Comparative analysis of various fuzzy clustering algorithms for linearly and non-linearly separable data

Fuzzy clustering is an unsupervised technique in which an object belongs to more than one cluster. In this paper, we have implemented and compared eight fuzzy clustering algorithms, FCM, IFCM, KFCM, and KIFCM with the Euclidean distance metric and same algorithms with the weighted mean distance metric, i.e., FCM-ϭ, IFCM-ϭ, KFCM-ϭ, and KIFCM-ϭ. None of the previous reviews in the literature have assessed the effectiveness of these algorithms on linearly and nonlinearly separable data. So, in this comparative analysis, we are focusing on data separability, also considering other factors such as noise-free and noisy data, the presence, and absence of outliers (if any), as well as clusters of varied size, shape, and density. We have conducted the experiment on twelve 2-D synthetic datasets and five real datasets from the UCI repository. It is observed that for linearly separable data, KIFCM and IFCM-ϭ perform considerably better in the presence of noise and outliers whereas for non-linearly separable data, KFCM, KFCM-ϭ, KIFCM, and KIFCM-ϭ perform better.