Multiple kernel dimensionality reduction based on collaborative representation for set oriented image classification.

• A theoretical framework of set oriented dimensionality reduction is proposed. • A new criterion for set oriented feature extraction based on CR is proposed. • An optimization framework based on race ratio maximization is developed. • Extensive experiments are conducted to show the effectiveness of our method. Given that collaborative representation (CR) methods have achieved great success in traditional single image based classification, recently, researchers have exploited the mechanism of collaborative representation to handle the case of image set based classification problem. However, without considering a proper criterion for feature extraction, this extension of collaborative representation mechanism suffers from the misleading coefficients of the incorrect classes on the uncontrolled datasets with small class separability. To address this limitation, inspired by large margin principle in discriminative analysis that aims to separately exploit the inter-class and intra-class variability, this paper proposes a novel theoretical framework of set oriented multiple kernel learning for dimensionality reduction based on collaborative representation classification. To achieve this framework, we integrate the learning of an optimal kernel from the multiple base kernels and a discriminative projection into a unified formulation. Moreover, robust feature information can be effectively extracted by minimizing the intra-class reconstruction residual and maximizing the inter-class reconstruction residual of the regularized hull modeled for the image sets. Since the criterion of feature extraction conforms to the mechanism of the collaborative representation classifier, the collaborative representation coefficients in our model can be much discriminative across classes. Notably, this research has important theoretical significance in improving the classification performance for collaborative representation classifier from the perspective of large margin discriminative learning. By employing the method of trace ratio maximization, we also develop a framework to solve the resulting nonconvex optimization problem efficiently. Extensive experiments on benchmark datasets well demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]