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However, inherent technical limitations in biomedical studies often result in the generation of feature-rich and sample-limited datasets. Analyzing such data using conventional modalities often proves to be challenging since the repeated, high-dimensional measurements overload the outlook with inconsequential variations that must be filtered from the data in order to find the true, biologically relevant signal. Tensor methods for the analysis and meaningful representation of multiway data may prove useful to the biological research community by their advertised ability to tackle this challenge. In this study, we present <jats:sc>tcam<\/jats:sc>\u2014a new unsupervised tensor factorization method for the analysis of multiway data. Building on top of cutting-edge developments in the field of tensor-tensor algebra, we characterize the unique mathematical properties of our method, namely, 1) preservation of geometric and statistical traits of the data, which enable uncovering information beyond the inter-individual variation that often takes over the focus, especially in human studies. 2) Natural and straightforward out-of-sample extension, making <jats:sc>tcam<\/jats:sc> amenable for integration in machine learning workflows. A series of re-analyses of real-world, human experimental datasets showcase these theoretical properties, while providing empirical confirmation of <jats:sc>tcam<\/jats:sc>\u2019s utility in the analysis of longitudinal \u2019omics data.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010212","type":"journal-article","created":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T17:37:42Z","timestamp":1657906662000},"page":"e1010212","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":31,"title":["Dimensionality reduction of longitudinal \u2019omics data using modern tensor factorizations"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2918-6406","authenticated-orcid":true,"given":"Uria","family":"Mor","sequence":"first","affiliation":[]},{"given":"Yotam","family":"Cohen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0737-5425","authenticated-orcid":true,"given":"Rafael","family":"Vald\u00e9s-Mas","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9697-0380","authenticated-orcid":true,"given":"Denise","family":"Kviatcovsky","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5775-2110","authenticated-orcid":true,"given":"Eran","family":"Elinav","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1688-9030","authenticated-orcid":true,"given":"Haim","family":"Avron","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,7,15]]},"reference":[{"issue":"6","key":"pcbi.1010212.ref001","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1016\/j.medj.2021.04.006","article-title":"Machine learning in clinical decision making","volume":"2","author":"L Adlung","year":"2021","journal-title":"Med"},{"issue":"5","key":"pcbi.1010212.ref002","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1038\/s41591-019-0414-6","article-title":"A longitudinal big data approach for precision health","volume":"25","author":"SMSF Rose","year":"2019","journal-title":"Nature Medicine"},{"issue":"1","key":"pcbi.1010212.ref003","first-page":"1","article-title":"MetaLonDA: a flexible R package for identifying time intervals of differentially abundant features in metagenomic longitudinal studies","volume":"6","author":"AA Metwally","year":"2018","journal-title":"Microbiome 2018 6:1"},{"issue":"APR","key":"pcbi.1010212.ref004","doi-asserted-by":"crossref","first-page":"785","DOI":"10.3389\/fmicb.2018.00785","article-title":"SplinectomeR Enables Group Comparisons in Longitudinal Microbiome Studies","volume":"0","author":"RR Shields-Cutler","year":"2018","journal-title":"Frontiers in Microbiology"},{"issue":"1","key":"pcbi.1010212.ref005","first-page":"1","article-title":"MiRKAT-S: a community-level test of association between the microbiota and survival times","volume":"5","author":"A Plantinga","year":"2017","journal-title":"Microbiome 2017 5:1"},{"key":"pcbi.1010212.ref006","first-page":"1","article-title":"Context-aware dimensionality reduction deconvolutes gut microbial community dynamics","author":"C Martino","year":"2020","journal-title":"Nature Biotechnology"},{"issue":"7865","key":"pcbi.1010212.ref007","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1038\/s41586-021-03671-4","article-title":"Evaluating microbiome-directed fibre snacks in gnotobiotic mice and humans","volume":"595","author":"O Delannoy-Bruno","year":"2021","journal-title":"Nature"},{"issue":"1","key":"pcbi.1010212.ref008","doi-asserted-by":"crossref","DOI":"10.1186\/s13059-020-01977-6","article-title":"Avocado: a multi-scale deep tensor factorization method learns a latent representation of the human epigenome","volume":"21","author":"J Schreiber","year":"2020","journal-title":"Genome Biology"},{"issue":"6","key":"pcbi.1010212.ref009","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1016\/j.neuron.2018.05.015","article-title":"Unsupervised Discovery of Demixed, Low-Dimensional Neural Dynamics across Multiple Timescales through Tensor Component Analysis","volume":"98","author":"AH Williams","year":"2018","journal-title":"Neuron"},{"issue":"1-4","key":"pcbi.1010212.ref010","doi-asserted-by":"crossref","DOI":"10.1002\/sapm192761164","article-title":"The Expression of a Tensor or a Polyadic as a Sum of Products","volume":"6","author":"FL Hitchcock","year":"1927","journal-title":"Journal of Mathematics and Physics"},{"key":"pcbi.1010212.ref011","unstructured":"Harshman Ra. 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