Globalized and localized canonical correlation analysis with multiple empirical kernel mapping

Canonical Correlation Analysis (CCA) reveals linear correlation relationship between two feature sets, but fails to discover nonlinear relationship. Kernel CCA (KCCA) overcomes such a shortcoming. Unfortunately, both of them fail to discover local structure of features whereas Locality Preserving CCA (LPCCA) possesses this ability. It is found that LPCCA ignores relationship between global and local structures of features. Moreover, these CCA-based methods have no ability to deal with single-view data which only has single feature set. To this end, we apply Multiple Explicitly Kernel Mapping (MEKM) to the application at first and take global and local structures of features into account. The proposed method is named Globalized and Localized CCA with MEKM (GLCCA-MEKM). Experiments validate that (i) introducing MEKM can map original features into multiple feature spaces so that multiple feature sets of data are obtained. Further in these feature spaces, nonlinear correlation relationship between features are also gotten; (ii) taking global and local structures of features into account makes the mapped features keep both original global and local properties. These processes make GLCCA-MEKM possess the ability to deal with single-view data and be locality-preserving. Therefore, GLCCA-MEKM has below contributions. First, GLCCA-MEKM can inherit the advantages of traditional MEKM, deal with single-view data, and reveal nonlinear correlation relationship between two feature sets. Second, GLCCA-MEKM extracts both global and local structural information more reasonably and coordinates their relationship well. In doing so, mapped features can keep original global and local properties. Finally, classifiers with GLCCA-MEKM obtain better classification performances.