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Stochastic Proximity Embedding: A Simple, Fast and Scalable Algorithm for Solving the Distance Geometry Problem

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Distance Geometry

Abstract

Stochastic proximity embedding (SPE) is a simple, fast, and scalable algorithm for generating low-dimensional Euclidean coordinates for a set of data points so that they satisfy a prescribed set of geometric constraints. Like other related methods, SPE starts with a random initial configuration and iteratively refines it by updating the positions of the data points so as to minimize the violation of the input constraints. However, instead of minimizing all violations at once using a standard gradient minimization technique, SPE stochastically optimizes one constraint at a time, in a manner reminiscent of back-propagation in artificial neural networks. Here, we review the underlying theory that gives rise to the SPE formulation and show how it can be successfully applied to a wide range of problems in data analysis, with particular emphasis on computational chemistry and biology.

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Author information

Authors and Affiliations

  1. Janssen Research & Development, Johnson & Johnson, Welsh & McKean Roads, Spring House, PA, 19477, USA

    Dimitris K. Agrafiotis & Eric Yang

  2. GlaxoSmithKline, 1250 S. Collegeville Road, Mail Code UP12-210, Collegeville, PA, 19426, USA

    Deepak Bandyopadhyay

Authors
  1. Dimitris K. Agrafiotis
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  2. Deepak Bandyopadhyay
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  3. Eric Yang
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Corresponding author

Correspondence to Dimitris K. Agrafiotis .

Editor information

Editors and Affiliations

  1. IRISA, University of Rennes 1, avenue du General Leclerc, Rennes, 35042, France

    Antonio Mucherino

  2. , Dept of Applied Maths (IMECC-UNICAMP), State University of Campinas, Campinas, 13081, Brazil

    Carlile Lavor

  3. , LIX, Ecole Polytechnique, Palaiseau, 91128, France

    Leo Liberti

  4. Instituto Alberto Luiz Coimbra de, Pos-Graduacao e Pesquisa de, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil

    Nelson Maculan

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Agrafiotis, D.K., Bandyopadhyay, D., Yang, E. (2013). Stochastic Proximity Embedding: A Simple, Fast and Scalable Algorithm for Solving the Distance Geometry Problem. In: Mucherino, A., Lavor, C., Liberti, L., Maculan, N. (eds) Distance Geometry. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5128-0_14

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