Multilinear Common Component Analysis via Kronecker Product Representation | Zendy

Kohei Yoshikawa | Zendy; Shuichi Kawano | Zendy

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Multilinear Common Component Analysis via Kronecker Product Representation

Author(s) -

Kohei Yoshikawa,

Shuichi Kawano

Publication year - 2021

Publication title -

neural computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.235

H-Index - 169

eISSN - 1530-888X

pISSN - 0899-7667

DOI - 10.1162/neco_a_01425

Subject(s) - multilinear map , kronecker product , kronecker delta , tensor product , multilinear algebra , covariance , mathematics , representation (politics) , tensor (intrinsic definition) , component (thermodynamics) , component analysis , convergence (economics) , algorithm , pairwise comparison , algebra over a field , computer science , pure mathematics , statistics , physics , quantum mechanics , division algebra , politics , political science , law , economics , filtered algebra , thermodynamics , economic growth

We consider the problem of extracting a common structure from multiple tensor data sets. 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 that lose little information of the multiple tensor data sets. We also develop an estimation algorithm for MCCA that guarantees mode-wise global convergence. Numerical studies are conducted to show the effectiveness of MCCA.

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