Kernel-based conditional canonical correlation analysis via modified Tikhonov regularization

This paper proposes a new conditional kernel CCA (canonical correlation analysis) algorithm and exploits statistical consistency of it via modified Tikhonov regularization scheme, which is a continuous study of [11]. A new measure which characterizes consistency of learning ability is discussed based on the notion of distance between feature subspaces. The consistency analysis is conducted under the assumptions of normalized cross-covariance operators, which is mild and can be constructed by means of mean square contingency. Meantime, the relationship between this new measure and previous consistency scheme is investigated. Furthermore, we study conditional kernel CCA in a more general scenario by means of the trace operator.