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A proof of the metric properties of the symmetric scaling‐nesting dissimilarity measure and related symmetry deficiency measures
Author(s) -
Mezey Paul G.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)63:1<105::aid-qua14>3.0.co;2-b
Subject(s) - metric (unit) , nesting (process) , similarity (geometry) , scaling , measure (data warehouse) , simple (philosophy) , symmetry (geometry) , multidimensional scaling , mathematics , scaling law , similitude , statistical physics , computer science , geometry , physics , artificial intelligence , data mining , statistics , image (mathematics) , philosophy , operations management , materials science , epistemology , economics , metallurgy
The scaling‐nesting similarity measures were proposed earlier for an intuitively simple shape comparison of molecular “bodies” enclosed by isodensity surfaces. Similarity measures have extended utility and provide rigorous comparisons which can be treated by well‐known mathematical techniques if they fulfill the conditions for a metric. Here, a proof is presented showing that the symmetric scaling‐nesting dissimilarity measure is indeed a proper metric. Some additional features, relevant to the newly proven properties of these similarity measures, are discussed. © 1997 John Wiley & Sons, Inc.