An α-Divergence Approach To Robust Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a widely used mutivariate statistical technique for exploring the relationship between two multivariable datasets. It extracts existing relationship information by finding pairs of linear combinations from the two sets of variables with maximum correlation. In some applications however, the observed datasets may be contaminated by outliers and the standard CCA methods are sensitive to the presence of outliers in the datasets. In this paper, a robust CCA (RCCA) algorithm is presented. It is obtained using the interpretation of CCA as a latent variable model with two Gaussian random vectors and a robust loss function derived from the $\alpha$-divergence as an alternative to maximum likelihood. Compared to existing robust CCA approaches, the proposed loss has the advantage of belonging to class of redescending M-estimators, guaranteeing inference stability for large deviation from the Gaussian nominal noise model. Experimental results on simulated and real datasets show that the proposed RCCA outperforms some existing robust and standard CCA methods.