Cluster Canonical Correlation Analysis

Abstract

In this paper we present cluster canonical cor-relation analysis (cluster-CCA) for joint dimen-sionality reduction of two sets of data points. Unlike the standard pairwise correspondence be-tween the data points, in our problem each set is partitioned into multiple clusters or classes, where the class labels define correspondences be-tween the sets. Cluster-CCA is able to learn dis-criminant low dimensional representations that maximize the correlation between the two sets while segregating the different classes on the learned space. Furthermore, we present a kernel extension, kernel cluster canonical correlation analysis (cluster-KCCA) that extends cluster-CCA to account for non-linear relationships. Cluster-(K)CCA is shown to be computationally efficient, the complexity being similar to stan-dard (K)CCA. By means of experimental evalu-ation on benchmark datasets, cluster-(K)CCA is shown to achieve state of the art performance for cross-modal retrieval tasks. 1