Seminars/Colloquia/Invited Talks

Seminars

Michael Trosset

Multidimensional Scaling for LDDMM Dissimilarity Matrices

PLACE:	Clark 314
EVENT:	CIS Seminar Series
DATE:	August 16, 2005
TIME:	3:30 - 4:30

Abstract

Abstract: Researchers affiliated with the Center for Imaging Science have developed a morphometric technique, Large Deformation Diffeomorphic Metric Mapping (LDDMM), that measures a directed dissimilarity of one image from another. The fact that LDDMM naturally produces dissimilarity data invites the subsequent use of multidimensional scaling (MDS) to embed the dissimilarities in Euclidean space, thereby permitting one to visualize relations between the images and to apply a variety of classical multivariate techniques, e.g., linear discriminant analysis (LDA). However, traditional MDS methods are not ideally suited to address certain peculiarities of LDDMM data. This presentation initiates a program to develop customized embedding tools for use with LDDMM data. Issues to be discussed include: (1) LDDMM dissimilarities are directed, i.e., the measured dissimilarity from image A to image B typically differs from the measured dissimilarity from image B to image A. What are suitable ways to resolve this asymmetry? (2) The collection of images to which LDDMM is applied may be structured. For example, Jovicich et al applied LDDMM to left and right hippocampal shapes, resulting in left and right asymmetric dissimilarity matrices. How should this structure affect emebdding? (3) Jovicich et al used classical MDS to embed dissimilarities, then performed LDA. What are the potential pitfalls of this sequence of operations? This presentation will be somewhat speculative and (I hope) highly interactive. My goals are, first, to make the case that MDS should be viewed as a flexible methodology that can be customized to the needs of LDDMM, and, second, to learn more about LDDMM so that I can begin developing appropriate embedding tools.

Brief biography

Michael Trosset received his Ph.D. in statistics from the University of California at Berkeley. His research interests include computational statistics, particularly the development of tractable formulations of and efficient numerical algorithms for multidimensional scaling and related multivariate techniques; the design and analysis of computer experiments; and stochastic optimization. He is an associate editor of the Journal of Computational and Graphical Statistics, and of the Journal of Multivariate Analysis. Dr. Trosset is professor of Mathematics at the College of William and Mary.