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Notes on quantitative structure‐properties relationships (QSPR) (1): A discussion on a QSPR dimensionality paradox (QSPR DP) and its quantum resolution
Author(s) -
CarbóDorca Ramon,
Gallegos Ana,
Sánchez Ángel J.
Publication year - 2009
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21145
Subject(s) - quantitative structure–activity relationship , curse of dimensionality , mathematics , matrix (chemical analysis) , dimension (graph theory) , similarity (geometry) , molecular descriptor , computational chemistry , computer science , artificial intelligence , chemistry , pure mathematics , machine learning , statistics , chromatography , image (mathematics)
Classical quantitative structure‐properties relationship (QSPR) statistical techniques unavoidably present an inherent paradoxical computational context. They rely on the definition of a Gram matrix in descriptor spaces, which is used afterwards to reduce the original dimension via several possible kinds of algebraic manipulations. From there, effective models for the computation of unknown properties of known molecular structures are obtained. However, the reduced descriptor dimension causes linear dependence within the set of discrete vector molecular representations, leading to positive semi‐definite Gram matrices in molecular spaces. To resolve this QSPR dimensionality paradox (QSPR DP) here is proposed to adopt as starting point the quantum QSPR (QQSPR) computational framework perspective, where density functions act as infinite dimensional descriptors. The fundamental QQSPR equation, deduced from employing quantum expectation value numerical evaluation, can be approximately solved in order to obtain models exempt of the QSPR DP. The substitution of the quantum similarity matrix by an empirical Gram matrix in molecular spaces, build up with the original non manipulated discrete molecular descriptor vectors, permits to obtain classical QSPR models with the same characteristics as in QQSPR, that is: possessing a certain degree of causality and explicitly independent of the descriptor dimension. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009