kernel canonical correlation analysis (KCCA) is a recently addressed supervised machine learning methods, which shows to be a powerful approach of extracting nonlinear features for face classification and other applications. However, the standard KCCA algorithm may suffer from computational problem as the training set increase. To overcome the drawback, we propose a threestage method to improve the performance of KCCA. Firstly, a scheme based on geometrical consideration is proposed to enhance the extraction efficiency. The algorithm can select a subset of samples whose projections in feature space (Hilbert space) are sufficient to represent all of the data in feature space. Subsequently, an improved algorithm inspired by principal component analysis (PCA) is developed. The algorithm can select the most contributive eigenvectors for training and classification instead of considering all the ones. Finally, a multi-class classification method based on support vectors data description (SV...