A Mean Field Annealing Algorithm for Fuzzy Clustering

Abstract

In the classical clustering, an item must entirely belong to a cluster. Fuzzy clustering, however, describes more accurately the ambiguous type of structure in data. Fuzzy clustering is useful for partitioning a set of objects into a certain number of groups by assigning the membership probabilities to each object. In fuzzy clustering, the membership of each datum in each cluster is represented by the membership matrix. In the proposed method, the elements of membership matrix are updated in parallel until they reach one of the global optimal solutions. It differs from the traditional fuzzy clustering methods. In classical fuzzy clustering, the centroid vectors of the clusters in the space are calculated, and then the membership probability matrix is determined, and the process is repeated until the optimum solution is found. By contrast, the method proposed here perturbs the membership probability, and determines whether the the perturbed state should be accepted or not according to the changes of the energy. One Variable Stochastic Simulated Annealing(OVSSA), a continuous valued version of the Mean Field Annealing(MFA) algorithm which is known as a massively parallel algorithm, is employed as an optimization technique. The MFA combines characteristics of the simulated annealing and the neural network and exhibits the rapid convergence of the neural network while preserving the solution quality afforded by Stochastic Simulated Annealing(SSA).