Determining the number of clusters using information entropy for mixed data

作     者：Liang, Jiye Zhao, Xingwang Li, Deyu Cao, Fuyuan Dang, Chuangyin 

作者机构：Shanxi Univ Key Lab Cornputat Intelligence & Chinese Informat Minist Educ Sch Comp & Informat Technol Taiyuan 030006 Shanxi Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China 

出 版 物：《PATTERN RECOGNITION》 (图形识别)

年 卷 期：2012年第45卷第6期

页      面：2251-2265页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China [71031006, 70971080, 60970014] Special Prophase Project on National Key Basic Research and Development Program of China (973) [2011CB311805] Foundation of Doctoral Program Research of Ministry of Education of China Key Problems in Science and Technology Project of Shanxi [20110321027-01] 

主　　题：Clustering Mixed data Number of clusters Information entropy Cluster validity index k-Prototypes algorithm 

摘      要：In cluster analysis, one of the most challenging and difficult problems is the determination of the number of clusters in a data set, which is a basic input parameter for most clustering algorithms. To solve this problem, many algorithms have been proposed for either numerical or categorical data sets. However, these algorithms are not very effective for a mixed data set containing both numerical attributes and categorical attributes. To overcome this deficiency, a generalized mechanism is presented in this paper by integrating Renyi entropy and complement entropy together. The mechanism is able to uniformly characterize within-cluster entropy and between-cluster entropy and to identify the worst cluster in a mixed data set. In order to evaluate the clustering results for mixed data, an effective cluster validity index is also defined in this paper. Furthermore, by introducing a new dissimilarity measure into the k-prototypes algorithm, we develop an algorithm to determine the number of clusters in a mixed data set. The performance of the algorithm has been studied on several synthetic and real world data sets. The comparisons with other clustering algorithms show that the proposed algorithm is more effective in detecting the optimal number of clusters and generates better clustering results. (C) 2011 Elsevier Ltd. All rights reserved.