A regularized kernel CCA contrast function for ICA.

A new kernel based contrast function for independent component analysis (ICA) is proposed. This criterion corresponds to a regularized correlation measure in high dimensional feature spaces induced by kernels. The formulation is a multivariate extension of the least squares support vector machine (LS-SVM) formulation to kernel canonical correlation analysis (CCA). The regularization is incorporated naturally in the primal problem leading to a dual generalized eigenvalue problem. The smallest generalized eigenvalue is a measure of correlation in the feature space and a measure of independence in the input space. Due to the primal-dual nature of the proposed approach, the measure of independence can also be extended to out-of-sample points which is important for model selection ensuring statistical reliability of the proposed measure. Computational issues due to the large size of the matrices involved in the eigendecomposition are tackled via the incomplete Cholesky factorization. Simulations with toy data, images and speech signals show improved performance on the estimation of independent components compared with existing kernel-based contrast functions.