Capped norm linear discriminant analysis and its applications
This work addresses robustness issues in LDA for data analysis applications, but it is incremental as it builds on existing LDA methods with a new norm.
The authors tackled the sensitivity of classical linear discriminant analysis (LDA) to outliers and noise by proposing a novel capped l_{2,1}-norm LDA (CLDA) method, which effectively removes extreme outliers and suppresses noise, as demonstrated through experiments on artificial, UCI, and image datasets.
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, in this paper, we introduce capped l_{2,1}-norm of a matrix, which employs non-squared l_2-norm and "capped" operation, and further propose 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 be also viewed as a weighted LDA. CLDA is solved through a series of generalized eigenvalue problems with theoretical convergency. The experimental results on an artificial data set, some UCI data sets and two image data sets demonstrate the effectiveness of CLDA.