Scaled Euclidean distances: a general dissimilarity index with a suitably defined geometrical foundation

DOI10.1007/S10910-011-9920-6zbMath1317.51020OpenAlexW2170294889WikidataQ62511142 ScholiaQ62511142MaRDI QIDQ427456

Ramon Carbó-Dorca

Publication date: 13 June 2012

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-011-9920-6

zbMATH Keywords

quantum similarityCarbó similarity indexEuclidian distancesgeneralized Carbó similarity indicesgeneralized scalar productsHodgkin-Richards similarity indexscaled Euclidian distance dissimilarity index

Mathematics Subject Classification ID

Real and complex geometry (51M99)

Related Items (6)

Simple comparison of atomic population and shape atomic populations distributions between two molecular structures with a coherent number of atoms ⋮ Collective Euclidian distances and quantum similarity ⋮ Symmetrical overlap transformations of function basis sets: the LCAO MO and quantum similarity practical cases ⋮ Geometry of \(n\)-dimensional Euclidean space Gaussian enfoldments ⋮ A theorem on the Gram matrix of a polyhedron ⋮ Quantum polyhedra, definitions, statistics and the construction of a collective quantum similarity index

Cites Work

• Shells, point cloud huts, generalized scalar products, cosines and similarity tensor representations in vector semispaces
• Molecular quantum similarity measures in Minkowski metric vector semispaces
• The relationship between the eigenvalues and eigenvectors of a similarity matrix and its associated Carbó index matrix
• Quantum similarity and discrete representation of molecular sets
• Quantum similarity, volume functions and generalized Carbó indices
• Definition of norm coherent generalized scalar products and quantum similarity
• On quantum molecular similarity measures (QMSM) and indices (QMSI)
• Shell partition and metric semispaces: Minkowski norms, root scalar products, distances and cosines of arbitrary order
• A mathematical discussion on density and shape functions, vector semispaces and related questions
• Encyclopedia of Distances

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