A novel supervised correlation analysis based on partial differential equations for multi-feature extraction and fusion

In high dimensional data analysis, canonical correlation analysis (CCA) mainly studies the linear correlation between two sets of features and it is an effective two-view feature extraction method. However, CCA cannot extract the features that are invariant under some transforms. Moreover, CCA is an unsupervised learning algorithm which does not contain the class label information. These limits the classification performance to some extent. In this paper, a novel learning algorithm is proposed, called supervised CCA based on partial differential equations (SCCA-PDEs), which considers both invariance of the features under some transforms and discriminative. More concretely, SCCA-PDEs firstly extracts the feature matrix of each view by using the evolutionary process of PDEs; and then the between-class and within-class scatter matrices are introduced into the criterion function to enhance the discriminative power of features, which results in not only maximizing the correlation between two feature vectors, but also maximizing between-class separability and simultaneously minimizing within-class cohesiveness; and next fuse the extracted features by two given fusion strategy to form discriminative feature vectors for classification tasks. The experimental results on several benchmark databases show that SCCA-PDEs has better discriminating power and robustness than the existing related algorithms.