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A self-organizing principle for learning nonlinear manifolds

Summary: A self-organizing principle for learning
nonlinear manifolds
Dimitris K. Agrafiotis* and Huafeng Xu
3-Dimensional Pharmaceuticals, Inc., 665 Stockton Drive, Exton, PA 19341
Edited by Michael Levitt, Stanford University School of Medicine, Stanford, CA, and approved October 9, 2002 (received for review July 17, 2002)
Modern science confronts us with massive amounts of data:
expression profiles of thousands of human genes, multimedia
documents, subjective judgments on consumer products or polit-
ical candidates, trade indices, global climate patterns, etc. These
data are often highly structured, but that structure is hidden in a
complex set of relationships or high-dimensional abstractions.
Here we present a self-organizing algorithm for embedding a set
of related observations into a low-dimensional space that pre-
serves the intrinsic dimensionality and metric structure of the data.
The embedding is carried out by using an iterative pairwise
refinement strategy that attempts to preserve local geometry
while maintaining a minimum separation between distant objects.
In effect, the method views the proximities between remote
objects as lower bounds of their true geodesic distances and uses
them as a means to impose global structure. Unlike previous


Source: Agrafiotis, Dimitris K. - Molecular Design and Informatics Group, Johnson & Johnson Pharmaceutical Research and Development


Collections: Chemistry; Computer Technologies and Information Sciences