Robust Local Principal Component Analyzer with Fuzzy Clustering

Non-linear extensions of Principal Component Analysis (PCA) have been developed for detecting the lower-dimensional representations of real world data sets and local linear approaches are used widely because of their computational simplicity and understandability. Fuzzy c-Varieties (FCV) is the linear fuzzy clustering algorithm that estimates local principal component vectors as the vectors spanning prototypes of clusters. Least squares techniques, however, often fail to account for “outliers”, which are common in real applications. In this paper, we propose a technique for making the FCV algorithm robust to intra-sample outliers. The objective function based on the lower rank approximation of the data matrix is minimized by a robust M-estimation algorithm that is similar to FCM-type iterative procedures.