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Summary: Multidimensional Scaling and
Visualization of Large Molecular
Similarity Tables
DIMITRIS K. AGRAFIOTIS, DMITRII N. RASSOKHIN,
VICTOR S. LOBANOV
3-Dimensional Pharmaceuticals, Inc., 665 Stockton Drive, Exton, Pennsylvania 19341
Received 21 June 2000; accepted 27 September 2000
ABSTRACT: Multidimensional scaling (MDS) is a collection of statistical
techniques that attempt to embed a set of patterns described by means of a
dissimilarity matrix into a low-dimensional display plane in a way that preserves
their original pairwise interrelationships as closely as possible. Unfortunately,
current MDS algorithms are notoriously slow, and their use is limited to small
data sets. In this article, we present a family of algorithms that combine nonlinear
mapping techniques with neural networks, and make possible the scaling of very
large data sets that are intractable with conventional methodologies. The method
employs a nonlinear mapping algorithm to project a small random sample, and
then "learns" the underlying transform using one or more multilayer
perceptrons. The distinct advantage of this approach is that it captures the
nonlinear mapping relationship in an explicit function, and allows the scaling
of additional patterns as they become available, without the need to reconstruct
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