The power and deflation method based kernel principal component analysis

Kernel principal component analysis (KPCA) is a popular nonlinear feature extraction method. It generally uses eigen-decomposition technique to extract the principal components in feature space. But the method is infeasible for large-scale data set because of the storage and computational problem. To overcome these disadvantages, an efficient iterative method of computing kernel principal components is proposed. First, the Power iteration is introduced to compute the first eigenvalue and corresponding eigenvector. Then the deflation method is repeatedly applied to achieve other higher order eigenvectors. In the process of computation, the kernel matrix needs not to compute and store in advance. The space and time complexity of the proposed method is greatly reduced. The effectiveness of proposed method is validated from experimental results.