Non-Linear canonical correlation analysis using Alpha-Beta divergence

Abhijit Mandal, Andrzej Cichocki

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 ∈ R{double-struck}P and y ∈ ℝQ, ABCA finds directions, wx ∈ R{double-struck}P and wy ∈ ℝQ, such that the AB-divergence between the joint distribution of (wTxx; wTyy) and the product 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 wTxx and wTyy, 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,

Original languageEnglish (US)
Pages (from-to)2788-2804
Number of pages17
JournalEntropy
Volume15
Issue number7
DOIs
StatePublished - Jul 2013

Keywords

  • Ab divergence
  • Canonical correlation analysis (CCA)
  • Non-linearity
  • Robustness
  • Sparseness constraints
  • Tensor

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