Stomped-t: A novel probability distribution for rough-probabilistic clustering

Rough clustering is one of the principal research areas in data mining, machine learning, pattern recognition, and bioinformatics. Among different variants of rough clustering, rough-probabilistic clustering is a new concept introduced recently. In rough-probabilistic clustering, a class is defined as the union of two disjoint regions, namely, a crisp lower approximation region and a probabilistic boundary region. In this regard, stomped normal (SN) distribution provides a statistical modeling of the data set in rough-probabilistic clustering framework. The SN distribution models the central tendency, dispersion, and width of the lower approximation region of each class using its mean, variance, and width parameter, respectively. However, it does not take into consideration the property of kurtosis of the class distribution, which controls the concentration of values around mean and shape of the tail of data distribution. In this background, a novel probability distribution, named stomped-t (St) distribution, is introduced in the paper for rough-probabilistic clustering. The proposed probability distribution incorporates the property of kurtosis into the SN framework. The proposed St probability distribution is then integrated within the rough-probabilistic clustering framework for precise and robust clustering of the data. The efficacy of the proposed clustering algorithm is demonstrated for unsupervised data clustering and image segmentation problems, along with a comparative performance analysis with related algorithms.