  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.
