{"681076":{"#nid":"681076","#data":{"type":"event","title":"CSIP Seminar | Nonnegative rank: myths, conjectures, and canonical edges","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003EDate:\u003C\/strong\u003E\u0026nbsp;Monday, March 14, 2025\u003Cbr\u003E\u003Cstrong\u003ETime:\u003C\/strong\u003E\u0026nbsp;3:00 p.m. - 4:00 p.m.\u003Cbr\u003E\u003Cstrong\u003ELocation:\u0026nbsp;\u003C\/strong\u003ECentergy Building 5126\u003Cbr\u003E\u003Cstrong\u003ESpeaker:\u003C\/strong\u003E\u0026nbsp;Daniel Pimentel Alarcon\u003Cbr\u003E\u003Cstrong\u003ESpeakers\u0027 Title:\u003C\/strong\u003E\u0026nbsp;Assistant Professor in the Wisconsin Institute for Discovery and the Department of Biostatistics and Medical Informatics at UW-Madison\u003Cbr\u003E\u003Cstrong\u003ESeminar Title:\u003C\/strong\u003E\u0026nbsp;Nonnegative rank: myths, conjectures, and canonical edges\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EAbstract:\u0026nbsp;\u003C\/strong\u003EGiven a matrix X, nonnegative matrix factorization (NMF) aims to find the smallest nonnegative matrices U and V such that X=UV\u0027. The nonnegative rank of X is the number of columns in U (and V). Surprisingly, nobody knows how to find this number! One of the main reasons is that NMF is ill-posed with infinitely many feasible solutions. In this talk, I will introduce what we call nonnegative canonical edges (NCEs), which reveal the optimal (maximal volume) solution to NMF. This is analogous to the Moore-Penrose pseudo-inverse, which selects the optimal (minimum-norm) solution to ill-posed least-squares problems. We conjecture that NCEs hold the key to determining the nonnegative rank, and I will discuss our ideas to determine this number exactly and finally give a definitive answer to NMF.\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EBio: \u003C\/strong\u003EDaniel is an Assistant Professor in the Wisconsin Institute for Discovery and the Department of Biostatistics and Medical Informatics at UW-Madison. Before that, he was an Assistant Professor in the Computer Science Department at Georgia State University. He got his PhD in Electrical and Computer Engineering at UW-Madison. His research focuses on learning from messy data \u2013 that is, data with missing values, nonnegativity constraints, mixtures, outliers, sparsity patterns, skewed classes, small sample size, and any peculiarity that breaks typical algorithms. To this end, he uses a combination of machine learning, optimization, algebraic geometry, and signal processing tools.\u003C\/p\u003E","summary":"","format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003EDaniel Pimentel Alarcon, an Assistant Professor in the Wisconsin Institute for Discovery and the Department of Biostatistics and Medical Informatics at UW-Madison, will present the seminar, \u0022Nonnegative rank: myths, conjectures, and canonical edges.\u0022\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":"Daniel Pimentel Alarcon, an Assistant Professor in the Wisconsin Institute for Discovery and the Department of Biostatistics and Medical Informatics at UW-Madison, will present the seminar, \u0022Nonnegative rank: myths, conjectures, and canonical edges.\u0022"}],"uid":"36558","created_gmt":"2025-03-11 18:32:49","changed_gmt":"2025-03-11 18:36:53","author":"zwiniecki3","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2025-03-14T15:00:00-04:00","event_time_end":"2025-03-14T16:00:00-04:00","event_time_end_last":"2025-03-14T16:00:00-04:00","gmt_time_start":"2025-03-14 19:00:00","gmt_time_end":"2025-03-14 20:00:00","gmt_time_end_last":"2025-03-14 20:00:00","rrule":null,"timezone":"America\/New_York"},"location":" CSIP Library (Centergy Building, Room 5126)","extras":[],"groups":[{"id":"1255","name":"School of Electrical and Computer Engineering"}],"categories":[],"keywords":[{"id":"192224","name":"CSIP Seminar"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}