DRAFT
Caltech Logo

H.B. Keller Colloquium

Monday, January 31, 2022
4:00pm to 5:00pm
Add to Cal
Online Event
Online Nonnegative Matrix Factorization and Applications
Deanna Needell, Professor of Mathematics Dunn Family Endowed Chair in Data Theory ~ Executive Director, Institute for Digital Research and Education, Department of Mathematics, University of California - Los Angeles,

Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of dependent data streams remains largely unexplored. In this talk, we present results showing that a non-convex generalization of the well-known OMF algorithm for i.i.d. data converges almost surely to the set of critical points of the expected loss function, even when the data matrices are functions of some underlying Markov chain satisfying a mild mixing condition. As the main application, by combining online non-negative matrix factorization and a recent MCMC algorithm for sampling motifs from networks, we propose a novel framework of Network Dictionary Learning that extracts `network dictionary patches' from a given network in an online manner that encodes main features of the network. We demonstrate this technique on real-world data and discuss recent extensions and variations.

For more information, please contact Diana Bohler by phone at 6263951768 or by email at [email protected].