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Aiming to improve the robustness and adaptiveness of the recently investigated capped norm linear discriminant analysis (CLDA), this paper proposes a regularized linear discriminant analysis based on the generalized capped l 2 , q -norm (GCLDA). Compared to CLDA, there are two improvements in GCLDA. Firstly, GCLDA uses the capped l 2 , q -norm rather than the capped l 2 , 1 -norm to measure the within-class and between-class distances for arbitrary q > 0 . By selecting an appropriate q, GCLDA is adaptive to different data, and also removes extreme outliers and suppresses the effect of noise more effectively. Secondly, by taking into account a regularization term, GCLDA not only improves its generalization ability but also avoids singularity. GCLDA is solved through a series of generalized eigenvalue problems. Experiments on an artificial dataset, some real world datasets and a high-dimensional dataset demonstrate the effectiveness of GCLDA. [ABSTRACT FROM AUTHOR]

Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, this paper introduces a capped l2,1-norm of a matrix, which employs non-squared l2-norm and "capped" operation, and further proposes a novel capped l2,1-norm linear discriminant analysis, called CLDA. Due to the use of capped l2,1-norm, CLDA can effectively remove extreme outliers and suppress the effect of noise data. In fact, CLDA can also be viewed as a weighted LDA and is solved through a series of generalized eigenvalue problems. The experimental results on an artificial data set, some UCI data sets and two image data sets demonstrate the effectiveness of CLDA. [ABSTRACT FROM AUTHOR]

Two-dimensional linear discriminant analysis (2DLDA) is an effective matrix-based supervised dimensionality reduction method that expresses 2D data directly. However, 2DLDA magnifies the influence of outliers and noise since the construction of 2DLDA is based on squared Frobenius norm. To overcome its sensitivity, this paper investigates a two-dimensional capped l 2 , 1 -norm linear discriminant analysis, called 2DCLDA. The application of capped l 2 , 1 -norm makes 2DCLDA identify outliers and suppress the effect of noise effectively. To avoid singularity and give a stable performance, a regularization term is also considered in the between-class scatter. 2DCLDA is solved through a series of generalized eigenvalue problems, with each subproblem can be deemed as a weighted 2DLDA with regularization. It is proved that the proposed iteration algorithm monotonously decreases the objective of 2DCLDA. At last, 2DCLDA with its related approaches on several face image databases is compared, and the experimental results demonstrate the superiority of 2DCLDA, especially for noise data. [ABSTRACT FROM AUTHOR]