Multiview dimension reduction via Hessian multiset canonical correlations

Canonical correlation analysis (CCA) is a main technique of linear subspace approach for two-view dimension reduction by finding basis vectors with maximum correlation between the pair of variables. The shortcoming of the traditional CCA lies that it only handles data represented by two-view features and cannot reveal the nonlinear correlation relationship. In recent years, many variant algorithms have been developed to extend the capability of CCA such as discriminative CCA, sparse CCA, kernel CCA, locality preserving CCA and multiset canonical correlation analysis (MCCA). One representative work is Laplacian multiset canonical correlations (LapMCC) that employs graph Laplacian to exploit the nonlinear correlation information for multiview high-dimensional data. However, it possibly leads to poor extrapolating power because Laplacian regularization biases the solution towards a constant function. In this paper, we present Hessian multiset canonical correlations (HesMCC) for multiview dimension reduction. Hessian can properly exploit the intrinsic local geometry of the data manifold in contrast to Laplacian. HesMCC takes the advantage of Hessian and provides superior extrapolating capability and finally leverage the performance. Extensive experiments on several popular datasets for handwritten digits classification, face classification and object classification validate the effectiveness of the proposed HesMCC algorithm by comparing it with baseline algorithms including TCCA, KMUDA, MCCA and LapMCC. (C) 2017 Elsevier B.V. All rights reserved.