Kernel canonical correlation analysis via gradient descent

Abstract

Kernel canonical correlation analysis (CCA) is a powerful statistical tool characterizing nonlinear relations between two sets of multidimensional variables. It has been widely used in many branches of science and technology, e.g. bioinfomatics, multi-media information retrieval, cross-language document retrieval, fMRI (functional magnetic resonance imaging). Previous algorithms focus on sparsity analysis of kernel CCA. In this paper, from another viewpoint, we address a new gradient descent kernel CCA algorithm, which is based on the relation between kernel CCA and linear systems of equations. Meanwhile, stability analysis of the algorithm is addressed by means of suitable error decomposition formula and compact operator theory. Theoretical analysis is elegantly investigated in terms of choices of regularization parameter and step size. Experimental results on real-world datasets demonstrate the effectiveness of the algorithm for content-based image retrieval task. The results indicate that the proposed algorithm is stable and the performance is comparable with several state-of-the-art CCA algorithms.