报 告 人：徐金辉 纽约大学Buffalo分校教授
报告题目：A Unified Framework for Clustering Constrained Data without Locality Property
报告时间：2015年7月28日15:00
报告地点：静远楼0908室
主办单位：计算机学院、科技处
报告内容简介: In this talk, we consider a class of constrained clustering problems of points in R^d space, where d could be rather high. A common feature of these problems is that their optimal clusterings no long have the locality property (due to the additional constraints), which is a key property required by many algorithms for their unconstrained counterparts. To overcome the difficulty caused by the loss of locality, we present in this paper a unified framework, called Peeling-and-Enclosing, to iteratively solve two variants of the constrained clustering problems, constrained k-means clustering (k-CMeans) and constrained k-median clustering (k-CMedian). Our framework is based on two standalone geometric techniques, called Simplex Lemma and Weaker Simplex Lemma, for k-CMeans and k-CMedian, respectively. Simplex lemma (or weaker simplex lemma) enables us to efficiently approximate the mean (or median) point of an unknown set of points by searching a small-size grid, independent of the dimensionality of the space, in a simplex (or the surrounding region of a simplex), and thus can be used to handle high dimensional data. With these techniques, our framework generates, in nearly linear time (i.e., O(nd(logn)^(k+1))), O((logn)^k) k-tuple candidates for the k mean or median points, and one of them induces a (1+epsilon)-approximation for k-CMeans or k-CMedian, where n is the number of points. Combining this unified framework with a problem-specific selection algorithm (which
determines the best k-tuple candidate), we obtain a (1 + epsilon)-approximation for each of the constrained clustering problems. Our framework improves considerably the best known results for these problems. We expect that our technique will be applicable to other constrained clustering problems without locality.
徐金辉教授个人简介：
Dr. Xu is currently a professor ofComputer Science and Engineeringat the University at Buffalo(the State University ofNew York). He received his B.S. and M.S. degrees in Computer Science from the University of Science and Technology of China (USTC), and his Ph.D. degree in Computer Science and Engineering from the University of Notre Dame in 2000.
Dr. Xu's research interest lies in the fields ofAlgorithms, Computational Geometry, Combinatorial Optimization, Machine Learning, and Geometric Computingin Biomedical Imaging, Treatment Planning and Diagnosis, and Networking. His recent research has focused on the development of geometric algorithms and optimization methods for solving problems arising in biomedical imaging and cardiovascular interventional procedures.
Dr. Xu's research has been supported by National Science Foundation (NSF), National Institute of Health (NIH),NYSTAR, IBM, and University at Buffalo. He is a recipient of the NSF CAREER Award and the IBM Faculty Partnership Award.