Fuzzy Clustering with the Structural α-Entropy

We study fuzzy clustering with the structural α-entropy and present a unified framework for fuzzy clustering with fuzzy entropy, which can be regarded fuzzy clustering with fuzzy entropy as its special case. Then, aiming at weighting exponent m equal to the structural α-entropy index α in the presented unified framework, we obtain the fuzzy membership degrees and cluster centers using Lagrange method. Further, we propose the Structural α-entropy based fuzzy c-means (SEFCM) algorithm. Moreover, to solve clustering of the complicated data, we also present the Structural α-entropy based kernel fuzzy c-means (SEKFCM) algorithm. In experiment, some University of California Irvine (UCI) data sets and synthetic data sets are used to test the performance of the presented algorithms and the role of the structural α-entropy. The experimental results show that the presented algorithms obtain better clustering result.