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Entropy 2013, 15(7), 2788-2804; doi:10.3390/e15072788

Non-Linear Canonical Correlation Analysis Using Alpha-Beta Divergence

Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan
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Received: 14 June 2013 / Revised: 12 July 2013 / Accepted: 15 July 2013 / Published: 18 July 2013
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Abstract

We propose a generalized method of the canonical correlation analysis using Alpha-Beta divergence, called AB-canonical analysis (ABCA). From observations of two random variables, x RP and y RQ, ABCA finds directions, wx RP and wy RQ, such that the AB-divergence between the joint distribution of (wT x, wT y) and the product x y of their marginal distributions is maximized. The number of significant non-zero canonical coefficients are determined by using a sequential permutation test. The advantage of our method over the standard canonical correlation analysis (CCA) is that it can reconstruct the hidden non-linear relationship between wT xx and wT y, and it is robust against outliers. We extend ABCA when data are observed in terms of tensors. We further generalize this method by imposing sparseness constraints. Extensive simulation study is performed to justify our approach.
Keywords: canonical correlation analysis (CCA); non-linearity; AB-divergence; robustness; tensor; sparseness constraints. canonical correlation analysis (CCA); non-linearity; AB-divergence; robustness; tensor; sparseness constraints.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Mandal, A.; Cichocki, A. Non-Linear Canonical Correlation Analysis Using Alpha-Beta Divergence. Entropy 2013, 15, 2788-2804.

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