DeepAI AI Chat
Log In Sign Up

Hybrid Kronecker Product Decomposition and Approximation

by   Chencheng Cai, et al.
Rutgers University

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


page 15

page 16


Weighted Low Rank Matrix Approximation and Acceleration

Low-rank matrix approximation is one of the central concepts in machine ...

KoPA: Automated Kronecker Product Approximation

We consider matrix approximation induced by the Kronecker product decomp...

A Scalable Approach to Estimating the Rank of High-Dimensional Data

A key challenge to performing effective analyses of high-dimensional dat...

Stable Matrix Completion using Properly Configured Kronecker Product Decomposition

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

A Geometrical Approach to Topic Model Estimation

In the probabilistic topic models, the quantity of interest---a low-rank...

Fast High-Dimensional Kernel Filtering

The bilateral and nonlocal means filters are instances of kernel-based f...

Spectral estimation from simulations via sketching

Sketching is a stochastic dimension reduction method that preserves geom...