  Discovering the underlying low dimensional structure of high dimensional data
has attracted a significant amount of researches recently and has shown to have
a wide range of applications. As an effective dimension reduction tool,
singular value decomposition is often used to analyze high dimensional
matrices, which are traditionally assumed to have a low rank matrix
approximation. In this paper, we propose a new approach. We assume a high
dimensional matrix can be approximated by a sum of a small number of Kronecker
products of matrices with potentially different configurations, named as a
hybird Kronecker outer Product Approximation (hKoPA). It provides an extremely
flexible way of dimension reduction compared to the low-rank matrix
approximation. Challenges arise in estimating a hKoPA when the configurations
of component Kronecker products are different or unknown. We propose an
estimation procedure when the set of configurations are given and a joint
configuration determination and component estimation procedure when the
configurations are unknown. Specifically, a least squares backfitting algorithm
is used when the configuration is given. When the configuration is unknown, an
iterative greedy algorithm is used. Both simulation and real image examples
show that the proposed algorithms have promising performances. The hybrid
Kronecker product approximation may have potentially wider applications in low
dimensional representation of high dimensional data
