JSM 2005 Online Program

Abstract #302758

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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= Applied Session,

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Activity Number:	112
Type:	Invited
Date/Time:	Monday, August 8, 2005 : 10:30 AM to 12:20 PM
Sponsor:	Section on Nonparametric Statistics
Abstract - #302758
Title:	Nonlinear Dimension Reduction
Author(s):	Andreas Buja*+
Companies:	University of Pennsylvania
Address:	The Wharton School, Philadelphia, PA, 19104,
Keywords:
Abstract:	Nonlinear dimension reduction has been a topic of interest for at least half a century. Among older methods for nonlinear dimension reduction are several approaches originating in the psychometric literature such as multiple correspondence analysis, Kruskal-Shepard multidimensional scaling (MDS), and principal curves and surfaces as introduced by Hastie and Stuetzle. Recently, computer scientists in machine learning have proposed novel nonlinear dimension reduction schemes. One proposal, called InfoMap, is classical Torgerson-Young MDS applied to a novel distance matrix. The other proposal, called "Locally Linear Embedding" (LLE) is conceptually more novel in that it attempts to recreate local affine relations among neighboring points. In this talk, we will introduce a strong competitor of InfoMap and LLE. It is a localized variant of Kruskal-Shepard multidimensional scaling modified by ``repulsive forces'' between nonlocal objects.

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