Self-centralized jointly sparse maximum margin criterion for robust dimensionality reduction

Abstract

Linear discriminant analysis (LDA) is among the most popular supervised dimensionality reduction algorithms, which has been largely followed in the fields of pattern recognition and data mining. However, LDA has three major drawbacks. One is the challenge brought by small-sample-size (SSS) problem; second makes it sensitive to outliers due to the use of squared L2-norms in the scatter loss evaluation; the third is the case that the feature loadings in projection matrix are relatively redundant and there is a risk of overfitting. In this paper, we put forward a novel functional expression for LDA, which combines maximum margin criterion (MMC) with a weighted strategy formulated by L1,2-norms to against outliers. Meanwhile, we simultaneously realize the adaptive calculation of weighted intra-class and global centroid to further reduce the influence of outliers, and employ the L2,1-norm to constrain row sparsity so that subspace learning and feature selection could be performed cooperatively. Besides, an effective alternating iterative algorithm is derived and its convergence is verified. From the complexity analysis, our proposed algorithm can deal with large-scale data processing. Our proposed model can address the sensitivity problem of outliers and extract the most representative features while preventing overfitting effectively. Experiments performed on several benchmark databases demonstrate that the proposed algorithm is more effective than some other state-of-the-art methods and has better generalization performance.