Flexible Multi-View Dimensionality Co-Reduction.

Dimensionality reduction aims to map the high-dimensional inputs onto a low-dimensional subspace, in which the similar points are close to each other and vice versa. In this paper, we focus on unsupervised dimensionality reduction for the data with multiple views, and propose a novel method, called Multi-view Dimensionality co-Reduction. Our method flexibly exploits the complementarity of multiple views during the dimensionality reduction and respects the similarity relationships between data points across these different views. The kernel matching constraint based on Hilbert-Schmidt Independence Criterion enhances the correlations and penalizes the disagreement of different views. Specifically, our method explores the correlations within each view independently, and maximizes the dependence among different views with kernel matching jointly. Thus, the locality within each view and the consistence between different views are guaranteed in the subspaces corresponding to different views. More importantly, benefiting from the kernel matching, our method need not depend on a common low-dimensional subspace, which is critical to reduce the influence of the unbalanced dimensionalities of multiple views. Specifically, our method explicitly produces individual low-dimensional projections for individual views, which could be applied for new coming data in the out-of-sample manner. Experiments on both clustering and recognition tasks demonstrate the advantages of the proposed method over the state-of-the-art approaches.