norm optimization problem:\u003c/p\u003e\n\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ11\" class=\"mathdisplay\"\u003e$$\\begin{gathered} \\mathop {\\hbox{min} }\\limits_{{{Z^i}}} {\\left\\| {{Z^i}} \\right\\|_*} \\hfill \\\\ s.t.{x_i}={D^i}{Z^i}=\\sum\\limits_{{j \\ne i}} {{x_j}\\alpha _{j}^{i},{\\alpha ^i} \\geqslant 0} \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAmong them,\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$${D^i}=\\left[ {{x_1},{x_2}, \\cdots ,{x_n}} \\right] \\in {R^{m \\times \\left( {m+n} \\right)}}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({Z^i}=\\left[ {{z_1},{z_2}, \\cdots ,{z_n}} \\right] \\in {R^{m \\times n}}\\)\u003c/span\u003e \u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eis the low-rank representation coefficient matrix, and the calculation formula of the low-rank representation matrix W is as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ12\" class=\"mathdisplay\"\u003e$${W_{ij}}=Z_{j}^{i}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. Graph-based Semi-supervised Learning Method","content":"\u003cp\u003eThe graph method is a method based on the manifold assumption. Its goal is to find a classification function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f:V \\to R\\)\u003c/span\u003e\u003c/span\u003e in the graph, and the classification function f needs to meet two basic conditions.\u003c/p\u003e\n\u003cp\u003e(1) For labeled samples, the classification value should be as close as possible to the target value;\u003c/p\u003e\n\u003cp\u003e(2) The classification function should be as smooth as possible on the entire graph.\u003c/p\u003e\n\u003cp\u003eAn energy function framework can be represented by these two conditions, the first part is the loss term, and the second part is the regularizer.\u003c/p\u003e\n\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ13\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=Loss{\\text{ }}item+Regular{\\text{ }}term$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWith the energy function framework, we can obtain the classification function by optimizing the energy function. Currently, most graph-based semi-supervised learning uses this energy function framework. Their loss items and regular items may be different, and they belong to the same type of method. Next, a few more popular graph-based semi-supervised learning methods are introduced.\u003c/p\u003e\n\u003cp\u003e(1) Minimum cut method\u003c/p\u003e\n\u003cp\u003eThe purpose of learning is to find a minimum cut set, which cuts all the connections between the \"source\" and the \"well\" of the entire graph, so that the samples are \"cut\" into two categories. The \"+\" sample is connected to the \"source\", and the \"-\" sample is connected to all the \"wells\", as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe objective function is composed of two parts. The first part is the loss term, which is used to punish the mislabeled samples. The loss term can be obtained by adding the infinite coefficient \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\infty\\)\u003c/span\u003e\u003c/span\u003e to the square loss function, which can fix the class label of the marked sample. The loss term can be expressed as:\u003c/p\u003e\n\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ14\" class=\"mathdisplay\"\u003e$$\\infty \\sum\\limits_{{i=1}}^{l} {{{\\left( {{y_i} - f\\left( {{x_i}} \\right)} \\right)}^2}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe other part is the regular term, which is to make the adjacent sample labels as similar as possible, so that the labels distributed on the graph are smooth.\u003c/p\u003e\n\u003cp\u003eThe regular term is defined:\u003c/p\u003e\n\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ15\" class=\"mathdisplay\"\u003e$$\\frac{1}{2}\\sum\\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\\left( {f\\left( {{x_j}} \\right) - f\\left( {{x_i}} \\right)} \\right)}^2}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe energy function is:\u003c/p\u003e\n\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ16\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=\\infty \\sum\\limits_{{i=1}}^{l} {{{\\left( {{y_i} - f\\left( {{x_i}} \\right)} \\right)}^2}} {\\text{+}}\\frac{1}{2}\\sum\\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\\left( {f\\left( {{x_j}} \\right) - f\\left( {{x_i}} \\right)} \\right)}^2}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eSince the loss term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\infty \\sum\\limits_{{i=1}}^{l} {{{\\left( {{y_i} - f\\left( {{x_i}} \\right)} \\right)}^2}}\\)\u003c/span\u003e\u003c/span\u003e is 0, the energy function can be converted to:\u003c/p\u003e\n\u003cdiv id=\"Equ17\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ17\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=\\frac{1}{2}\\sum\\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\\left( {f\\left( {{x_j}} \\right) - f\\left( {{x_i}} \\right)} \\right)}^2}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e17\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eBecause of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({y_i} \\in \\left\\{ {0,1} \\right\\}\\)\u003c/span\u003e\u003c/span\u003e, the energy function can be transformed into:\u003c/p\u003e\n\u003cdiv id=\"Equ18\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ18\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=\\sum\\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e18\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn this way, the solution of semi-supervised learning can be transformed into a minimization problem,\u003c/p\u003e\n\u003cdiv id=\"Equ19\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ19\" class=\"mathdisplay\"\u003e$$F=\\arg {\\hbox{min} _{f\\left( x \\right) \\in \\left\\{ { - 1,1} \\right\\}}}E\\left( f \\right)$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e19\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e(2) Method based on Gaussian field and harmonic function\u003c/p\u003e\n\u003cp\u003eThe loss term uses the same loss term as the minimum cut method. In order to keep the target value of the labeled sample unchanged, the loss item sets an infinite weight. The regular term is different from the minimum cut method, and its classification range is relaxed to the real number domain R.\u003c/p\u003e\n\u003cp\u003eEnergy function definition:\u003c/p\u003e\n\u003cdiv id=\"Equ20\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ20\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=\\infty \\sum\\limits_{{i=1}}^{l} {{{\\left( {{y_i} - f\\left( {{x_i}} \\right)} \\right)}^2}} {\\text{+}}\\frac{1}{2}\\sum\\limits_{{i,j=1}}^{{l+u}} {{w_{ij}}{{\\left( {f\\left( {{x_j}} \\right) - f\\left( {{x_i}} \\right)} \\right)}^2}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e20\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAmong them, there is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f\\left( x \\right) \\in R\\)\u003c/span\u003e\u003c/span\u003e, and the energy function is represented by Laplacian \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta\\)\u003c/span\u003e\u003c/span\u003e of the denormalized graph:\u003c/p\u003e\n\u003cdiv id=\"Equ21\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ21\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=\\infty \\sum\\limits_{{i=1}}^{l} {{{\\left( {{y_i} - f\\left( {{x_i}} \\right)} \\right)}^2}} +{f^T}\\Delta f={f^T}\\Delta f$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e21\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe optimal solution of the above formula is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F=\\arg {\\hbox{min} _{f\\left| {{f_l}={X_l}} \\right.}}E\\left( f \\right)\\)\u003c/span\u003e\u003c/span\u003e, and its solution satisfies \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta f=0\\)\u003c/span\u003e\u003c/span\u003e on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_u}\\)\u003c/span\u003e\u003c/span\u003e. (Satisfying \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta f=0\\)\u003c/span\u003e\u003c/span\u003e function becomes a harmonic function), the harmonic function can be transformed into:\u003c/p\u003e\n\u003cdiv id=\"Equ22\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ22\" class=\"mathdisplay\"\u003e$$E\\left( j \\right)=\\frac{1}{{{d_j}}}\\sum\\limits_{{i\\sim j}} {{w_{ij}}} F\\left( j \\right),j=l+1,l+2, \\cdots ,l+u$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e22\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAmong them, there is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D=dia\\left( {{d_i}} \\right),{d_i}=\\sum\\limits_{j} {{w_{ij}}}\\)\u003c/span\u003e\u003c/span\u003e. The above equation is equivalent to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F=PF\\)\u003c/span\u003e\u003c/span\u003e, among them, there is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P={D^{ - 1}}W\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eIn order to calculate the harmonic solution, the weight matrix W is divided into four blocks:\u003c/p\u003e\n\u003cdiv id=\"Equ23\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ23\" class=\"mathdisplay\"\u003e$$\\begin{gathered} W=\\left[ {\\begin{array}{*{20}{c}} {{W_{ll}}}\u0026amp;{{W_{ll}}} \\\\ {{W_{ul}}}\u0026amp;{{W_{uu}}} \\end{array}} \\right] \\hfill \\\\ f=\\left[ {\\begin{array}{*{20}{c}} {{F_l}} \\\\ {{F_u}} \\end{array}} \\right] \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e23\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eFrom \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta f=0,{f_l}={Y_l}\\)\u003c/span\u003e\u003c/span\u003e, we can get:\u003c/p\u003e\n\u003cdiv id=\"Equ24\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ24\" class=\"mathdisplay\"\u003e$${F_u}={P_{uu}}{F_u}+{P_{ul}}{Y_l}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e24\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({F^*}\\)\u003c/span\u003e \u003c/span\u003e is recorded as the limit of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F_u}\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({F^*}{\\text{=}}\\mathop {\\lim }\\limits_{{n \\to \\infty }} {F_u}={\\left( {I - {P_{uu}}} \\right)^{ - 1}}{P_{ul}}{Y_l}\\)\u003c/span\u003e \u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eThe specific algorithm steps are as follows:\u003c/p\u003e\n\u003cp\u003eStep 1: the weight matrix W is constructed.\u003c/p\u003e\n\u003cp\u003eStep 2: The non-standardized graph Laplacian matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Delta\\)\u003c/span\u003e\u003c/span\u003e is calculated.\u003c/p\u003e\n\u003cp\u003eStep 3: Calculate\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({F_u}={P_{uu}}{F_u}+{P_{ul}}{Y_l}\\)\u003c/span\u003e \u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eStep 4: The limit \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F^*}\\)\u003c/span\u003e\u003c/span\u003e of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F_u}\\)\u003c/span\u003e\u003c/span\u003e is sought,\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({F^*}{\\text{=}}\\mathop {\\lim }\\limits_{{n \\to \\infty }} {F_u}={\\left( {I - {P_{uu}}} \\right)^{ - 1}}{P_{ul}}{Y_l}\\)\u003c/span\u003e \u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eStep 5: Each unlabeled sample label is predicted\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({y_i}=\\arg \\mathop {max}\\limits_{{j \\leqslant c}} F_{{ij}}^{*}\\left( {l \\leqslant i \\leqslant l+u} \\right)\\)\u003c/span\u003e \u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e(3) A method based on local consistency and global consistency\u003c/p\u003e\n\u003cp\u003eMost current semi-supervised learning methods based on graphs are local learning methods. From this perspective, a method based on local and global consistency is proposed. Similar to other graph-based semi-supervised learning methods, it makes the label information of each sample propagate to neighboring samples in an iterative manner (locality). The difference from other graph-based semi-supervised learning is that it adds a constraint. The condition requires the iteration to reach a global stable state before stopping propagation, which reflects the globality.\u003c/p\u003e\n\u003cp\u003eEnergy function definition:\u003c/p\u003e\n\u003cdiv id=\"Equ25\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ25\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=\\frac{1}{2}\\left( \\begin{gathered} \\mu \\sum\\limits_{{i=1}}^{n} {{{\\left\\| {{y_i} - f\\left( {{x_i}} \\right)} \\right\\|}^2}+} \\hfill \\\\ \\sum\\limits_{{i,j=1}}^{n} {{w_{ij}}{{\\left\\| {\\frac{1}{{\\sqrt {{d_{ii}}} }}f\\left( {{x_i}} \\right) - \\frac{1}{{\\sqrt {{d_{jj}}} }}f\\left( {{x_i}} \\right)} \\right\\|}^2}} \\hfill \\\\ \\end{gathered} \\right)$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e25\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eAmong them, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu \u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e is a regular parameter. The energy function is represented by the Laplacian S of the normalized graph:\u003c/p\u003e\n\u003cdiv id=\"Equ26\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ26\" class=\"mathdisplay\"\u003e$$E\\left( f \\right)=\\frac{1}{2}\\left( {\\mu \\sum\\limits_{{i=1}}^{n} {{{\\left\\| {{y_i} - f\\left( {{x_i}} \\right)} \\right\\|}^2}+} {f^T}Sf} \\right)$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e26\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eUnlike the Gaussian field, the locally consistent and global consistent methods have an additional loss term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu \\sum\\limits_{{i=1}}^{n} {{{\\left\\| {{y_i} - f\\left( {{x_i}} \\right)} \\right\\|}^2}}\\)\u003c/span\u003e\u003c/span\u003e. If there is an error in the marking of the marked sample, it will be punished. When \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu {\\text{=}}\\infty\\)\u003c/span\u003e\u003c/span\u003e, its energy function is the same as the high random field. The optimal solution is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F=\\arg \\hbox{min} E\\left( f \\right)\\)\u003c/span\u003e\u003c/span\u003e. The iterative equation is:\u003c/p\u003e\n\u003cdiv id=\"Equ27\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ27\" class=\"mathdisplay\"\u003e$$F\\left( t \\right)=\\alpha SF\\left( {t - 1} \\right)+\\left( {I - \\alpha } \\right)Y,\\alpha \\in \\left( {0,1} \\right)$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e27\u003c/div\u003e\n\u003c/div\u003e"},{"header":"6. Case Study","content":"\u003cp\u003eIn order to get the effect of the algorithm improvement, this paper experimented with the English text classification corpus data set of the natural language processing open platform to test the algorithm constructed in this paper. This paper respectively selects 20 documents from the data set in traffic, computer, sports, and economy to form a test data set. The experimental results are tested in the following two ways: fuzzy clustering considering the semantic contribution of feature items and fuzzy clustering without considering the semantic contribution of feature items. The comparison results are shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The corresponding statistical diagrams are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eComparison of the effect of fuzzy clustering considering the semantic contribution of feature items and fuzzy clustering without considering the semantic contribution of feature items\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\u003eProject\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003etraffic\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ecomputer\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003ephysical education\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eeconomic\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"4\" align=\"left\"\u003e\n\u003cp\u003eFuzzy clustering without considering semantic relations\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNumber of clustered text\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e18\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e19\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e23\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNumber of correct texts\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e16\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAccuracy\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.78\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.70\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRecall rate\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.71\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.81\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"4\" align=\"left\"\u003e\n\u003cp\u003eFuzzy clustering considering semantic relations\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNumber of clustered text\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e19\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e19\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e20\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e22\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eNumber of correct texts\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e16\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e16\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e17\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eAccuracy\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.80\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.85\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.81\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.78\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eRecall rate\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.76\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.81\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.81\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.86\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e"},{"header":"7. Conclusion","content":"\u003cp\u003eMany problems in the field of machine learning, such as classification, dimensionality reduction, clustering, etc., are closely related to graphs. It can be considered that the performance of these algorithms for different applications depends to a large extent on the constructed graph and the optimization on the graph. At present, most of the existing graph-based methods often rely on local nearest neighbor composition, or maintain a certain global property composition. However, how to construct a good graph has not been well studied. In response to this problem, after careful study of the existing image construction methods, we propose a new composition framework. First, we construct a 1-norm graph as the main graph, and then construct a k-nearest neighbor graph as the auxiliary graph, and finally superimpose the two in a certain proportion to obtain a norm and nearest neighbor superposition (LNKNNS) graph. Finally, the performance of the model constructed in this paper is analyzed through experimental research. From the research results, it can be seen that the model constructed in this paper is relatively effective.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompliance with Ethical Standards\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interests\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis article does not contain any studies with human participants performed by any of the authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData will be made available on request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eQ. Wan, and Y. 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Vo, \u0026ldquo;K-Medoids algorithm used for english sentiment classification in a distributed system,\u0026rdquo; Computer Modelling and New Technologies, vol. 22, no. 1, pp. 20-39, 2018. \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":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Unsupervised learning, machine learning, image recognition, part-of-speech recognition","lastPublishedDoi":"10.21203/rs.3.rs-2575502/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2575502/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe traditional English part-of-speech analysis model fails to meet people\u0026rsquo;s actual needs due to the fact that the accuracy and other parameters are not up to standard. Facing large-scale English text data, quickly and accurately obtaining the key information needed and improv-ing the efficiency and accuracy of clustering have always been the focus of attention. However, the inherent characteristics of English text make it impossible to accurately calculate the traditional feature weight calculation method, and it\u0026rsquo;s part of speech is difficult to recognize. Moreover, in order to obtain a structure closer to the real data, this paper fuses the norm graph and the k-nearest neighbor graph, proposes a new composition framework, and combines it with two common propagation algorithms to complete the classification task. In addition, in order to obtain the improvement effect of the algorithm, the algorithm is tested on the English text classification corpus data set of the natural language processing open platform, and a control experiment is set to analyze the model performance. Finally, this article combines mathematical statistics to process data and draw corresponding charts.\u003c/p\u003e","manuscriptTitle":"Unsupervised machine learning and image recognition model application in English part-of-speech feature learning Under the open platform environment","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-02-23 19:17:37","doi":"10.21203/rs.3.rs-2575502/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2023-02-22T11:42:58+00:00","index":0,"fulltext":""},{"type":"editorAssigned","content":"","date":"2023-02-15T08:02:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Soft Computing","date":"2023-02-11T03:11:32+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"adf0c788-337c-4d75-b884-d88593f6c19a","owner":[],"postedDate":"February 23rd, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T20:44:59+00:00","versionOfRecord":{"articleIdentity":"rs-2575502","link":"https://doi.org/10.1007/s00500-023-08206-9","journal":{"identity":"soft-computing","isVorOnly":false,"title":"Soft Computing"},"publishedOn":"2023-04-26 20:35:28","publishedOnDateReadable":"April 26th, 2023"},"versionCreatedAt":"2023-02-23 19:17:37","video":"","vorDoi":"10.1007/s00500-023-08206-9","vorDoiUrl":"https://doi.org/10.1007/s00500-023-08206-9","workflowStages":[]},"version":"v1","identity":"rs-2575502","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2575502","identity":"rs-2575502","version":["v1"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}