{"paper_id":"3f3f9745-327b-4615-a990-a18c823fef77","body_text":"Feature selection with vector-symbolic architectures: a case study on\nmicrobial profiles of shotgun metagenomic samples of colorectal cancer\nFabio Cumbo 1, Simone Truglia 2, Emanuel Weitschek 2, Daniel Blankenberg 1,3,*\n1 Center for Computational Life Sciences, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA\n2 Department of Engineering, Uninettuno University, Rome, Italy\n3 Department of Molecular Medicine, Cleveland Clinic Lerner College of Medicine, Case Western Reserve\nUniversity, Cleveland, OH, USA\n* T o whom correspondence should be addressed. Email: blanked2@ccf.org\nABSTRACT\nThe continuingly decreasing cost of next-generation sequencing has recently led to a significant increase in\nthe number of microbiome-related studies, providing invaluable information for understanding\nhost-microbiome interactions and their relation to diseases. A common approach in metagenomics consists\nof determining the composition of samples in terms of the amount and types of microbial species that\npopulate them, with the goal to identify microbes whose profiles are able to differentiate samples under\ndifferent conditions with advanced feature selection techniques. Here we propose a novel backward\nvariable selection method based on the hyperdimensional computing paradigm, which takes inspiration\nfrom how the human brain works in the classification of concepts by encoding features into vectors in a\nhigh-dimensional space. We validated our method on public metagenomic samples collected from patients\naffected by colorectal cancer in a case/control scenario, by performing a comparative analysis with other\nstate-of-the-art feature selection methods, obtaining promising results.\nAUTHOR SUMMARY\nCharacterizing the microbial composition of metagenomic samples is crucial for identifying potential\nbiomarkers that can distinguish between healthy and diseased states. However, the high dimensionality\nand complexity of metagenomic data present significant challenges in the context of accurately selecting\nfeatures. Our backward variable selection method, based on the hyperdimensional computing paradigm,\noffers a promising approach to overcoming these challenges. By effectively reducing the feature space\nwhile preserving essential information, this method enhances the ability to detect critical microbial\nsignatures associated with diseases like colorectal cancer, leading to more precise diagnostic tools.\nKeywords machine learning, hyperdimensional computing, vector-symbolic architecture, feature selection,\nmetagenomics, colorectal cancer\nINTRODUCTION\nOver the last decade, the cost of next-generation sequencing technologies has steadily decreased, a trend\nthat is expected to continue. This reduction has positively impacted all areas of the life sciences, resulting in\nthe generation of substantial biomedical data. Metagenomics, which involves the study of microorganisms\n1\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\nin biological samples and their relationship to pathological conditions and environmental factors, is one field\nthat has particularly benefited from these advancements. Metagenomics frameworks that rely on\nsophisticated statistical analysis and machine learning techniques allow the identification of relevant\nsignatures across a wide range of pathologic conditions by inspecting differences in the abundance of\nspecific microbial species in large cohorts of samples in a case/control scenario. Many studies have\ndemonstrated the involvement of microbes in the genesis and development of a multitude of health-related\nconditions, including cancer.\nHere we focus in particular on the disease of colorectal cancer (CRC), which is the second most common\ncause of cancer death worldwide (916,000 deaths) and the third for number of cases per year (1.93 million\ncases in 2020) according to the World Health Organization [1]. Additionally, the American Cancer Society\n(ACS) indicates that the 5-year survival rate (i.e., percentage of people affected by the same type and\nstage of cancer still alive after 5 years from the first diagnosis) is approximately 65% when the cancer is\ndetected at an early stage [2]. Therefore, noninvasive methods allowing early detection of CRC are crucial\nto enhancing patient survival. Numerous studies have recently examined the difference in the abundance of\nspecific microbes in metagenomics samples (usually fecal samples in the case of CRC) collected from case\nand healthy individuals in order to establish whether it can be used as a fast, accurate, and noninvasive tool\nfor diagnosing the disease [3].\nHere we propose a novel stepwise feature selection method following a backward variable elimination\nstrategy based on the brain-inspired hyperdimensional computing paradigm. Hyperdimensional (HD)\ncomputing is a relatively new computational paradigm that aims to replicate the structure and function of the\nbrain in order to perform various computational tasks. It is based on the idea that the brain uses distributed\nrepresentations to encode and process information which is represented by unique vectors in a\nhigh-dimensional space [4–6]. These vectors are often referred to as “semantic pointers” because they are\nthought to encode the meaning of the information they represent [7].\nThis technology has been recently adopted to perform various computational tasks such as classification,\nclustering, and pattern recognition in different scientific domains [8–12]. One of the key benefits of HD\ncomputing is its efficiency because vectors used to represent information are distributed throughout the\nhigh-dimensional space, making it possible to perform many operations in parallel, which makes it\nwell-suited for handling large amounts of data. It is brain-inspired in the sense that every concept is\nencoded into vectors in a high-dimensional space that can be combined together with simple arithmetic\noperations in order to represent more complex concepts, in the same way the human brain works with the\nassociative memory for distinguishing very similar concepts by remembering patterns [4,13,14]. We\nintegrated our method as a subroutine of chopin2 [15,16], an open-source Python 3.8 package originally\ndeveloped for classifying massive datasets with commodity hardware.\nT o the best of our knowledge, this is the first attempt of building a feature selection method following this\nemerging computing paradigm.\nRESULTS\nWe applied our feature selection algorithm on the relative abundance profiles of 241 microbial species\ndetected in 193 CRC and control samples obtained from the merging of three whole genome shotgun\nsequencing datasets retrieved through the curatedMetagenomicsData package [17] for R:\n2\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\nThomasAM_2018a, ThomasAM_2018b, and ThomasAM_2019_c (see the Methods section for additional\ndetails). T aking in mind the well-known sexual dimorphism in individuals affected by CRC [18] and recent\nstudies that identified some gut-bacteria as possible age-specific biomarkers for the identification of CRC\n[19–21], we stratified the samples according to biological sex (male and female) and age category (adult\nand senior with age ≤65 and >65 respectively). For each of these datasets, we transformed the species\nprofiles into a binary matrix with 0 and 1 values only, where we consider the presence/absence of microbes\nindependently from their level of relative abundance (RA) (1 if the RA of a particular species in a specific\nsample is >0, otherwise 0). Feature selection and HD classification model results on binarized and relative\nabundance datasets are shown in T able 1A.\nA Samples\n(CRC)\nSamples\n(Control)\nData\ntype\nSelected\nfeatures\nBest\naccuracy\nRetrain\niterations Time Memory\n(up to) Models B Selected\nfeatures\nSub-optimal\naccuracy\n(>70%)\nUnstratified 101 92\nRA 71 70.50% 0.2 14.61m 14.81GB 7,594 52 70.40%\nbinary 23 81.31% 0.2 4.03m 7.54GB 2,913 4 71.99%\nw/ male only 67 53\nRA 132 74.17% 0.8 22.68m 13.30GB 15,816 4 71.67%\nbinary 31 78.33% 0.0 5.20m 6.97GB 5,730 3 75.83%\nw/ female only 34 39\nRA 22 69.71% 0.2 11.60m 12.87GB 10,530 5 72.48%\nbinary 17 79.43% 1.2 4.68m 6.65GB 9,115 2 75.33%\nw/ adult only 59 50\nRA 44 73.51% 0.0 19.10m 13.20GB 14,288 8 70.69%\nbinary 54 84.33% 3.0 14.11m 8.44GB 15,465 2 75.19%\nw/ senior only 42 42\nRA 69 72.57% 12.6 18.70m 13.00GB 14,977 3 71.40%\nbinary 33 82.28% 0.8 5.43m 6.68GB 9,295 4 75.07%\nTable 1: Panel A: Feature selection and classification results on (i) the whole dataset resulting from the merging of\nthe MetaPhlAn3 profile tables of ThomasAM_2018a, ThomasAM_2018b, and ThomasAM_2019_c (here called\nUnstratified), and the same merged table stratified by biological sex and age category, by considering (ii) male\nsubjects (w/ male only), (ii) female subjects (w/ female only), adult subjects (age ≤65, here called w/ adult only), and\nsenior subjects (age >65, here called w/ senior only). Every dataset presents the same number of features (241\nspecies) and it is processed twice with relative abundance (RA) and binary presence (binary) microbial profiles, by\nreporting the number of selected features, the best accuracy, the number of retraining iterations (average on the\nnumber of folds) for the classification model with the best accuracy, the computational time used to build and\nevaluate all the HD classification models up to the end of the feature selection algorithm (in minutes – m), and the\namount of allocated memory, in addition to the total number of produced classification models; Panel B: Number of\nfeatures selected by chopin2 from sub-optimal HD classification models whose accuracy rate is lower than the best\none but always >70% with the minimum number of selected features.\nIt is worth noting that 10,000 was selected for HD vector dimensionality and 1,000 as the number of HD\nlevels for the datasets with RA profiles, while only 2 HD levels were specified for the binary representations\nof microbial profiles. The maximum number of retraining iterations was set to 10, with retraining terminated\nwhen the error rate for an iteration does not vary from the previous round. Here, the accuracy threshold has\nbeen set to 60%, while the accuracy uncertainty percentage has been set to 1%. Finally, every\nclassification model was subjected to 5-fold cross validation. The computational time is reported in T able 1A\nand refers to the total amount of time required for building and evaluating all the HD models generated\nduring the backward variable elimination process. Computation and evaluation of the HD models was\nperformed on a high-performance computing machine comprising 4 Intel Xeon Platinum 8276L CPUs (128\ncores/224 threads) @ 2.20GHz and 6TB of RAM using 80 cores at most. Running time and memory\n3\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\nconsumption profiles have been computed with memory-profiler v0.61.0 with an average of 13.43GB of\nallocated RAM in case of RA models and 7.25GB in case of binary models.\nIn terms of accuracy, the HD models built on top of the binary datasets (data type binary) always reached\nover 78% of accuracy, which is also always higher than the accuracy of the same models built over the\nrelative abundance profiles (data type RA; 74.17% accuracy in the best case, 69.71% accuracy in the worst\ncase).\nIn T able 1A, we also reported the number of selected features related to the best classification model\ngenerated through the iterative steps of our algorithm (see the Availability section for the complete list of\nselected microbial species). It is worth noting that, in order to reach these results, the software generated\nand evaluated over 32 thousand classification models in total (see column Models in T able 1A).\nSub-optimal classification models significantly reduced the number of relevant features\nwith a minimal loss of accuracy\nHere, we also considered sub-optimal results (classification models with lower accuracy rate, always\ngreater than 70%, with the minimum number of selected features) for the binary models, since we noticed\nthat the algorithm extracted a very small number of features able to distinguish the CRC class of samples\nfrom the control class of samples with an accuracy slightly lower than the best one. Sub-optimal results are\nsummarized in T able 1B. Since the results about the RA datasets are always worse in terms of accuracy\nand number of selected features, here we focused on the classification and feature selection results of\nmodels built on the binarized datasets only.\nThe best sub-optimal HD model built on top of the binarized Unstratified dataset was able to discriminate\nthe CRC and Control samples with 71.99% of accuracy by considering only 4 features (species). Here we\nreport all of them with their prevalence percentage (P) in both CRC and control samples (P CRC and PControl\nrespectively): Eubacterium ventriosum (PCRC=54.46%; PControl=38.05%), Firmicutes bacterium CAG 145\n(PCRC=53.47%; PControl=29.35%), Gemella morbillorum (PCRC=39.6%; PControl=3.26%), and Parvimonas micra\n(PCRC=46.53%; PControl=9.78%).\nDespite the feature selection algorithm extracting only 4 species from the Unstratified dataset while building\na high accuracy classification model, results on the same dataset stratified by biological sex and age\ncategory are characterized by an even smaller set of features able to discriminate samples with roughly the\nsame level of accuracy (always >70%).\nThe algorithm selected 3 features only for the dataset with samples from male individuals with a\nclassification model that reached 75.83% accuracy: Anaerotruncus colihominis (PCRC=58.21%;\nPControl=32.07%), Bifidobacterium pseudocatenulatum (PCRC=23.88%; PControl=60.38%), and Parvimonas\nmicra (PCRC=44.78%; PControl=7.55%). The number of species selected for the dataset with samples from\nfemale individuals is 2, while the achieved accuracy is 75.33%: Blautia sp CAG 257 (PCRC=14.71%;\nPControl=35.9%) and Gemella morbillorum (PCRC=50%; PControl=2.56%).\nThe two datasets stratified on the age category are also characterized by a similar situation. Our method\nselected 2 species for the dataset with samples from adult individuals with a 75.19% accurate classification\nmodel: Oscillibacter sp CAG 241 (PCRC=57.63%; PControl=38%) and Parvimonas micra (PCRC=59.32%;\n4\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\nPControl=6%). Similarly, the model built on the dataset with samples from senior individuals produced an\naccuracy of 75.07% with 4 species: Actinomyces sp HMSC035G02 (PCRC=35.71%; PControl=26.19%),\nBifidobacterium pseudocatenulatum (PCRC=16.67%; PControl=47.62%), Streptococcus pasteurianus\n(PCRC=11.9%; PControl=0%), and Streptococcus salivarius (PCRC=50%; PControl=88.1%).\nDifferential abundance analysis of species selected with sub-optimal models confirms\nknown microbial biomarkers\nThese results show a prevalence of the Firmicutes phyla among all the selected species (9 out of 11). Here\nwe computed the log2 fold change (log2FC) of all the species highlighted by our algorithm as the log2 of\nthe mean relative abundance of the case samples on the mean of the relative abundance of the control\nsamples (mean CRC/meanControl). Only 4 out of a total of 11 species have an absolute value of log2FC ≥ 1:\nGemella morbillorum (log2FC=3.6 in unstratified, log2FC=4.28 in female), Parvimonas micra (log2FC=2.25\nin unstratified, log2FC=3.3 in adult), Bifidobacterium pseudocatenulatum (log2FC=-1.33 in male,\nlog2FC=-1.51 in senior), and Blautia sp CAG 257 (log2FC=-1.28 in female).\nFor these 4 species with absolute value of log2FC ≥ 1 selected from the dataset with unstratified samples,\nonly 2 species belonging to the Firmicutes phylum exhibited statistically significant differential relative\nabundance according to the Wilcoxon rank-sum test (whose p-values have been corrected for multiple\nhypothesis testing with the Benjamini-Hochberg procedure): Gemella morbillorum (p-value=1.32e-5;\nFDR=1.59e-3), and Parvimonas micra (p-value=1.05e-5; FDR=1.59e-3). These statistically significant\nspecies have been selected according to the thresholds of 0.05 on their p-values (p-value ≤ 0.05) and 0.2\non the FDR (FDR ≤ 0.2).\nWe repeated the same statistical analysis on the other four datasets whose samples have been stratified\naccording to biological sex and age, obtaining the same effect as correcting the Wilcoxon test for these\ncovariates. In the case of the dataset with samples from male individuals only, the 2 selected species that\nhave an absolute value of log2FC ≥ 1 also have statistical significance of differential relative abundance\naccording to the Wilcoxon test and the same threshold of 0.05 and 0.2 on the p-value and the FDR\nrespectively: Bifidobacterium pseudocatenulatum (p-value=6.15e-4; FDR=7.42e-2) and Parvimonas micra\n(p-value=4.77e-4; FDR=7.42e-2). For the dataset with samples from female individuals, only one species\nresulted in statistical significance among the two with an absolute value of log2FC ≥ 1: Gemella morbillorum\n(p-value=5.05e-4; FDR=1.21e-1).\nFollowing the same thresholds, the statistical test highlighted one significant species with log2FC ≥ 1 in the\ncase of the dataset with samples from adult individuals: Parvimonas micra (p-value=1.72e-6;\nFDR=4.16e-4). Finally, there are no statistically significant species for the dataset with samples from senior\nindividuals according to the same threshold used for the other datasets.\nAccording to the most recent updates of the Disbiome database [22], at the time of writing, 2 out of the 3\nstatistically significant and differentially abundant species identified here are linked to studies in which\nCRC-affected individuals are involved. Their abundance has already been proposed as possible biomarker\nfor the detection of the disease and are well know to be involved in the destabilization of the colonic wall of\nthe gut, reported as possible cause of progression of CRC: Gemella morbillorum [23,24] and Parvimonas\nmicra [23,25,26].\n5\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\nAlthough the Bifidobacterium pseudocatenulatum does not show up in the Disbiome database as linked to\nCRC, it has also been recently reported as a possible biomarker for the disease [27].\nA comparison with classical wrapper-based feature selection methods\nIn order to validate our method, we performed a comparative analysis with different feature selection\nstrategies based on Random Forest, Decision Tree, Support Vector Machine (SVM), Logistic Regression,\nand Extreme Gradient Boosting (XGBoost), on the same binarized datasets in 5-folds cross-validation.\nT able 2 shows the results in terms of features which have been selected in at least 4 out of 5 folds and the\naccuracy reached by the classical classification models. Features have been selected according to their\nimportance which produced the classification model with the best accuracy.\nRandom Forest Decision Tree SVM Logistic Regression XGBoost\nF ACC t F ACC t F ACC t F ACC t F ACC t\nUnstratified 2 80.30% 16m 1 72.56% 1s 6 77.70% 33s 11 81.86% 11s 18 79.79% 28m\nw/ male only 13 83.33% 28m NA 65.83% 1s 5 81.66% 44s 2 80.00% 10s 5 76.66% 3m\nw/ female only 1 78.09% 15m 1 76.57% 1s 3 76.57% 36s 2 78.00% 8s 1 80.85% 2m\nw/ adult only 18 89.00% 16m 1 80.77% 1s 1 80.64% 20s 3 87.18% 9s 2 84.37% 3m\nw/ senior only 2 77.50% 10m 1 72.57% 1s 4 75.00% 37s 4 73.82% 9s 2 70.07% 2m\nTable 2: Feature selection based on the importance of the features assigned by specific machine learning models\n(Random Forest, Decision Tree, Support Vector Machine - SVM, Logistic Regression, and Extreme Gradient\nBoosting - XGBoost) built on the 5 unstratified and stratified datasets, reporting the number of selected features (F),\nthe accuracy (ACC), and running time (t) in seconds (s) and minutes (m). Models have been 5-fold cross-validated,\nand the accuracy (ACC) is the mean value among the models with the highest accuracy in all 5 folds. We\nconsidered a feature as selected if it turns out to be significant in at least 4 out of 5 folds (columns Features). The\naccuracy levels are color coded according to the difference in accuracy with respect to the chopin2 results in T able\n1 (light red if the accuracy is lower than the accuracy computed on the classification model built with chopin2, dark\nred with NA value if no features were significant in at least 4 out of 5 folds, while no color has been applied in cases\nwhere the classical approaches performed better than the level of accuracy computed on the chopin2 models).\nNote that chopin2 performed better in terms of accuracy compared to most of the classification techniques\nadopted in this comparative analysis (in average, +2.87% for the Unstratified dataset, +0.84% for the male\nonly dataset, +1.42% for the female only dataset, -0.06% for the adult only dataset, and +8.49% for the\nsenior only dataset). Also note that in the case of Support Vector Machine and Logistic Regression models,\nwe computed the absolute values on the feature coefficients in order to consider the importance of the\nfeatures both with negative and positive effects.\nNote that 4 out of 4 species selected by chopin2 in the context of the sub-optimal model built on top of the\nUnstratified dataset were found to be also relevant for at least one out of 5 feature selection techniques\napplied on the same dataset (i.e., Eubacterium ventriosum , Firmicutes bacterium CAG 145, Gemella\nmorbillorum, and Parvimonas micra). For the stratified datasets, the number of features selected by\nchopin2 that are also significant for at least one of the 5 classical feature selection techniques are: 2/3 (i.e.,\nBifidobacterium pseudocatenulatum and Parvimonas micra) and 1/2 (i.e., Gemella morbillorum ) for the\ndataset with samples from male only and female only individuals respectively, and 1/2 (i.e., Parvimonas\n6\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\nmicra) and 2/4 (i.e., Bifidobacterium pseudocatenulatum and Streptococcus salivarius) for the datasets with\nsamples stratified by age category (adult only and senior only respectively).\nIt is worth noting that, although the feature selection technique implemented in chopin2 relies on the\nbackward variable elimination strategy by iteratively removing features at each step as explained in the\nMethods section, and thus most of its running time is dedicated to the construction and evaluation of\nmultiple classification models, our approach produced more accurate results compared to the 5 classical\nmachine learning approaches adopted in this analysis. In particular, considering all 5 datasets, chopin2\ngenerated over 105 thousand models in our experimentation in roughly 2 hours, which is the same time\nrequired for running the whole comparative analysis.\nThe comparative analysis has been performed in Python 3.8 with the support of the scikit-learn library\nv0.22.1 without tuning of methods’ parameters. A complete overview of the results, together with the code\nto fully reproduce them, is available on Zenodo (see the Availability section). It is also worth noting that we\nhave not shown here a comparative analysis on the datasets with microbial relative abundance profiles. We\nhave not discussed these results since the classification models built on the binarized datasets always\nperformed better in terms of accuracy and extracted features. However, classification and feature selection\nresults for these models are also available on Zenodo.\nDISCUSSION\nHere, we presented a novel feature selection algorithm based on the backward variable elimination\nstrategy. It has been developed on top of a supervised classifier built according to the hyperdimensional\ncomputing paradigm, originally proposed for classifying massive datasets with commodity hardware. T o the\nbest of our knowledge, this is the first feature selection method working entirely with vector-symbolic\narchitectures. We want to stress the point that, despite the fact that we tested our method on biological\ndata, the software is domain-agnostic and can be easily applied on data from different knowledge domains.\nSpecifically, we tested our algorithm on abundance profiles of microbes in metagenomic samples of stool in\na case/control scenario related to CRC. We identified 11 species able to discriminate case and control\nsamples with high accuracy. Only 3 of them, i.e. Bifidobacterium pseudocatenulatum, Gemella morbillorum,\nand Parvimonas micra, have been highlighted by the statistical analysis and are well-known in literature to\nbe linked in some way to the pathogenesis of the disease or as a possible cause of development of CRC.\nHowever, 3 of the remaining 8 species, Eubacterium ventriosum , Streptococcus pasteurianus, and\nStreptococcus salivarius, are also linked to CRC despite their abundance profiles not showing any\nstatistical significance between case and control samples [28–33]. Finally, there is no mention in the CRC\nliterature about the remaining 5 species (Firmicutes bacterium CAG 145, Anaerotruncus colihominis,\nBlautia sp CAG 257, Oscillibacter sp CAG 241, and Actinomyces sp HMSC035G02), and they must be\nfurther investigated to determine their role in relation to their abundance as possible rapid and non-invasive\ndiagnostic tool for colorectal cancer in sex- and age-specific individuals.\nWe are planning to apply the same technique to support large-scale metagenomic analyses in relation to\nother pathologies, not necessarily limited to cancer diseases. We are confident this will highlight new\ninsights and will help define new highly-accurate non-invasive diagnostic tools for the detection of such\npathologies. Additionally, recent advancements in the development of novel techniques for identifying and\nprofiling unknown microbes [34] drastically increase the number of microbial species quantified in\nmetagenomic samples to tens of thousands. Classifying this kind of datasets can be challenging for the\n7\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\nstate-of-the-art classification and feature selection methods, and the technique we proposed in this\nmanuscript can be a valid solution for efficiently dealing with such a massive number of features.\nFurthermore, we are also working on improving the overall performance of chopin2 by running the process\nof building hypervectors on GPUs and on distributed environments powered by Apache Spark in order to\nunlock new potentialities of the software for scaling on hundreds of thousands of features.\nMATERIALS AND METHODS\nWe focused our analysis on the relative abundance (RA) of microbial species profiled over 101 stool\nsamples of patients affected by CRC, in addition to 92 samples from stool of healthy individuals [35,36].\nThe authors of the selected studies aimed at identifying microbial signatures were able to discriminate the\nCRC class of samples from the control ones with high accuracy in fecal samples from shotgun\nmetagenomics sequencing. Here we attempt to reproduce the same results with a novel HD-oriented\napproach. It is worth noting that the 193 samples come from three different datasets (i.e.\nThomasAM_2018a, ThomasAM_2018b, and ThomasAM_2019_c) and their metadata, as well as their\nmicrobial abundance profiles originally performed with MetaPhlAn3 [37], have been obtained through\ncuratedMetagenomicData [17] package for R.\nT able 3 shows a summary of the 193 metagenomic samples involved in this analysis. It is worth noting that\n113 out of 193 samples come from antibiotics-free individuals, while for the remaining samples this\ninformation is lacking. Furthermore, these three datasets also contain 27 samples of patients affected by\nAdenoma. However, the number of Adenoma patients is too unbalanced compared to the number of CRC\nand control samples, thus we excluded them from our analysis.\nNumber of\nsamples\nSex\n(F/M)\nAge (years)\nmean\n(stdev)\nrange\n(min–max)\nN adult\n(age ≤ 65)\nN senior\n(age > 65)\nColorectal Cancer (CRC) 101 34/67 62.41 (11.75) 28–84 59 42\nControl 92 39/53 62.85 (10.53) 40–81 50 42\nTable 3: Demographic summary of all metagenomic samples involved in this study and retrieved from public\ndatasets. They comprise 193 stool samples distributed over two classes (Colorectal Cancer, and Controls) from\nfemale and male subjects ranging from 28 up to 84 years old grouped in two sub-classes (adult and senior)\naccording to the threshold of 65 years old.\nWe finally looked at the distribution of the samples over the age of the 193 individuals involved in the study\nin order to check whether the number of samples in a class is too unbalanced compared to the number of\nsamples in the other class and vice versa also in relation to biological sex (male and female). The\ndistribution charts are shown in Figure 1, Panels A, B, and C. Considering the similar trend of the number of\nsamples from female and male individuals over the control and CRC classes, we opted to consider all the\n193 samples for our study.\n8\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\nFigure 1: (Panels A, B, and C) Distribution of the 193 samples over the control and CRC classes in relation to the\nage and biological sex of the involved individuals. Panel A shows the overall distribution of all samples, while Panel\nB and C show the distribution of control and CRC samples respectively. It is worth noting that samples have been\ngrouped according to 5-years age intervals and the vertical dashed line at year 65 in all the three panels represent\nthe time point where an adult turns senior; (Panels D and E) Compact view of the microbial composition in the 193\nCRC and Control samples. Panel D shows the total number of phyla, classes, orders, families, genera, and species\nunder the Bacteria kingdom, while the barplot in Panel E shows the number of species for each of the 8 phyla\ndetected in the dataset by MetaPhlAn3.\nPreprocessing of microbial profiles\nSince these samples come from different datasets, we first excluded those microbial species that have not\nbeen detected in all the three studies by MetaPhlAn3. We can safely exclude these species by simply\nadding their relative abundances to the unclassified profile, which contains the abundance of all the\nunknown microbial species that MetaPhlAn3 was not able to detect in a particular sample, resulting in a\ntotal of 337 species. We repeated the same process for very low abundant species with a relative\nabundance lower than 1% (66 species), as well as species detected in less than 5% of the samples (30\nspecies) in order to decrease the possibility of erroneous classifications. This reduced the total number of\nprofiled microbes to 241 bacterial species whose distribution is shown in Figure 1 (241 species, 103\ngenera, 42 families, 25 orders, 17 classes, and 8 phyla as reported in Panel D, with a majority of species\nunder the Firmicutes phylum (56.4%) as shown in Panel E). It is worth to note that MetaPhlAn3 reports a\nrelative abundance profile for each of the taxonomic levels, from the kingdom down to the species, for each\ndetected microbe. However, here we focused on the species level only.\nDefining the Vector-Symbolic Architecture and Machine Learning Model\n9\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\nAs widely described in previous studies [4,38–40], designing an analysis following the hyperdimensional\ncomputing principles means that every atomic element in the input dataset must be first encoded into\nhigh-dimensional vectors. Every operation is thus reduced to dealing with a very limited set of arithmetic\nfunctions applied on the encoded vectors in the high-dimensional space. The set of vectors and functions is\ncalled vector-symbolic architecture (VSA) [4].\nWe designed the procedure described in Algorithm 1 to build a classification model over a VSA defined on\nan input numerical dataset:\nAlgorithm 1: Encoding data into high-dimensional vectors\nInput: dataset D with S set of features,\nnumber of hyperdimensional level vectors L,\nvectors dimensionality d,\nnumber of retraining iterations R\nOutput: the vector-symbolic representation of D\n1: levels ← list of level vectors\n2: base ← random bipolar vector of length d\n3: for level = 1, 2, …, L\n4: if level > 1\n5: # Flip N numbers of random element in base\nbase ← flip(base, N)\n6: append(levels, base)\n7: # Split the dataset D into training and test sets\ntraining, test ← split(D)\n8: F ← number of features in S\n9: R ← maximum number of retraining iterations\n10: C ← list of classes in D\n11: classes ← empty list with vector representations of classes in C\n12: for class in C\n13: # Initialize the class vector\nvector ← [0…0]\n14: for sample in training[class]\n15: for n = 0, 1, …, F-1 in S\n16: level ← get level vector from levels associated to the value under sample[n]\n17: level ← rotate level by p positions\n18: vector ← element-wise sum level and vector\n19: append(classes, vector)\n20: prev_errors ← 0\n21: # Compute the model error rate\ncurr_errors ← evaluate(classes, training)\n22: iterations ← count retraining iterations\n23: while curr_errors != prev_errors and iterations < R\n24: for sample, class in training\n25: # Compute the cosine similarity between sample and the class vectors in classes\nclosest ← class of the closest vector in classes\n26: if closest != class\n10\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\n27: # Element-wise subtract sample from the closest class vector in classes\n# Element-wise sum sample to its class vector in classes\nclasses ← adjust(classes, sample)\n28: prev_errors ← curr_errors\n29: curr_errors ← evaluate(classes, training)\n30: return classes\nAlgorithm 1: Pseudocode of the procedure designed to build a vector-symbolic architecture and machine learning\nmodel implemented in chopin2. It is composed of three main steps: (i) the generation of hyperdimensional level\nvectors, (ii) the definition of the vector representations of classes whose set represents the model, and (iii) the\nretraining process (error mitigation) for optimizing the model’s prediction power.\nFirst, it is important to have a look at the distribution of the numerical values in the input dataset. In the case\nof microbial profiles here analyzed, we know that values range from 0 to 100 because they express relative\nabundances. This information, as well as the precision of the numerical values, is extremely relevant\nbecause every single value must be encoded into a random bipolar vector (containing 1 and -1 values only)\nin the high-dimensional space (i.e. the length of vectors, usually 10,000). These vectors are usually built\nstarting from a single random vector and iteratively flipping values under a certain amount of random\npositions (N elements are flipped where N is equal to the vector dimensionality d divided by 2 over the total\nnumber of level vectors L). This guarantees that adjacent vectors are more similar compared to all the other\nlevel vectors by also maintaining their quasi-orthogonality in the high-dimensional space. Vectors must be\napproximately orthogonal so that they resolve at discernable distance from each other and thus could\nrepresent different concepts (e.g., the number 0.002 is different from the number 0.0019, no matter how\nclose these numbers are, and thus they must be encoded into two approximately orthogonal vectors so that\nthey can be easily discriminated just by computing their distance in the high-dimensional space). These\nvectors are called HD levels and represent the associative memory. The generation of HD levels is the first\nstep towards the encoding of a numerical dataset and it is described in Algorithm 1, lines 1–6. It is worth to\nnote that two different numbers can actually be mapped to the same level vector according to the total\nnumber of levels and the global numerical interval in the dataset (e.g., if a dataset contains numbers\nbetween 0.0 and 100.0, and the number of level vectors is 100, every number between 0.1 and 1.0 is\nmapped to the same level vector).\nAs every classification method usually works, the set of samples in the dataset must be first decomposed\ninto training and test sets (Algorithm 1, line 7). The next step consists in building a vector representation of\neach class by encoding and combining all the vector representations of the samples in the training set. In\norder to do that, a sample is first encoded by binding (element-wise sum) all the vector representations of\nthe features under that specific sample. The position of the features is also relevant in defining the encoded\nvector associated with the samples. In order to also track the feature information, the vector representation\nof a specific numerical value is rotated (by permuting values) by n positions with n equal to the position of\nthe feature in the dataset (n = 0…F-1, with F equal to the number of features in the dataset; the vector\nrepresentation of the numerical value under the first feature is not permuted, while the vector associated\nwith the numerical value under the second feature is permuted of a single position, and so on up to the last\nfeature in the dataset). The vector representations of the samples belonging to a specific class are finally\nbounded together for building the vector representation of that specific class. The set of vectors, one for\neach class, together with the HD levels and this specific way of encoding data, represents the\n11\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\nvector-symbolic architecture, i.e., our classification model. The process of encoding data into vectors and\ncombining them to produce the vector representation of classes is described in Algorithm 1, lines 7–19.\nThe vector representation of a class is thus built by bounding together all the vector representations of\nsamples that belong to that specific class. This operation is extremely easy but summing up vectors also\nleads to the introduction of noise that affects the prediction power of the whole classification model. We can\nreduce the inevitable effects of introducing noise with an error mitigation technique known as retraining.\nThis process works by first predicting the class of the training samples that is established by computing the\ninner-product (cosine similarity) between the vector representation of the training samples and each vector\nrepresentation of the classes. The closest class is the prediction. In the case of a misclassification, the\nvector representation of the test sample is element-wise subtracted from the misclassified class vector in\norder to reduce the noise that led to misclassifying the sample, while it is also element-wise added to the\ncorrect class vector to amplify the informative signal of the test sample in the correct class. This process\ncan be performed iteratively many times, usually until the error-rate in a specific iteration converges, i.e., it\ndoes not change anymore compared to the previous iteration (Algorithm 1, lines 20–29).\nIn order to test the model and evaluate its accuracy in correctly predicting the right class, the same process\nof encoding samples is applied to the test set. The class associated with a sample in the test set is\npredicted by computing the inner-product of its vector representation and each vector representation of the\nclasses built and adjusted during the previous step. Finally, the accuracy of the classification model is\ncomputed as the number of correctly classified samples on the total number of samples in the test set.\nFormalizing the feature selection problem\nHere we formally define our feature selection method which belongs to the backward variable elimination\nclass of algorithms. It works by iteratively removing those features that do not have a significant\ndiscriminative power for describing observations belonging to a specific class of samples. More specifically,\nconsidering a dataset D with a set S of features, it starts by building a HD classification model considering\nall the S features. The iterative part of the algorithm starts if the accuracy of the model is greater than a\nspecific threshold only.\nDuring the first iteration, it generates all the possible combinations of features by creating S sets of S-1\nfeatures (by excluding a specific feature in all of the S sets of features). Then, it builds a HD classification\nmodel for each of the S sets of features. It keeps track of the features excluded from the specific set of\nfeatures in case the classification models produced the best accuracy in this specific iteration. Subsequent\niterations work in the same way as the first one, except that the initial set of features is now permanently\nlacking of the previously excluded irrelevant features. It finally stops processing the input dataset when the\nbest accuracy reached in a specific iteration is lower than a predefined threshold (e.g. it may not make\nsense to keep removing features from a dataset whose classification model has an accuracy <50%) or\nwhen there are no other features available in the set of features. Pseudocode for this approach is\nsummarized in Algorithm 2.\nAlgorithm 2: Stepwise Feature Selection as Backward Variable Elimination\nInput: dataset D with S set of features,\nnumber of hyperdimensional level vectors L,\n12\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\nvectors dimensionality d,\nnumber of retraining iterations R\nOutput: reduced set S with selected features only\n1: B ← empty bucket for taking track of irrelevant features\n2: T ← accuracy threshold\n3: # Build a HD model considering all the features in S according to Algorithm 1\n# Define ACC as the accuracy of the HD model\nACC ← HD(D, S, L, d, R)\n4: while ACC ≥ T and S is not empty:\n5: M ← empty bucket for taking track of models accuracy and missing features\n6: for each combination of S-1 features:\n7: f ← missing feature\n8: # Build a HD model considering all the S-f features according to Algorithm 1\n# Define ACC as the accuracy of the HD model\nACC ← HD(D, S-f, L, d, R)\n9: # Keep track of the missing feature and ACC\nappend(M, <ACC, f>)\n10: ACC ← best accuracy among those in M\n11: f ← missing feature associated to the best ACC in M\n12: # Add the missing feature f associated to the best ACC to the bucket B\nappend(B, <f>)\n13: # Remove the features in B from S\nS ← S-B\n14: return S\nAlgorithm 2: Pseudocode of the stepwise backward variable elimination algorithm implemented in chopin2. Given\na dataset D in input with S features, it iteratively builds a HD classification model by removing irrelevant features\nthat do not contribute to increasing the accuracy of the model itself. It iteratively generates all possible\ncombinations of S-1 features, and it definitively removes the irrelevant feature associated with the model with the\nbest accuracy. It keeps removing features until the best reached accuracy is greater than a specific threshold or\nwhen it runs out of features.\nT o further illustrate this approach, consider the visual representation of the feature selection algorithm in\nFigure 2. It starts with an example dataset with five features and an empty bucket for taking track of the\nirrelevant features. It first builds a HD classification model by considering all five features (S={F1, F2, F3,\nF4, F5}) in the input dataset to make sure that there is enough informative content to distinguish the\ndifferent class of samples with a minimum level of accuracy, here fixed to 70% (step 1). The immediate next\nstep consists in generating all possible combinations of sets of S-1 features. Figure 2 (step 2) shows five\nsets of four features each (i.e. (i) F2, F3, F4, and F5, (ii) F1, F3, F4, and F5, (iii) F1, F2, F4, and F5, (iv) F1,\nF2, F3, and F5, and (v) F1, F2, F3, and F4). For each of them, the algorithm creates a HD classification\nmodel that in this particular example produced a 93% as the best accuracy with the second set of features.\nOne of the classification models reached an accuracy of 68%, which is lower than the accuracy threshold of\n70%, and thus it must be discarded. Here we also introduced the concept of “accuracy uncertainty\npercentage”, which is a percentage that must be subtracted to the best accuracy in order to define a\nthreshold for establishing whether the accuracy reached by the other models is high enough to be\nconsidered as a good result. In this case, the best accuracy is 93% and the “accuracy uncertainty\n13\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\npercentage” has been fixed to 5%. Thus, the threshold is defined as 88% (93% minus its 5%), and the best\nresults in this iteration are the second and third models with 93% and 91% of accuracy respectively. The\nalgorithm proceeds by applying the same strategy on the third iteration (step 3) by first reshaping the set S\nof features removing F2 and F3 which are the features that have been excluded for the generation of the\nbest classification models during the previous iteration. Here, the best accuracy is 90% reached by the last\nmodel. There are no other models that must be considered in this iteration since the accuracy reached by\nthe other models is lower than 85% (90% minus its 5%), and in any case lower than the accuracy threshold\nof 70%. The last iteration (step 4) starts by again reshaping the set of features S removing F5 in addition to\nF2 and F3. It generates two classification models with only one feature each. Their accuracy is high enough\nto pass the accuracy threshold, but the best accuracy in this iteration is lower than the best accuracy\nreached on the previous iteration (step 3). Thus, the algorithm concluded by selecting F1 and F4 as the\nbest features able to discriminate the samples in the input dataset with high accuracy, while F2, F3, and F4\ndo not significantly contribute to increasing the accuracy of the classification model.\nFigure 2: Schematic representation of the backward variable selection algorithm on a dataset with 5 features\n(F1-5). The first step simply runs the HD classification algorithm on the whole set of features and proceeds if the\naccuracy of the model is greater than the predefined threshold of 70%. During the second step, five HD models are\ngenerated, one for each combination of features by excluding one feature only (i.e., by moving the removed\nfeatures to the initially empty bucket). Models with accuracy <70% are automatically excluded (red areas), while the\nexcluded features (F2 and F3) of the models with 93% and 91% of accuracy (because 93% is the best reached\naccuracy and 91% is high enough according to the uncertainty percentage of 5%) are considered to proceed with\nthe third iteration. The algorithm proceeds by generating three models with all the combinations of remaining\nfeatures minus one. The accuracy of two models does not satisfy the minimum accuracy threshold of 70%, while\none model reaches 90% of accuracy with three removed features (F2, F3, and F5). The last iteration produces two\nclassification models because only two features remained active at this point. Their accuracy is way lower than the\nbest accuracy reached by the model at the third iteration (90%). Thus, the algorithm ends by reporting F1 and F4 as\nthe minimum set of features for which the software is able to produce a classification model with high accuracy.\nIt is worth noting that the algorithm is extremely parallelizable at the single iteration level, since the\ngeneration of the HD classification models are completely unrelated from each other. Also note that the\nsame strategy can be easily applied in a reverse order, following a forward variable selection approach, by\nadding features one by one instead of removing variables. However, this mode is not currently implemented\nin chopin2.\n14\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\nAVAILABILITY\nMetaPhlAn3 profiles of the analyzed metagenomic samples and their metadata are publicly available\nthrough the R package curatedMetagenomicData. The proposed algorithm is implemented as a subroutine\nof the Python 3.8 software chopin2, whose source code is available on GitHub under the GPL-3.0 license at\nhttps://github.com/cumbof/chopin2, it has been designed through the hdlib [41] Python library also available\non GitHub at https://github.com/cumbof/hdlib, and it is distributed through the Python Package Index (pip\ninstall chopin2) and Conda (conda install -c conda-forge chopin2). It is also available on the Galaxy\nplatform [42,43] through the official T oolShed [44] at https://toolshed.g2.bx.psu.edu/view/iuc/chopin2 after\nbeing revised and approved by the Intergalactic Utilities Commission (IUC). A tutorial for the Galaxy tool is\navailable on the Galaxy Training Network [45–47] at https://gxy.io/GTN:T00337. Classification models and\nfeature selection results presented with this manuscript are fully reproducible and available on Zenodo at\nhttps://doi.org/10.5281/zenodo.11397775.\nACKNOWLEDGEMENTS\nWe wish to thank the Italian inter-university consortium CINECA for assigning us supercomputing resources\n(project HDCOMP , grant number HP10CA0SGK to FC) that we extensively used to preliminarily test our\nalgorithm. We would also like to thank Dr. Jayadev Joshi and Dr. Bryan Raubenolt of the Center for\nComputational Life Sciences, Lerner Research Institute of the Cleveland Clinic, for their constructive critical\nfeedback.\nAUTHOR CONTRIBUTIONS\nConception and design of the study, FC; Software design and development, FC and ST ; Methodology and\nanalysis, FC, ST , and EW; Results interpretation, FC and DB; Research supervision, EW and DB;\nManuscript preparation FC; All authors provided critical revision of the manuscript and approved the final\nversion for submission.\nCONFLICT OF INTEREST\nDB has a significant financial interest in GalaxyWorks, a company that may have a commercial interest in\nthe results of this research and technology. This potential conflict of interest has been reviewed and is\nmanaged by the Cleveland Clinic.\nFUNDING\nThis work has been supported by the National Institutes of Health [U24HG006620, U24CA231877].\nREFERENCES\n15\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\n1. World Health Organization. Cancer. 2022. Available:\nhttps://www.who.int/news-room/fact-sheets/detail/cancer\n2. Survival Rates for Colorectal Cancer. 2022. Available:\nhttps://www.cancer.org/cancer/colon-rectal-cancer/detection-diagnosis-staging/survival-rates.html\n3. Li S, Liu J, Zheng X, Ren L, Yang Y , Li W, et al. Tumorigenic bacteria in colorectal cancer: mechanisms\nand treatments. Cancer Biol Med. 2021. doi:10.20892/j.issn.2095-3941.2020.0651\n4. Kanerva P . Hyperdimensional computing: An introduction to computing in distributed representation\nwith high-dimensional random vectors. Cognit Comput. 2009;1: 139–159.\ndoi:10.1007/s12559-009-9009-8\n5. Karunaratne G, Le Gallo M, Cherubini G, Benini L, Rahimi A, Sebastian A. In-memory\nhyperdimensional computing. Nature Electronics. 2020;3: 327–337. doi:10.1038/s41928-020-0410-3\n6. Kanerva P . Hyperdimensional computing: An algebra for computing with vectors. Advances in\nSemiconductor T echnologies. Wiley; 2022. pp. 25–42. doi:10.1002/9781119869610.ch2\n7. Blouw P , Solodkin E, Thagard P , Eliasmith C. Concepts as Semantic Pointers: A Framework and\nComputational Model. Cogn Sci. 2016;40: 1128–1162. doi:10.1111/cogs.12265\n8. Imani M, Kong D, Rahimi A, Rosing T . VoiceHD: Hyperdimensional Computing for Efficient Speech\nRecognition. 2017 IEEE International Conference on Rebooting Computing (ICRC). 2017. pp. 1–8.\ndoi:10.1109/ICRC.2017.8123650\n9. Imani M, Bosch S, Datta S, Ramakrishna S, Salamat S, Rabaey JM, et al. QuantHD: A Quantization\nFramework for Hyperdimensional Computing. IEEE Trans Comput Aided Des Integr Circuits Syst.\n2020;39: 2268–2278. doi:10.1109/TCAD.2019.2954472\n10. Neubert P , Schubert S, Protzel P . An Introduction to Hyperdimensional Computing for Robotics. KI -\nKünstliche Intelligenz. 2019;33: 319–330. doi:10.1007/s13218-019-00623-z\n11. Pale U, T eijeiro T , Atienza D. Multi-Centroid Hyperdimensional Computing Approach for Epileptic\nSeizure Detection. Front Neurol. 2022;13: 816294. doi:10.3389/fneur.2022.816294\n12. Menon A, Natarajan A, Agashe R, Sun D, Aristio M, Liew H, et al. Efficient emotion recognition using\nhyperdimensional computing with combinatorial channel encoding and cellular automata. Brain Inform.\n2022;9: 14. doi:10.1186/s40708-022-00162-8\n13. Plate TA. Holographic reduced representations. IEEE Trans Neural Netw. 1995;6: 623–641.\ndoi:10.1109/72.377968\n14. Levy SD, Gayler R. Vector Symbolic Architectures: A New Building Material for Artificial General\nIntelligence. Proceedings of the 2008 conference on Artificial General Intelligence 2008: Proceedings\nof the First AGI Conference. NLD: IOS Press; 2008. pp. 414–418. Available:\nhttps://dl.acm.org/doi/abs/10.5555/1566174.1566215\n15. Imani M, Huang C, Kong D, Rosing T . Hierarchical Hyperdimensional Computing for Energy Efficient\nClassification. 2018 55th ACM/ESDA/IEEE Design Automation Conference (DAC). 2018. pp. 1–6.\n16\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\ndoi:10.1109/DAC.2018.8465708\n16. Cumbo F , Cappelli E, Weitschek E. A Brain-Inspired Hyperdimensional Computing Approach for\nClassifying Massive DNA Methylation Data of Cancer. Algorithms. 2020;13: 233.\ndoi:10.3390/a13090233\n17. Pasolli E, Schiffer L, Manghi P , Renson A, Obenchain V, Truong DT , et al. Accessible, curated\nmetagenomic data through ExperimentHub. Nat Methods. 2017;14: 1023–1024.\ndoi:10.1038/nmeth.4468\n18. Abancens M, Bustos V, Harvey H, McBryan J, Harvey BJ. Sexual Dimorphism in Colon Cancer. Front\nOncol. 2020;10: 607909. doi:10.3389/fonc.2020.607909\n19. Zhang Y-K, Zhang Q, Wang Y-L, Zhang W-Y , Hu H-Q, Wu H-Y , et al. A Comparison Study of Age and\nColorectal Cancer-Related Gut Bacteria. Front Cell Infect Microbiol. 2021;11: 606490.\ndoi:10.3389/fcimb.2021.606490\n20. Mukherji R, Weinberg BA. The gut microbiome and potential implications for early-onset colorectal\ncancer. Colorectal Cancer. 2020;9: CRC25. doi:10.2217/crc-2020-0007\n21. Rebersek M. Gut microbiome and its role in colorectal cancer. BMC Cancer. 2021;21: 1325.\ndoi:10.1186/s12885-021-09054-2\n22. Janssens Y , Nielandt J, Bronselaer A, Debunne N, Verbeke F , Wynendaele E, et al. Disbiome\ndatabase: linking the microbiome to disease. BMC Microbiol. 2018;18: 50.\ndoi:10.1186/s12866-018-1197-5\n23. Yachida S, Mizutani S, Shiroma H, Shiba S, Nakajima T , Sakamoto T , et al. Metagenomic and\nmetabolomic analyses reveal distinct stage-specific phenotypes of the gut microbiota in colorectal\ncancer. Nat Med. 2019;25: 968–976. doi:10.1038/s41591-019-0458-7\n24. Yang J, Li D, Yang Z, Dai W, Feng X, Liu Y , et al. Establishing high-accuracy biomarkers for colorectal\ncancer by comparing fecal microbiomes in patients with healthy families. Gut Microbes. 2020;11:\n918–929. doi:10.1080/19490976.2020.1712986\n25. Yu J, Feng Q, Wong SH, Zhang D, Liang QY , Qin Y , et al. Metagenomic analysis of faecal microbiome\nas a tool towards targeted non-invasive biomarkers for colorectal cancer. Gut. 2017;66: 70–78.\ndoi:10.1136/gutjnl-2015-309800\n26. Baxter NT , Ruffin MT 4th, Rogers MAM, Schloss PD. Microbiota-based model improves the sensitivity\nof fecal immunochemical test for detecting colonic lesions. Genome Med. 2016;8: 37.\ndoi:10.1186/s13073-016-0290-3\n27. Hasan R, Bose S, Roy R, Paul D, Rawat S, Nilwe P , et al. Tumor tissue-specific bacterial biomarker\npanel for colorectal cancer: Bacteroides massiliensis, Alistipes species, Alistipes onderdonkii,\nBifidobacterium pseudocatenulatum, Corynebacterium appendicis. Arch Microbiol. 2022;204: 348.\ndoi:10.1007/s00203-022-02954-2\n28. Wu Y , Jiao N, Zhu R, Zhang Y , Wu D, Wang A-J, et al. Identification of microbial markers across\npopulations in early detection of colorectal cancer. Nat Commun. 2021;12: 3063.\n17\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nFeature Selection with Vector-Symbolic Architectures\ndoi:10.1038/s41467-021-23265-y\n29. Azimi M, Keshavarz Shahbaz S, Mansourabadi AH, Mohamed Khosroshahi L, Pourkalhor S,\nRezakhani M, et al. Intestinal Microbiota: Novel Personalized Cancer Immunotherapy in Colorectal\nCancer. Int Arch Allergy Immunol. 2022;183: 1147–1165. doi:10.1159/000525695\n30. Gospodinova GR, Demirevska L, Daskalov I, Dimitrov GD. A Rare Case of Streptococcus pasteurianus\nEndocarditis Signaling Colon Cancer. Cureus. 2023;15: e48328. doi:10.7759/cureus.48328\n31. Sánchez JC, García-Garrote F , Coira A, López-Agreda H, Alonso-García MP . Colorectal neoplasia\nassociated with Streptococcus gallolyticus subspecies pasteurianus. Lancet Infect Dis. 2014;14:\n272–273. doi:10.1016/S1473-3099(14)70031-3\n32. Afek S, Sperber AD, Almog Y . Carcinoma of the colon presenting as Streptococcus salivarius sepsis. J\nClin Gastroenterol. 2004;38: 86–87. doi:10.1097/00004836-200401000-00021\n33. Lawrence GW, McCarthy N, Walsh CJ, Kunyoshi TM, Lawton EM, O’Connor PM, et al. Effect of a\nbacteriocin-producing on the pathogen in a model of the human distal colon. Gut Microbes. 2022;14:\n2100203. doi:10.1080/19490976.2022.2100203\n34. Blanco-Miguez A, Beghini F , Cumbo F , McIver LJ, Thompson KN, Zolfo M, et al. Extending and\nimproving metagenomic taxonomic profiling with uncharacterized species with MetaPhlAn 4. bioRxiv.\n2022. p. 2022.08.22.504593. doi:10.1101/2022.08.22.504593\n35. Thomas AM, Manghi P , Asnicar F , Pasolli E, Armanini F , Zolfo M, et al. Author Correction:\nMetagenomic analysis of colorectal cancer datasets identifies cross-cohort microbial diagnostic\nsignatures and a link with choline degradation. Nat Med. 2019;25: 1948.\ndoi:10.1038/s41591-019-0663-4\n36. Wirbel J, Pyl PT , Kartal E, Zych K, Kashani A, Milanese A, et al. Meta-analysis of fecal metagenomes\nreveals global microbial signatures that are specific for colorectal cancer. Nat Med. 2019;25: 679–689.\ndoi:10.1038/s41591-019-0406-6\n37. Beghini F , McIver LJ, Blanco-Míguez A, Dubois L, Asnicar F , Maharjan S, et al. Integrating taxonomic,\nfunctional, and strain-level profiling of diverse microbial communities with bioBakery 3. Elife. 2021;10.\ndoi:10.7554/eLife.65088\n38. Rahimi A, Kanerva P , Rabaey JM. A Robust and Energy-Efficient Classifier Using Brain-Inspired\nHyperdimensional Computing. Proceedings of the 2016 International Symposium on Low Power\nElectronics and Design. New York, NY , USA: Association for Computing Machinery; 2016. pp. 64–69.\ndoi:10.1145/2934583.2934624\n39. Ge L, Parhi KK. Classification Using Hyperdimensional Computing: A Review. IEEE Circuits and\nSystems Magazine. Secondquarter 2020;20: 30–47. doi:10.1109/MCAS.2020.2988388\n40. Schlegel K, Neubert P , Protzel P . A comparison of vector symbolic architectures. Artificial Intelligence\nReview. 2021. doi:10.1007/s10462-021-10110-3\n41. Cumbo F , Weitschek E, Blankenberg D. hdlib: A Python library for designing Vector-Symbolic\nArchitectures. J Open Source Softw. 2023;8: 5704. doi:10.21105/joss.05704\n18\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint \n\nCumbo F . et al. 2024\n42. Giardine B, Riemer C, Hardison RC, Burhans R, Elnitski L, Shah P , et al. Galaxy: a platform for\ninteractive large-scale genome analysis. Genome Res. 2005;15: 1451–1455. doi:10.1101/gr.4086505\n43. Galaxy Community. The Galaxy platform for accessible, reproducible, and collaborative data analyses:\n2024 update. Nucleic Acids Res. 2024;52: W83–W94. doi:10.1093/nar/gkae410\n44. Blankenberg D, Von Kuster G, Bouvier E, Baker D, Afgan E, Stoler N, et al. Dissemination of scientific\nsoftware with Galaxy T oolShed. Genome Biol. 2014;15: 403. doi:10.1186/gb4161\n45. Batut B, Hiltemann S, Bagnacani A, Baker D, Bhardwaj V, Blank C, et al. Community-Driven Data\nAnalysis Training for Biology. Cell Syst. 2018;6: 752–758.e1. doi:10.1016/j.cels.2018.05.012\n46. Clements D, Hiltemann S, Batut B, Rasche H, Heydarian M, The Galaxy Training Network. Using the\nGalaxy Training Network tutorial library for bioinformatics training programs. J Biomol T ech. 2020;31:\nS2. Available: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7424776/\n47. Hiltemann S, Rasche H, Gladman S, Hotz H-R, Larivière D, Blankenberg D, et al. Galaxy Training: A\npowerful framework for teaching! PLoS Comput Biol. 2023;19: e1010752.\ndoi:10.1371/journal.pcbi.1010752\n19\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted November 20, 2024. ; https://doi.org/10.1101/2024.11.18.624180doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}