Non-Linear Canonical Correlation Analysis Using Alpha-Beta Divergence

DOI Web Site 1 Citations Open Access
  • Abhijit Mandal
    Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan
  • Andrzej Cichocki
    Laboratory for Advanced Brain Signal Processing, RIKEN Brain Science Institute, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan

Description

<jats:p>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.</jats:p>

Journal

  • Entropy

    Entropy 15 (7), 2788-2804, 2013-07-18

    MDPI AG

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