Abstract. When applied to high-dimensional pattern classification tasks such as face recognition, traditional kernel discriminant analysis methods often suffer from two problems: 1) small training sample size compared to the dimensionality of the sample (or mapped kernel feature) space, and 2) high computational complexity. In this chapter, we introduce a new kernel discriminant learning method, which attempts to deal with the two problems by using regularization and subspace decomposition techniques. The proposed method is tested by extensive experiments performed on real face databases. The obtained results indicate that the method outperforms, in terms of classification accuracy, existing kernel methods, such as kernel Principal Component Analysis and kernel Linear Discriminant Analysis, at a significantly reduced computational cost.