Cost Sensitive Semi-Supervised Canonical Correlation Analysis for Multi-view Dimensionality Reduction

To deal with the cost sensitive and semi-supervised learning problems in Multi-view Dimensionality Reduction (MDR), we propose a Cost Sensitive Semi-Supervised Canonical Correlation Analysis \((\hbox {CS}^{3}\hbox {CCA}). \hbox {CS}^{3}\hbox {CCA}\) first uses the \(L_2\) norm approach to obtain the soft label for each unlabeled data, and then embed the misclassification cost into the framework of Canonical Correlation Analysis (CCA). Compared with existing CCA based methods, \(\hbox {CS}^{3}\hbox {CCA}\) has the following advantages: (1) It uses the \(L_2\) norm approach to infer the soft label for unlabeled data, which is computationally efficient and effective, especially for cost sensitive face recognition. (2) The objective function of \(\hbox {CS}^{3}\hbox {CCA}\) not only maximizes the soft cost sensitive within-class correlations and minimizes the soft cost sensitive between-class correlations in the inter-view, but also considers the class imbalance problem simultaneously. With the discriminant projections learned by \(\hbox {CS}^{3}\hbox {CCA}\), we employ it for cost sensitive face recognition. The experimental results on four well-known face data sets, including AR, Extended Yale B, PIE and ORL, demonstrate the effectiveness of \(\hbox {CS}^{3}\hbox {CCA}\).