Sensitivity analysis in robust and kernel canonical correlation analysis

Abstract

A number of measures of canonical correlation coefficient are now used in 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 simulation and also from the view point of sensitivity. In this paper an attempt has been made to compare performances of kernel canonical correlation coefficients (Gaussian, Laplacian and Polynomial) with that of classical and robust canonical correlation coefficient measures using simulation and influence function. We investigate the bias, standard error, MSE, qualitative robustness index, sensitivity curve of each estimator under a variety of situations and also employ boxplots and scatter plots of canonical variates to judge their performances. We observe 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.