Fuzzy-Possibilistic Product Partition: A Novel Robust Approach to c-Means Clustering

Abstract

One of the main challenges in the field of c-means clustering models is creating an algorithm that is both accurate and robust. In the absence of outlier data, the conventional probabilistic fuzzy c-means (FCM) algorithm, or the latest possibilistic-fuzzy mixture model (PFCM), provide highly accurate partitions. However, during the 30-year history of FCM, the researcher community of the field failed to produce an algorithm that is accurate and insensitive to outliers at the same time. This paper introduces a novel mixture clustering model built upon probabilistic and possibilistic fuzzy partitions, where the two components are connected to each other in a qualitatively different way than they were in earlier mixtures. The fuzzy-possibilistic product partition c-means (FP³CM) clustering algorithm seems to fulfil the initial requirements, namely it successfully suppresses the effect of outliers situated at any finite distance and provides partitions of high quality.