Randomized Sketching for Scalable Nonnegative Matrix Factorization

Abstract: Nonnegative Matrix Factorization (NMF) is a well-known tool for simplifying and interpreting complex entry-wise nonnegative datasets. Its applications include topic modeling, image processing, hyperspectral and audio unmixing, among others. However, scaling NMF to significantly large datasets is computationally challenging. In this talk, I will talk about the recently introduced, flexible and theoretically grounded framework for performing NMF efficiently by randomized compression techniques. Using data-aware or oblivious sketching methods, we can find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or twice. To achieve this goal, we formulate optimization problems based solely on compressed data and show that the resulting factorization closely approximates the original matrix. These problems can be efficiently solved by various algorithms, and I will specifically discuss the adaptations of the popular multiplicative updates method.

Bio: Liza Rebrova is an Assistant Professor in the Department of Operations Research and Financial Engineering (ORFE) at Princeton University. She received her Ph.D. in Mathematics from the University of Michigan in 2018. Prior to joining Princeton, she was an Assistant Adjunct Professor in the Department of Mathematics at UCLA and a postdoctoral scholar in the Computational Research Division at Lawrence Berkeley National Laboratory. She works in randomized numerical linear algebra, mathematics of data and stochastic optimization, aiming to develop theoretically justified and computationally efficient randomized methods for large-scale problems.