Abstract

Nonnegative Matrix Factorization (NMF) has attracted much attention during the past decade as a dimension reduction method in data mining and analytics. NMF gives a lower rank approximation formed by two nonnegative factors, providing more meaningful results with better interpretation in many applications. Numerous success stories were reported in application areas including text processing, computer vision, bioinformatics, and chemometrics.

In this talk we review several NMF algorithms with Frobenius norm minimization available in the literature using a block coordinate descent framework. This framework readily allows us to understand various properties of several of the promising NMF algorithms such as those based on alternating nonnegativity constrained least squares (ANLS). We also introduce fast algorithms that utilize active-set type methods and ANLS. Many of these algorithms can be naturally extended to obtain nonnegative tensor factorizations (NTF) efficiently, as well as sparse NMF and NTF based on L1 norm regularization. Extensive comparisons of algorithms using various data sets from text analysis and image analysis are presented. In addition, we introduce fast NMF algorithms with Bregman divergence, adaptive NMF algorithms for rank modifications and updated data, symmetric NMF, and their performances in clustering and video analysis. 


Bio: Prof. Haesun Park received her B.S. degree in Mathematics from Seoul National University, Seoul Korea, in 1981 with summa cum laude and the University President's Medal for the top graduate, and her M.S. and Ph.D. degrees in Computer Science from Cornell University, Ithaca, NY, in 1985 and 1987, respectively. She was on the faculty of the Department of Computer Science and Engineering, University of Minnesota, Twin Cities, from 1987 to 2005. From 2003 to 2005, she served as a program director for the Computing and Communication Foundations Division at the National Science Foundation, Arlington, VA, U.S.A. 

Since July 2005, she has been a professor in the School of Computational Science and Engineering at the Georgia Institute of Technology, Atlanta, Georgia. Her research interests include numerical algorithms, data analysis, visual analytics, bioinformatics, and parallel computing where she has published extensively. She is the director of the NSF/DHS FODAVA-Lead (Foundations of Data and Visual Analytics) project where the goal is to create mathematical and computational foundations for data and visual analytics. Prof. Park has served on numerous editorial boards including IEEE Transactions on Pattern Analysis and Machine Intelligence, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, and has served as a conference co-chair for SIAM International Conference on Data Mining in 2008 and 2009.