Plenary Lecture
On Maximum Likelihood Clustering via a Multimodal Probability Model
Professor Miin-Shen Yang
Department of Applied Mathematics
Chung Yuan Christian University
Chung-Li 32023, Taiwan
E-mail: msyang@math.cycu.edu.tw
Abstract: Clustering is a method for finding structure in a data set. Clustering methods can be generally categorized as either having a (probability) model-based approach or a nonparametric approach. For a model-based approach, there are two ways to use a probability model for clustering. One is based on the expectation & maximization (EM), and the other is based on the classification maximum likelihood (CML). For a nonparametric approach, clustering methods are generally based on an objective function of similarity or dissimilarity measures, and partitional methods are popularly used, such as k-means and fuzzy c-means, etc. In this lecture, we first consider the maximum likelihood (ML) estimation for the proposed multimodal probability model (MPM) to establish an ML clustering approach. According to the ML clustering, the relationships between most clustering algorithms and the MPM are established. We find that the MPM is actually a good basic probability model for most clustering methods. This ML clustering approach can lead to most clustering algorithms, such as EM, CML, k-means, fuzzy c-means, possibilistic c-means, mean shift, and latent class methods. We then construct two ML clustering frameworks based on the MPM for developing new clustering algorithms. One framework can develop penalized-type clustering algorithms. Another framework induces entropy-type clustering algorithms, especially with sample-weighted clustering. Several numerical and real data sets are made for comparisons. These experimental results show that these new constructions based on the ML clustering can produce useful and effective clustering algorithms.
Brief Biography of the Speaker: Prof. Miin-Shen Yang received the BS degree in mathematics from the Chung Yuan Christian University, Chung-Li, Taiwan, in 1977, the MS degree in applied mathematics from the National Chiao-Tung University, Hsinchu, Taiwan, in 1980, and the PhD degree in statistics from the University of South Carolina, Columbia, USA, in 1989.
In 1989, he joined the faculty of the Department of Mathematics in the Chung Yuan Christian University (CYCU) as an Associate Professor, where, since 1994, he has been a Professor. From 1997 to 1998, he was a Visiting Professor with the Department of Industrial Engineering, University of Washington, Seattle. During 2001-2005, he was the Chairman of the Department of Applied Mathematics in CYCU and now, he is the Director of Chaplain’s Office in CYCU. His research interests include applications of statistics, fuzzy clustering, neural fuzzy systems, pattern recognition and machine learning.
Dr. Yang was an Associate Editor of the IEEE Transactions on Fuzzy Systems (2005-2011), and is an Associate Editor of the Applied Computational Intelligence & Soft Computing and Editor-in-Chief of Advances in Computational Research. He was awarded with 2008 Outstanding Associate Editor of IEEE Transactions on Fuzzy Systems, IEEE; 2009 Outstanding Research Professor of Chung Yuan Christian University; 2010 Top Cited Article Award 2005-2010, Pattern Recognition Letters; 2012 Distinguished Professor of Chung Yuan Christian University; 2014 overseas academic scholar for The 111 Plan of China.