Multiview Jointly Sparse Discriminant Common Subspace Learning

Abstract

Multiview data leads to the demand for classifying samples from various views, and the large gap between different views makes the classification task challenging. Recently, researchers have extended linear discriminant analysis (LDA) to multi-view scenarios. However, the extended methods are generally associated with the small-class problem, that is, the projection size is limited by the number of classes. In addition, they are sensitive to variations in images or outliers. To solve these problems, this study proposes a generalized robust multiview discriminant analysis (GRMDA) to obtain a linear transform for each view and for learning multiview jointly sparse discriminant common subspace. GRMDA aims to achieve both maximal between-class and minimal within-class variation for data from multiple views in a common space. Instead of formulating the ratio trace problem, we reformulate GRMDA inspired by maximum margin criterion (MMC) to address the small-class problem. Moreover, the proposed method achieves stronger robustness by reconstructing the within-class and between-class scatter terms from the definition of L2,1 norm. Furthermore, GRMDA ensures joint sparsity using the L2,1 norm-based regularization term. Additionally, we present an iterative algorithm, convergence proof, and complexity analysis. Experiments on six popular databases, that is, COIL100, USPS/MNIST, Extended Yale Face B, AR, BBCSport, and multiple feature datasets, were conducted to evaluate the performance of GRMDA against the state-of-the-art multiview methods. The experimental results demonstrate that the proposed method can achieve a significant performance with strong robustness and fast convergence.