Multilinear Common Component Analysis via Kronecker Product Representation

We consider the problem of extracting a common structure from multiple tensor datasets. To obtain the common structure from the multiple tensor datasets, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs the common basis represented by linear combinations of original variables without losing the information of multiple tensor datasets as possible. We also develop an estimation algorithm of MCCA that guarantees mode-wise global convergence. The numerical studies are conducted to show the effectiveness of MCCA.