Improved fuzzy c-means clustering by varying the fuzziness parameter

Abstract

• Clustering results of vFCM are more closer to the minimum of the k means objective. • vFCM provides reduced sensitivity to initialization. • vFCM improves the clustering performance in high dimensions. • vFCM does not need careful tuning as FCM. • Experimental results of vFCM are similar to or better than k means and FCM. 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 v arying 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.