Affiliations: Dept. of Computer Science, Beijing Jiaotong University, Beijing, 100044, China. jianyu@bjtu.edu.cn | Dept.of Applied Maths, Chung Yuan Christian University, Chung-Li 32023, Taiwan. msyang@math.cycu.edu.tw | Center of Information Science, Peking University, Beijing, 100871, China. phao@cis.pku.edu.cn
Note: [] Address for correspondence: Dept. of Computer Science, Beijing Jiaotong University, Beijing, 100044, China This work is partially supported by NSFC Grant 6087503, 90820013, 61033013; 973 Program Grant 2007CB311002, Beijing Natural Science Foundation (Grant No. 4112046), the Fundamental Research Funds for the Central Universities (Grant No. 2009JBZ006-1).
Abstract: Cluster analysis is a tool for data analysis. It is a method for finding clusters of a data set with most similarity in the same group and most dissimilarity between different groups. In general, there are two ways, mixture distributions and classification maximum likelihood method, to use probability models for cluster analysis. However, the corresponding probability distributions to most clustering algorithms such as fuzzy c-means, possibilistic c-means, mode-seeking methods, etc., have not yet been found. In this paper, we construct a multimodal probability distribution model and then present the relationships between many clustering algorithms and the proposed model via the maximum likelihood estimation. Moreover, we also give the theoretical properties of the proposed multimodal probability distribution.
Keywords: Cluster analysis, probability density function
