KL-Divergence-Based and Manhattan Distance-Based Semisupervised Entropy-Regularized Fuzzy c-Means

In this paper, two types of semi-supervised fuzzy c -means algorithms are proposed. One feature of proposed algorithms is that they are based on an entropyregularized fuzzy c -means clustering algorithm, while conventional algorithms are based on standard fuzzy c -means. Another feature of proposed algorithms is that the membership updating equation can be obtained explicitly with any fuzzifier parameter value, while in conventional methods, the updating equation must be solved by some numerical method or by a numerically complex refinement with almost all fuzzifier parameters. The influence of supervisor-parameter and fuzzifier parameter on clustering results are discussed based on numerical experiments and compared to the conventional method, demonstrating the feasibility of proposed algorithms.