Seminar by Prof. Rong CHEN from Department of Statistics, Rutgers University

We consider the problem of matrix approximation, denoising and completion induced by the Kronecker product decomposition. Specifically, we propose to approximate a given matrix by the sum of a few Kronecker products of smaller matrices, which we refer to as the Kronecker product approximation (KoPA). Because the Kronecker product is an extension of the outer product from vectors to matrices, KoPA extends the low rank matrix approximation, and include the latter as a special case. Comparing with the latter, KoPA also offers a greater flexibility, since it allows the user to choose the configuration, which are the dimensions of the two matrices forming the Kronecker product. As the configuration to be used is usually unknown, an extended information criterion is used to select the configuration. The model is extended to allow for multiple terms with different configurations (hybrid-KoPA) for more efficient approximation and denoising. It is also used for matrix completion tasks, with superior theoretical and numerical properties.

Professor Rong Chen is a Distinguished Professor and the Chair at the Department of Statistics, Rutgers University, and he is one of few big academic giants in the area of time series analysis. Professor Chen is very active both in research and in professional services. He currently is the co-editor for Statistica Sinica, and was a co-editor for the Journal of Business and Economic Statistics in the past. He has served as the associate editor for many top journals in statistics. He has been actively involved in professional activities from all three big statistical societies, Institute of Mathematical Statistics (IMS), American Statistical Association (ASA) and International Statistical Institute (ISI). He is the Fellows of both IMS and ASA, and the elected member of ISI.