Compactness and Separateness Driven Fuzzy Clustering Validity Index Called TLW

The design of validity index of fuzzy clustering has always been a historical problem in fuzzy clustering field. When the distribution of cluster centers is very close, it is difficult for the existing fuzzy clustering validity indexes to obtain a reasonable cluster number, and the separation mechanism of these indexes is too simple. In order to solve the above problems, we propose a novel fuzzy clustering validity index called TLW (Tang-Li-Wang) index. Firstly, compactness is expressed as the ratio of the membership weighted distance value to the sample variance of the dataset. Secondly, the sum of the maximum distance between cluster centers and the mean distance is used in separateness, and the sample variance of cluster centers is introduced, and the two are multiplied to describe the separateness. Thirdly, on the basis of considering compactness and separateness, the introduction of cluster number can alleviate the phenomenon that the index value may change monotonically with the increase of cluster number. Finally, the classical FCM (Fuzzy C-Mean) algorithm is used to conduct experiments on indexes. Comparative experiments and analyses were carried out on 17 typical datasets and 12 clustering validity indexes. From the experimental results of normal simple datasets and high-dimensional difficult datasets, the proposed index shows some advantages. All in all, these results verify that the proposed TLW index has better accuracy and stronger stability.