Improved fuzzy c-means clustering by varying the fuzziness parameter

摘要

Fuzzy c-means (FCM) is one of the most frequently used methods for clustering, where the fuzziness weighting exponent m is a key hyper-parameter that directly affects the clustering performance. However, FCM requires careful tuning the fuzziness parameter which results in significant time costs. In this research, an improved FCM clustering by varying the fuzziness parameter, called vFCM, is proposed to overcome this issue, based on the facts that the FCM objective is easy to optimize when m is large, while more local valleys appear as m decreases, hence the optimization problem presents a search process from simple to complex when m varies from a large value to a small value approaching 1. Here, the nature of m is similar to the temperature parameter in the deterministic annealing, and moving along a sequence of the FCM objectives by a linear method that proposes to update m automatically provides a form of annealing. Extensive experiments on simulated and real-world data sets show that vFCM is not only more robust to initialization but also improves the clustering performance in high dimensions. Furthermore, the clustering results of vFCM have a low fluctuation according to different m , so it does not require careful tuning the fuzziness parameter. The time that vFCM takes is greatly reduced.(c) 2022 Elsevier B.V. All rights reserved.