Robust Extraction of Local Structures by the Minimum β-Divergence Method

This paper discusses a new highly robust learning algorithm for exploring local principal component analysis (PCA) structures in which an observed data follow one of several heterogeneous PCA models. The proposed method is formulated by minimizing β-divergence. It searches a local PCA structure based on an initial location of the shifting parameter and a value of the tuning parameter β. If the initial choice of the shifting parameter belongs to a data cluster, then the proposed method detects the local PCA structure of that data cluster, ignoring data in other clusters as outliers. We discuss the selection procedures for the tuning parameter β and the initial value of the shifting parameter μ in this article. We demonstrate the performance of the proposed method by simulation. Finally, we compare the proposed method with a method based on a finite mixture model.