Weight-based canonical sparse cross-view correlation analysis

As a powerful method for multi-view feature extraction, canonical correlation analysis (CCA) can find linear correlation relationship between feature sets from two views. However, CCA has two disadvantages. One is CCA cannot find nonlinear correlation relationship and the local structure of features; the other is CCA does not consider the structure and cross-view information in feature extraction. Thus, Kernel CCA and locality preserving CCA are proposed to overcome the first disadvantage, while Canonical Sparse Cross-view Correlation Analysis (CSCCA) and its kernel version, Kernel CSCCA (KCSCCA), are proposed to overcome the second one. But CSCCA and KCSCCA ignore the weights of data so that the differences between data are not considered. Since globalized and localized CCA considers the weights of data so as to reflect the global and local structure and information of features, this paper introduces the weights of data into CSCCA and proposes a weight-based CSCCA (WCSCCA). Furthermore, a kernel version of WCSCCA (KWCSCCA) is also proposed to find the nonlinear correlation relationship between two sets of features. WCSCCA has the following contributions. First, on the base of CSCCA, it considers the structure and cross-view information in feature extraction. Second, with the weights of data introduced, WCSCCA can make full use of the differences between data for feature extraction according to the global and local structures and information of features. Moreover, on the base of WCSCCA, KWCSCCA can find the nonlinear correlation relationship of features. Finally, for a fair comparison, this paper adopts similar experimental settings and data sets which are used in the experiments of CSCCA and KCSCCA. The experimental results show that WCSCCA and KWCSCCA (1) can preserve much discriminant information; (2) have best recognition accuracies in average compared with other CCA-related methods; (3) have smaller Rademacher complexities; (4) save time compared with CSCCA and KCSCCA, respectively.