A0764
Title: Matrix denoising and completion based on Kronecker product approximation
Authors: Han Xiao - Rutgers University (United States) [presenting]
Abstract: The problem of matrix denoising and completion is considered induced by the Kronecker product decomposition. Specifically, an approximation to a given matrix is proposed by the sum of a few Kronecker products of matrices, which is referred 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 includes it as a special case. Compared with the latter, KoPA also offers greater flexibility since it allows the user to choose the configuration, which are the dimensions of the two smaller matrices forming the Kronecker product. On the other hand, the configuration to be used is usually unknown and needs to be determined from the data in order to achieve the optimal balance between accuracy and parsimony. The use of extended information criteria is proposed to select the configuration. Under the paradigm of high dimensional analysis, it is shown that the proposed procedure is able to select the true configuration with probability tending to one, under suitable conditions on the signal-to-noise ratio. The superiority of KoPA is demonstrated over the low-rank approximations through numerical studies and several benchmark image examples.
