A Comparative Study of Kernel and Robust Canonical Correlation Analysis

A number of measures of canonical correlation coefficient are now used in multimedia related fields like object recognition, image segmentation facial expression recognition and pattern recognition in the different literature. Some robust forms of classical canonical correlation coefficient are introduced recently to address the robustness issue of the canonical coefficient in the presence of outliers and departure from normality. Also a few number of kernels are used in canonical analysis to capture nonlinear relationship in data space, which is linear in some higher dimensional feature space. But not much work has been done to investigate their relative performances through i) simulation from the view point of sensitivity, breakdown analysis as well as ii) using real data sets. In this paper an attempt has been made to compare performances of kernel canonical correlation coefficients (Gaussian function, Laplacian function and Polynomial function) with that of robust and classical canonical correlation coefficient measures using simulation with five sample sizes (50, 500, 1000, 1500 and 2000), influence function, breakdown point along with several real data and a multi-modal data sets, focusing on the specific case of segmented images with associated text. We investigate the bias, mean square error(MISE), qualitative robustness index (RI), sensitivity curve of each estimator under a variety of situations and also employ box plots and scatter plots of canonical variates to judge their performances. We have observed that the class of kernel estimators perform better than the class of classical and robust estimators in general and the kernel estimator with Laplacian function has shown the best performance for large sample size and break down is high in case of nonlinear data.