{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/supervised-multiway-factorization","title":"Supervised multiway factorization","arxiv_id":"1609.03228","date":"2016-09-11","proceeding":null,"authors":["Eric F. Lock","Gen Li"],"abstract":"We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway\n(i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP\ngeneralizes the supervised singular value decomposition (SupSVD) for\nvector-valued observations, to allow for observations that have the form of a\nmatrix or higher-order array. Such data are increasingly encountered in\nbiomedical research and other fields. We describe a likelihood-based latent\nvariable representation of the CP factorization, in which the latent variables\nare informed by additional covariates. We give conditions for identifiability,\nand develop an EM algorithm for simultaneous estimation of all model\nparameters. SupCP can be used for dimension reduction, capturing latent\nstructures that are more accurate and interpretable due to covariate\nsupervision. Moreover, SupCP specifies a full probability distribution for a\nmultiway data observation with given covariate values, which can be used for\npredictive modeling. We conduct comprehensive simulations to evaluate the SupCP\nalgorithm. We apply it to a facial image database with facial descriptors\n(e.g., smiling / not smiling) as covariates, and to a study of amino acid\nfluorescence. Software is available at https://github.com/lockEF/SupCP .","url_abs":"http://arxiv.org/abs/1609.03228v2","url_pdf":"http://arxiv.org/pdf/1609.03228v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"supervised-multiway-factorization","repo_url":"https://github.com/lockEF/SupCP","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}