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Linear discriminant analysis (LDA) is a well-known supervised method that can perform dimensionality reduction and feature extraction effectively. However, traditional LDA-based methods need to be turned into the trace ratio form to compute the closed-form solution, in which the within-class scatter matrix should be nonsingular. In this article, we design a new model named generalized robust linear discriminant analysis (GRLDA) method to tackle this disadvantage and improve the robustness. GRLDA uses L 2 , 1 -norm on both loss functions to reduce the influence of outliers and on regularization term to obtain joint sparsity simultaneously. The intrinsic graph and the penalty graph are constructed to characterize the intraclass similarity and interclass separability, respectively. A novel optimization method is proposed to solve the proposed model, in which a quadratic problem on the Stiefel manifold is involved to avoid the inverse computation on a singular matrix. We also analyze the computational complexity rigorously. Finally, the experimental results on face, object, and medical images exhibit the superiority of GRLDA. [ABSTRACT FROM AUTHOR]

• A multiview method, GRMDA, is proposed for extracting the robust and sparse features, which reconstructs within-class scatter term and between-class scatter term in multiview scenario using L 2 , 1 norm to enhance robustness. • We conduct the analysis of small-class problem and adopt another criterion inspired by MMC to solve this problem. In terms of overfitting problem, the L 2 , 1 norm is also imposed on the regularization term for extracting sparse features. • The paper presents an iterative algorithm to compute optimal linear transform for each view. The poof of convergence is provided, and the computational complexity is analyzed. Several experiments were conducted to evaluate the performance of GRMDA 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 L 2 , 1 norm. Furthermore, GRMDA ensures joint sparsity using the L 2 , 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. [ABSTRACT FROM AUTHOR]