An isometric representation problem in quantum multimolecular polyhedra and similarity

Abstract

Collective distances in quantum multimolecular polyhedra, which can be set as a scalar index associated to the variance vector, enhance the role of the pair density similarity matrix. This paper describes a simplified but efficient algorithm to compute triple, quadruple or higher order density similarity hypermatrices via an isometric decomposition of the pair similarity matrix. Such possibility opens the way to use these similarity elements in quantum QSAR and in the description of scalar condensed vector statistical like indices, for instance skewness and kurtosis. This might lead the way to describe the collective structure of quantum and classical multimolecular polyhedra. © 2015, Springer International Publishing Switzerland.