Using Cluster and Feature Weighted FCM for reducing ANFIS Rules

Fuzzy c-means (FCM) is assumed that all the features are of equal importance. In real applications, however, the importance of the features is different and there exist some features that are more important than the others. These important features should basically have more effects than the other features in the forming of optimal clusters. The basic FCM algorithm does not support this idea. Also, the FCM algorithm suffers from another problem; the algorithm is very sensitive to initialization, whereas a bad initialization leads to a poor local optimum. In this paper, motivated by these weaknesses of the FCM, the goal is to solve the two problems at the same time. In doing so, an automatic local feature weighting scheme is proposed to properly weight the features of each clusters. And, a cluster weighting process is performed to mitigate the initialization sensitivity of the FCM. Feature weighting and cluster weighting are performed simultaneously and automatically during the clustering process resulting in high quality clusters, regardless of the initial centers. Extensive experiments conducted on a synthetic dataset and 16 real world datasets indicate that the proposed algorithm outperforms the state-of-the-arts algorithms. The convergence proof of the proposed algorithm is also provided.