On Combining Trilinear Decomposition and ICA

GONG Xiaofeng; HAO Yana; LIN Qiuhua; LIU Zhiwen; XU Yougen

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On Combining Trilinear Decomposition and ICA

GONG Xiaofeng 1 * #,HAO Yana 2,LIN Qiuhua 2,LIU Zhiwen 3,XU Yougen 3

1.Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024

2.Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024

3.School of Information and Electronics, Bejing Institute of Technology,Beijing,10081

*Correspondence author

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Funding: This work was supported in part by Doctoral Fund of Ministry of Education of China（No.20110041120019）, National Natural Science Foundation of China （No.60971097, 61072098, and 61105008）

Opened online:21 June 2013

Accepted by: none

Citation: GONG Xiaofeng,HAO Yana,LIN Qiuhua.On Combining Trilinear Decomposition and ICA[OL]. [21 June 2013] http://en.paper.edu.cn/en_releasepaper/content/4548303

We present a new canonical polyadic decomposition (CPD) algorithm to exploit both source statistical independence and trilinear structure of a three-way tensor based on independent component analysis (ICA) and joint diagonalization (JD). More exactly, ICA is first performed on the matricized tensor to exploit the statistical independence in one mode, JD is then carried out upon the initial ICA results to restore the trilinear structure of the original tensor, and rank-1 approximation is finally used to extract the parallel factors. The proposed algorithm is able to overcome the converging difficulties of standard CPD in the presence of collinearities. Moreover, it is able to exploit the trilinearity of the target tensor more thoroughly than existing methods that combine CPD and ICA, and thus is less sensitive to the incorporated ICA stage than these methods. Simulations are provided to compare the proposed algorithm with both standard CPD algorithms and algorithms that combine CPD and ICA.

Keywords:Independent Component Analysis; Canonical Polyadic Decomposition; Joint Diagonalization; Tensor

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