Degenerate expectation-maximization algorithm for local dimension reduction

Dimension reduction techniques based on principal component analysis (PCA) and factor analysis are commonly used in statistical data analysis. The effectiveness of these methods is limited by their global nature. Recent efforts have focused on relaxing global restrictions in order to identify subsets of data that are concentrated on lower dimensional subspaces. In this paper, we propose an adaptive local dimension reduction method, called the Degenerate Expectation-Maximization Algorithm (DEM). This method is based on the finite mixture model. We demonstrate that the DEM yields significantly better results than the local PCA (LPCA) and other related methods in a variety of synthetic and real datasets. The DEM algorithm can be used in various applications ranging from clustering to information retrieval.