Linked Tucker2 Decomposition for Flexible Multi-block Data Analysis

In this paper, we propose a new algorithm for a flexible group multi-way data analysis called the linked Tucker2 decomposition (LT2D). The LT2D can decompose given multiple tensors into common factor matrices, individual factor matrices, and core tensors, simultaneously. When we have a set of tensor data and want to estimate common components and/or individual characteristics of the data, this decomposition model is very useful. In order to develop an efficient algorithm for the LT2D, we imposed orthogonality constraints to factor matrices and applied alternating least squares (ALS) algorithm to the optimization criterion. We conducted some experiments to demonstrate the advantages and convergence properties of the proposed algorithm. Finally, we discuss potential applications of the proposed method.

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