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 the entire map. A novel encoding scheme is described, allowing this methodology to be used with a wide variety of input data representations and similarity functions. The potential of the algorithm is illustrated in the analysis of two combinatorial libraries and an ensemble of molecular conformations. The method is particularly useful for extracting low-dimensional Cartesian coordinate vectors from large binary spaces, such as those encountered in the analysis of large chemical data sets. c  2001 John Wiley & Sons, Inc. J Comput Chem 22: 488–500, 2001 Keywords: data mining; data analysis; pattern recognition; dimensionality reduction; feature extraction; nonlinear mapping; Sammon mapping; multidimensional scaling; neural network; combinatorial chemistry; molecular similarity; molecular diversity; conformational analysis; distance geometry Correspondence to: D. K. Agrafiotis; e-mail: dimitris@3dp.com Journal of Computational Chemistry, Vol. 22, No. 5, 488–500 (2001) c  2001 John Wiley & Sons, Inc.