Clustering model and metric with continuous data
Proceedings of the conference on Data analysis, learning symbolic and numeric knowledge
On a class of fuzzy classification maximum likelihood procedures
Fuzzy Sets and Systems
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
A Similarity-Based Robust Clustering Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
General C-Means Clustering Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
A possibilistic approach to clustering
IEEE Transactions on Fuzzy Systems
The estimation of the gradient of a density function, with applications in pattern recognition
IEEE Transactions on Information Theory
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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. (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).)