Workshop

Complex data sets lying in high-dimensional spaces are by now a commonplace occurrence in many parts of science. There are many sources for this kind of data, including biology (genetic networks, phylogenetic trees, food webs, protein folding data, and neural networks), communications (internet data, cell phone networks), transportation problems, physics (even describing the position and momentum of a single particle requires six dimensions), and many others. The analysis of such data brings with it a set of di_cult challenges. An important one is the fact that high-dimensional sets cannot be visualized. Analysis and understanding of data sets in dimensions 1,2,and 3 is greatly simplified by visualization. It permits us to quickly identify qualitative aspects of the data, from which one can then frequently go further and obtain more precise quantitative information. This quick identification of qualitative aspects is typically unavailable in higher dimensions, and an important priority is to obtain methods to carry out such qualitative analysis, to act as substitutes for or complements to direct intuitive analysis. In recent years, there has been a great deal of work on the development of such methods, from a great variety of points of view and using a great variety of methods. The purpose of our meeting is to bring together mathematicians, statisticians, computer scientists, cognitive scientists, and learning theorists with two main goals, namely to clarify the status of the latest developments, and to make connections between these obviously related directions of research. Here is a list of some of the directions we expect to be represented at the meeting. • Multidimensional scaling and extensions, including the ISOMAP and LLE algorithms of J.Tenenbaum and S. Roweis, respectively. • Projection pursuit methods, including the applications of XGOBI, GGOBI, and other software. • Differential geometric methods, variational approaches to segmentation of images, and R.Coifmans work on diffusion geometries and harmonic analysis.  Topological methods, as exemplified by the work of H. Edelsbrunner and Carlsson-de Silva.  Description and analysis of families of 2-dimensional shapes in 3-space, as considered by D.Mumford and Carlsson-Collins-Guibas-Zomorodian  Study of data sets in spaces of phylogenetic trees embedded in the tree space of Billera- Holmes-Vogtmann. Schedule of Talks All talks will be in the lecture hall on the second floor at MSRI, 2850 Telegraph Avenue. Thursday, December 9 8:30 - 9:00 Registration 9:00 - 9:15 Welcome and Introduction 9:15 - 10:15 Gunnar Carlsson Algebraic Topology and Visualization 10:15 - 10:30 Morning Tea (Sixth floor) 10:30 - 11:15 Persi Diaconis Projection Pursuit 11:30 - 12:30 Susan Holmes Eigenspace Decompositions for Graphs 12:30 - 2:00 Lunch Break 2:00 - 3:00 Andreas Buja Nonlinear Dimension Reduction 3:00 - 3:30 Afternoon Tea (Sixth floor) 3:30 - 5:00 Discussion Session Moderators: Ed Wegman and Regina Liu Friday, December 10 9:00 - 10:00 Gunnar Carlsson Persistence with Applications 10:00 - 10:30 Morning Tea (Sixth floor) 10:30 - 11:15 Sam Roweis Manifold Learning 11:30 - 12:30 Vin De Silva Harmonic Forms in Computational Topology 12:30 - 2:00 Lunch Break 2:00 - 2:45 Carrie Grimes Hessian-based Locally Linear Embedding 2:45 - 3:00 Afternoon Tea (Sixth floor) 3:00 - 5:00 Discussion about implementations: Discussant leaders: Di Cook and Andreas Buja Saturday, December 11 9:00 - 10:00 Rick Vitale Gaussian Geometry 10:00 - 10:30 Morning Tea (Sixth floor) 10:30 - 11:15 Liza Levina Dimension Estimation 11:30 - 12:15 Debbie Swayne GGobi for Graphs 12:30 - 2:00 Lunch Break 2:00 - 2:45 Herbert Edelsbrunner Protein Docking with Elevation 2:45 - 3:00 Afternoon Tea (Sixth floor) 3:00 - 3:50 Afra Zomorodian Shape Description via Persistent Homology: Theory and Practice 4:00 - 5.00 Discussion about applications to Graphs Discussion Leaders: Stephen North and Susan Holmes Sunday, December 12 9:00 - 9:45 Di Cook Genegobi 9:50 - 10:30 Robert Ghrist Coordinate-free sensor networks 10:30 - 11:20 Tom Griffiths A split-merge sampler for discovering classes in relational data 11:30 - 12:15 Hal Varian Do not call list example. 11:30 - 2:00 Lunch Break 2:00 - 2:45 TBD 2:45 - 3:00 Afternoon Tea (Sixth floor) 3:00 - 5:00 TBD Monday, December 13 This day is set aside for informal discussions and talks whose desirability will emerge during the course of the workshop.