Multilinear Common Component Analysis via Kronecker Product Representation

TL;DR

This paper introduces a multilinear common component analysis method using Kronecker products to extract shared structures from multiple tensor datasets, with a guaranteed convergence algorithm and demonstrated effectiveness.

Contribution

It proposes a novel MCCA approach based on Kronecker products and provides a convergent estimation algorithm for tensor data analysis.

Findings

Effective extraction of common structures demonstrated

Algorithm guarantees mode-wise global convergence

Numerical studies confirm method's effectiveness

Abstract

We consider the problem of extracting a common structure from multiple tensor datasets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs a common basis represented by linear combinations of the original variables which loses as little information of the multiple tensor datasets. We also develop an estimation algorithm for MCCA that guarantees mode-wise global convergence. Numerical studies are conducted to show the effectiveness of MCCA.