Robust Intuitionistic Fuzzy C-means clustering for linearly and nonlinearly separable data

Intuitionistic Fuzzy C-means (IFCM) is a robust clustering method which is based upon intuitionistic fuzzy set theory. It uses Euclidean distance as a distance metric, hence can only cluster hyper spherically distributed data-sets in data space or in feature space. FCM and KFCM with a new distance measure (FCM-σ and KFCM-σ) can detect non-hyperspherical clusters in data space and feature space but they are sensitive to noise and produce inefficient results in the presence of noise. This paper present a robust Intuitionistic Fuzzy c-means(IFCM-σ) and a robust kernel Intutitionistic Fuzzy C-Means(KIFCM-σ) with a new distance metric that incorporates the distance variation in a cluster to regularize the distance between data point and the cluster centroid. Propose algorithms are the hybridization of IFCM, kernel function, and new distance metric in the data space and in the feature space which avoid various problems of IFCM and FCM-σ. Experiments are done using two-dimensional synthetic data-sets and noisy digital images, and results are compared with IFCM, KIFCM, FCM-σ and KFCM-σ. The results show that our proposed algorithms, especially KIFCM-σ are more effective.