KoPA: Automated Kronecker Product Approximation

by   Chencheng Cai, et al.

We consider matrix approximation induced by the Kronecker product decomposition. Similar as the low rank approximations, which seeks to approximate a given matrix by the sum of a few rank-1 matrices, we propose to use the approximation by the sum of a few Kronecker products, which we refer to as the Kronecker product approximation (KoPA). Although it can be transformed into an SVD problem, KoPA offers a greater flexibility over low rank approximation, since it allows the user to choose the configuration of the Kronecker product. On the other hand, the configuration (the dimensions of the two smaller matrices forming the Kronecker product) to be used is usually unknown, and has to be determined from the data in order to obtain optimal balance between accuracy and complexity. We propose to use an extended information criterion to select the configuration. Under the paradigm of high dimensionality, we show 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. We demonstrate the performance and superiority of KoPA over the low rank approximations thought numerical studies, and a real example in image analysis.


page 3

page 22

page 24

page 25


Hybrid Kronecker Product Decomposition and Approximation

Discovering the underlying low dimensional structure of high dimensional...

Matrix Approximation under Local Low-Rank Assumption

Matrix approximation is a common tool in machine learning for building a...

Low-Rank Boolean Matrix Approximation by Integer Programming

Low-rank approximations of data matrices are an important dimensionality...

Stable Matrix Completion using Properly Configured Kronecker Product Decomposition

Matrix completion problems are the problems of recovering missing entrie...

Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations

Rank-revealing matrix decompositions provide an essential tool in spectr...

Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions

We present an entanglement analysis of quantum superpositions correspond...

Approximate Simultaneous Diagonalization of Matrices via Structured Low-Rank Approximation

Approximate Simultaneous Diagonalization (ASD) is a problem to find a co...

Please sign up or login with your details

Forgot password? Click here to reset