Centroid origin shift of quantum object sets and molecular point clouds description and element comparisons

• DOI: 10.1007/s10910-011-9960-y
• Publication Date: 2011-12-24T13:12:47Z
• Authors: Ramon Carbó-Dorca; Emili Besalú
• Keywords: Centroid; Similarity (geometry); Cardinality (data modeling)

Shifting the origin of a known quantum object set (QOS) or of some discrete molecular point cloud (MPC) by choosing the centroid of such sets, leads to the way to produce quantum similarity matrices (SM) and tensors, which can be systematically referred to a canonical origin, whatever their nature, dimension or cardinality. In this paper the source, significance and properties of such centroid origin shift and the characteristics of the resultant shifted SM are discussed in deep. From such an analysis some interesting applications emerge; as, for instance, a new collection of MPC ordering possibilities. In addition, although all the procedures in this work are described by means of a quantum similarity theoretical background, based on QOS structure within the space of molecules, everything can be also easily implemented in a classical QSPR framework made of molecular numerical images attached to discrete molecular vectors, constructed with well-defined descriptor parameters.