News & Events - Detail

03/21: Surajit Ray, Dept. of Mathematics and Statistics, Boston University
ECE Colloquium: Modal Inference: Building the bridge between nonparametric clustering and mixture analyses
4:00PM (reception for attendees begins at 3:30pm), PHO339

Abstract
Multivariate mixtures provide flexible methods for both fitting and partitioning high-dimensional data. Ray and Lindsay(2005) show that the topography of multivariate mixtures, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a ridgeline manifold that contains all critical points as well as the ridges of the density. To use this rich feature for data analysis we first construct an extension of EM algorithm that can be used to find the modes of a mixture density. Even in very high dimensions the computational complexity of our EM algorithm is extremely low. In addition, the method of steepest ascent can be used to assign the individual data points to modes, providing a clustering of data points through their modal association.

These tools can be used in various ways. For one, we can take a conventional mixture analysis and cluster together those components whose contribution is actually unimodal. This cluster could then represent a single true component with a more complex distribution. We can also turn kernel density estimation into clustering tool in which the data points become identified with each other by their association with a common mode of the density estimator. If in addition we let the bandwidth parameter go from 0 to infinity, we can construct a hierarchical clustering of the data points. In addition to providing satisfying clustering results that lie somewhere between clustering algorithms and a formal mixture analysis, the estimation method raises interesting inferential questions that lie somewhere between the two points of view.

Application of modal clustering will be discussed in the context of image segmentation.

Speaker's Bio
Surajit Ray earned his PhD from Penn State in 2003 and joined the University of North Carolina at Chapel Hill as a Visiting Assistant professor. In 2006, he joined Boston University's faculty as an Assistant Professor in the Department of Mathematics and Statistics. His research interests are in the area of statistical model selection and the theory and geometry of mixture models. He is especially interested in challenges presented by "large magnitude", both in the dimension of data vectors and in the number of vector. Core areas of model selection research include multivariate mixture and structural equations models. Key collaborative activities involve projects in immunlogy and medical image segmentation, with especial focus on statistical distributions on manifolds and high dimensional low sample size geometry.

For more information, please visit Surajit's home @ bu.edu.