{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:44Z","timestamp":1760147564219,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,11]],"date-time":"2023-02-11T00:00:00Z","timestamp":1676073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1837985","T32GM070449"],"award-info":[{"award-number":["1837985","T32GM070449"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University of Michigan NIH NIGMS Bioinformatics Training","award":["1837985","T32GM070449"],"award-info":[{"award-number":["1837985","T32GM070449"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Over the past decades, there has been an increase of attention to adapting machine learning methods to fully exploit the higher order structure of tensorial data. One problem of great interest is tensor classification, and in particular the extension of linear discriminant analysis to the multilinear setting. We propose a novel method for multilinear discriminant analysis that is radically different from the ones considered so far, and it is the first extension to tensors of quadratic discriminant analysis. Our proposed approach uses invariant theory to extend the nearest Mahalanobis distance classifier to the higher-order setting, and to formulate a well-behaved optimization problem. We extensively test our method on a variety of synthetic data, outperforming previously proposed MDA techniques. We also show how to leverage multi-lead ECG data by constructing tensors via taut string, and use our method to classify healthy signals versus unhealthy ones; our method outperforms state-of-the-art MDA methods, especially after adding significant levels of noise to the signals. Our approach reached an AUC of 0.95(0.03) on clean signals\u2014where the second best method reached 0.91(0.03)\u2014and an AUC of 0.89(0.03) after adding noise to the signals (with a signal-to-noise-ratio of \u221230)\u2014where the second best method reached 0.85(0.05). Our approach is fundamentally different than previous work in this direction, and proves to be faster, more stable, and more accurate on the tests we performed.<\/jats:p>","DOI":"10.3390\/a16020104","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T01:48:56Z","timestamp":1676252936000},"page":"104","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quadratic Multilinear Discriminant Analysis for Tensorial Data Classification"],"prefix":"10.3390","volume":"16","author":[{"given":"Cristian","family":"Minoccheri","sequence":"first","affiliation":[{"name":"Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1029-6664","authenticated-orcid":false,"given":"Olivia","family":"Alge","sequence":"additional","affiliation":[{"name":"Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA"}]},{"given":"Jonathan","family":"Gryak","sequence":"additional","affiliation":[{"name":"Computer Science Department, Queen\u2019s College, CUNY, New York, NY 11367, USA"}]},{"given":"Kayvan","family":"Najarian","sequence":"additional","affiliation":[{"name":"Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA"},{"name":"Michigan Institute for Data Science (MIDAS), University of Michigan, Ann Arbor, MI 48109, USA"},{"name":"Michigan Center for Integrative Research in Critical Care (MCIRCC), University of Michigan, Ann Arbor, MI 48109, USA"},{"name":"Emergency Medicine, University of Michigan, Ann Arbor, MI 48109, USA"}]},{"given":"Harm","family":"Derksen","sequence":"additional","affiliation":[{"name":"Mathematics Department, Northeastern University, Boston, MA 02115, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2524","DOI":"10.1109\/TPAMI.2014.2342214","article-title":"Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification","volume":"36","author":"Li","year":"2014","journal-title":"IEEE Trans. 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