Nonlinear Component Analysis for Large-Scale Data Set Using Fixed-Point Algorithm

Nonlinear component analysis is a popular nonlinear feature extraction method. It generally uses eigen-decomposition technique to extract the principal components. 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 based on fixed-point algorithm is proposed.The kernel principle components can be iteratively computed without the eigen-decomposition. The space and time complexity of proposed method is reduced to o(m) and o(m), respectively, where m is the number of samples. More important, it still can be used even if traditional eigen-decomposition technique cannot be applied when faced with the extremely large-scale data set. The effectiveness of proposed method is validated from experimental results.