A note on robust kernel principal component analysis

Extending the classical principal component analysis (PCA), the kernel PCA (Scholkopf, Smola and Muller, 1998) effectively extracts nonlinear structures of high dimensional data. But similar to PCA, the kernel PCA can be sensitive to outliers. Various approaches have been proposed in the literature to robustify the classical PCA. However, it is not immediately clear how these approaches can be "kernelized" in practice. In this paper, we propose a robust kernel PCA procedure. We show that the proposed method can be easily computed. Simulations and a real example in the financial service also demonstrate the competitive performance of our approach when there are outlying observations.