Fuzzy Clustering with M-Estimators

We present an extension of the FCM over the loss functions used in the M-estimators of robust statistics akin to the generalization of the fuzzy-C-means algorithms over the norm distances [1]. The effect of these estimators in reducing the bias of the outliers while estimating the cluster prototypes are studied and compared. The comparisons have been done over synthetic data as well as simulated data consisting of range sensor readings representative of the objects in the neighborhood of a navigating mobile robot. For the synthetic data set the comparison is attempted over the popular FCM algorithm. For the sensory data set the Adaptive Fuzzy Clustering (AFC) algorithm [2] has been employed and extended over the loss functions of robust statistics. The AFC is utilized considering the shape of the objects encountered by the robot in a typical indoor environment.