Robust local subspace learning by linear fuzzy clustering with Alternative c-Means criterion

Alternative c-Means model is a method for robustifying cluster estimation, in which a modified distance measure instead of the conventional Euclidean distance is used based on the robust M-estimation concept. In this paper, Fuzzy c-Varieties (FCV), which learns local subspace (i.e., FCV achieves local principal component analysis), is extended to a robustified version by using Alternative c-Means criterion. In order to replace the least square measure with alternative c-Means criterion, the clustering criteria of distances between data samples and linear prototypes are calculated by the lower rank approximation concept. Because the proposed method can extract local principal components in a robust way based on an iterative optimization scheme with additional typicality weights in a pseudo-M-estimation procedure, robust subspace learning can be performed in local area and achieves the lower dimensional visualization by using local principal components. In numerical experiments, the robust feature of the proposed model and the local lower visualization using Iris data set are demonstrated.