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Journal of Molecular Graphics and Modelling 22 (2003) 133140 A modified update rule for stochastic proximity embedding

Summary: Journal of Molecular Graphics and Modelling 22 (2003) 133140
A modified update rule for stochastic proximity embedding
Dmitrii N. Rassokhin, Dimitris K. Agrafiotis
3-Dimensional Pharmaceuticals Inc., 665 Stockton Drive, Exton, PA 19341, USA
Received 18 December 2002; received in revised form 6 June 2003; accepted 6 June 2003
Recently, we described a fast self-organizing algorithm for embedding a set of objects into a low-dimensional Euclidean space in a way
that preserves the intrinsic dimensionality and metric structure of the data [Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 1586915872]. The
method, called stochastic proximity embedding (SPE), attempts to preserve the geodesic distances between the embedded objects, and
scales linearly with the size of the data set. SPE starts with an initial configuration, and iteratively refines it by repeatedly selecting pairs of
objects at random, and adjusting their coordinates so that their distances on the map match more closely their respective proximities. Here,
we describe an alternative update rule that drastically reduces the number of calls to the random number generator and thus improves the
efficiency of the algorithm.
2003 Elsevier Inc. All rights reserved.
Index terms: Stochastic proximity embedding; Multidimensional scaling; Non-linear mapping; Sammon mapping; Non-linear manifold; Manifold learning;
Dimensionality reduction; Data mining; Conformational analysis; Combinatorial chemistry; Molecular similarity; Molecular diversity; QSAR
Keywords: Stochastic proximity embedding; Multidimensional scaling; Nonlinear mapping; Sammon mapping; Principal component analysis
1. Introduction
Extracting knowledge from large volumes of data is a
prevalent theme in modern scientific research. The problem


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


Collections: Chemistry; Computer Technologies and Information Sciences