Plenary Lecture

On Robust Expectation & Maximization Clustering Algorithm

Professor Miin-Shen Yang
Chung Yuan Christian University
E-mail: msyang@math.cycu.edu.tw

Abstract: Data analysis is a science for analyzing data in real world, and clustering is a useful tool for data analysis. In general, clustering is a method for finding structure in a data set characterized by the greatest similarity within the same cluster and the greatest dissimilarity between different clusters. It is a branch in multivariate statistical analysis and an unsupervised learning in pattern recognition. From the statistical point of view, clustering methods could be divided into nonparametric and probability model-based approaches. For a nonparametric approach, clustering methods may be based on an objective function of similarity or dissimilarity measures, such as hierarchical clustering and k-means, fuzzy c-means, possibilistic c-means and mean shift, etc. On the other hand, the probability model-based approach assumes that the data set follows a mixture model of probability distributions so that the mixture likelihood approach to clustering is a popular clustering method, in which the expectation & maximization (EM) algorithm is the most used method. However, the EM algorithm for Gaussian mixture models is quite sensitive to initial values and the number of its components needs to be given a priori. To resolve these drawbacks of the EM, we develop a robust-type EM clustering algorithm for Gaussian mixture models. We first create a new way to solve these initialization problems so that it will be robust to initials and different cluster volumes. We then construct a schema to automatically obtain an optimal number of clusters. Therefore, the proposed EM algorithm will be robust to initialization and also different cluster volumes with automatically obtaining an optimal number of clusters. Some experimental examples with artificial datasets and real datasets are used to compare our robust EM algorithm with existing clustering methods. The results demonstrate the superiority and usefulness of our proposed method.

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 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 the Chung Yuan Christian University. 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 Appointment Professorship of Chung Yuan Christian University.

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