A Robust Nonlinear Kalman Smoothing Approach for Dynamic Matrix Factorization

The modeling of data as the product of two lower-dimensional (often matrix-valued) latent variables or factors has been widely used in applications as varied as psychometrics, finance, recommender systems, DNA microarray analysis, and foreground/background video separation. In finance, the factors often correspond to market segments and market styles; in recommender systems, the factors correspond to users and items. In many cases, the data matrices under investigation are dynamic, i.e., are functions of time. Matrix factorization methods have a long history in statistics and signal processing, but most methods deal with the case where either both factors are not time-varying or one of the factors is not [1]– [3]. In contrast, we formulate an approach for factoring dynamic matrices into two time-varying low-dimensional matrices [4], [5]. The proposed method uses recent developments in robust nonlinear Kalman smoothing [6].