Capped norm linear discriminant analysis and its applications

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 l(2,1)-norm of a matrix, which employs non-squared l(2)-norm and capped operation, and further proposes a novel capped l(2,1)-norm linear discriminant analysis, called CLDA. Due to the use of capped l(2,1)-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.

Automated summary

Classical linear discriminant analysis (LDA) is sensitive to outliers and noise due to its reliance on squared Frobenious norm. To address this issue, a novel method called capped l(2,1)-norm linear discriminant analysis (CLDA) is proposed in this paper, which employs non-squared l(2)-norm and capped operation to improve robustness. Experimental results on various datasets demonstrate the effectiveness of CLDA in removing outliers and suppressing noise.