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Title:
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RANK BASES IN SPACES OF FINITE METRICS |
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Author(s):
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Archil Maysuradze |
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ISBN:
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978-972-8924-40-9 |
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Editors:
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Jörg Roth, Jairo Gutiérrez and Ajith P. Abraham (series editors: Piet Kommers, Pedro Isaías and Nian-Shing Chen) |
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Year:
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2007 |
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Edition:
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Single |
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Keywords:
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Similarity processing, metrics on finite sets, rank of metrics, preservation of properties, multidimensional scaling. |
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Type:
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Short Paper |
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First Page:
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187 |
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Last Page:
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191 |
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Language:
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English |
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Cover:
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Full Contents:
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click to dowload 
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Paper Abstract:
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A technique to effectively process pairwise distances between the elements of a finite set is considered. The technique
accelerates some data mining procedures dealing with similarity, proximity and so on. A special family of sets of finite
metrics is introduced. The conditions are established under which sets from the family are bases for a special linear vector
space. It is shown that the transition from the representation of a finite metric in the traditional form to its representation
in any of the considered bases and back can be effectively calculated. It is shown that the nonnegativity of the
decomposition of a finite metric in the considered bases is a sufficient condition for the semimetric axioms to hold for
this metric, and a necessary and sufficient condition for the metric to have a given rank. Sets from the considered families
are indicated that characterize largest-volume cones of metrics. |
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