Fuzzy c-Means for Data with Tolerance

Abstract

This article presents two new clustering algorithms which are based on the entropy regularized fuzzy c-means and can treat data with some errors. The first, the tolerance which means the permissible range of the error is introduced into optimization problems which relate with clustering, and the tolerance is formulated. The next, the problems are solved using Kuhn-Tucker conditions. The last, the algorithms are constructed based on the results of solving the problems.