{"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/probabilistic-parafac2","title":"Probabilistic PARAFAC2","arxiv_id":"1806.08195","date":"2018-06-21","proceeding":null,"authors":["Philip J. H. Jørgensen","Søren F. V. Nielsen","Jesper L. Hinrich","Mikkel N. Schmidt","Kristoffer H. Madsen","Morten Mørup"],"abstract":"The PARAFAC2 is a multimodal factor analysis model suitable for analyzing\nmulti-way data when one of the modes has incomparable observation units, for\nexample because of differences in signal sampling or batch sizes. A fully\nprobabilistic treatment of the PARAFAC2 is desirable in order to improve\nrobustness to noise and provide a well founded principle for determining the\nnumber of factors, but challenging because the factor loadings are constrained\nto be orthogonal. We develop two probabilistic formulations of the PARAFAC2\nalong with variational procedures for inference: In the one approach, the mean\nvalues of the factor loadings are orthogonal leading to closed form variational\nupdates, and in the other, the factor loadings themselves are orthogonal using\na matrix Von Mises-Fisher distribution. We contrast our probabilistic\nformulation to the conventional direct fitting algorithm based on maximum\nlikelihood. On simulated data and real fluorescence spectroscopy and gas\nchromatography-mass spectrometry data, we compare our approach to the\nconventional PARAFAC2 model estimation and find that the probabilistic\nformulation is more robust to noise and model order misspecification. The\nprobabilistic PARAFAC2 thus forms a promising framework for modeling multi-way\ndata accounting for uncertainty.","url_abs":"http://arxiv.org/abs/1806.08195v1","url_pdf":"http://arxiv.org/pdf/1806.08195v1.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":"probabilistic-parafac2","repo_url":"https://github.com/philipjhj/VBParafac2","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}