Plenary Lecture

A Similarity-Based Clustering Method for Data on the Unit Hypersphere

Professor Miin-Shen Yang
Department of Applied Mathematics
Chung Yuan Christian University

Abstract: Directional data has been used in biology, geology, medicine, meteorology and oceanography. Clustering is a useful tool for the analysis of these (directional) data on the unit hypersphere. In general, the EM algorithm with a mixture of von Mises-Fisher distributions is one of the most commonly used clustering methods for high-dimensionally directional data. However, the EM algorithm is sensitive to initialization, noise and outlier where the number of clusters needs to be assigned a priori. The similarity-based clustering method (SCM), proposed by Yang and Wu (2004), can solve the initialization sensitive problem without a priori number of clusters. SCM can also tolerate noise and outliers. However, it only works for data in Euclidean space. In this paper, we first define the distance measure for data on the unit hypersphere and then modify SCM such that it can cluster data on the unit hypersphere. An effective and robust approach to clustering for data on the unit hypersphere is then proposed that will be robust to initialization, noise and outlier without the need to assign the number of clusters for the analysis of data on the unit hypersphere. Some numerical and real-data examples with comparisons demonstrate the effectiveness and superiority of the proposed method. Finally, the proposed clustering algorithm is applied to cluster exoplanet data of extrasolar planets.

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 from 2001 to 2016, he was the Director of Chaplain’s Office in CYCU. Since 2012, he has been a Distinguished Professor of the Department of Applied Mathematics in CYCU. His research interests include fuzzy clustering, applications of statistics, 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 Award of CYCU; 2010 Top Cited Article Award 2005-2010, Pattern Recognition Letters; 2012-2018 Distinguished Professor of CYCU; 2016 Outstanding Research Award of CYCU; 2013-2017 overseas academic scholar for the 111 Plan of China.

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