Power-regularized fuzzy c-means clustering with a fuzzification parameter less than one

The present study proposes two types of powerregularized fuzzy c-means (pFCM) clustering algorithms with a fuzzification parameter less than one, which supplements previous work on pFCM with a fuzzification parameter greater than one. Both the proposed methods are essentially identical to each other, but not when fuzzification parameter values are specified. Theoretical discussion reveals the property of the proposed methods, and some numerical results substantiate the property of the proposedmethods and show that the proposed methods outperform two conventional methods from an accuracy point of view.