Hybrid Kronecker Product Decomposition and Approximation

Discovering underlying low dimensional structure of a high-dimensional matrix is traditionally done through rank approximations in the form sum rank-one matrices. In this article, we propose new approach. We assume can be approximated by small number Kronecker products matrices with potentially different configurations, named as hybrid outer Product Approximation (hKoPA). It provides an extremely flexible way dimension reduction compared to low-rank approximation. Challenges arise estimating hKoPA when configurations component are or unknown. estimation procedure set given, and joint configuration determination Specifically, least squares backfitting algorithm used given. When unknown, iterative greedy developed. Both simulation real image examples show that proposed algorithms have promising performances. Some identifiability conditions also provided. The product approximation may wider applications representation data. Supplementary materials for article available online.