On metric spaces arising during formalization of problems of recognition and classification. Part 2: Density properties

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• 作者：I. Yu. Torshin ; K. V. Rudakov
• 关键词：algebraic approach ; the theory of classification of feature values ; metric analysis ; metric condensations ; topological neighborhood
• 刊名：Pattern Recognition and Image Analysis
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：26
• 期：3
• 页码：483-496
• 全文大小：548 KB
• 刊物类别：Computer Science
• 刊物主题：Pattern Recognition
  Image Processing and Computer Vision
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6212
• 卷排序：26

文摘

In order to obtain tractable formal descriptions of poorly formalized problems within the context of the algebraic approach to pattern recognition, we develop methods for analyzing metric configurations. In this paper, using the concepts of σ-isomorphism and σ-completion of metric configurations, a system of criteria for assessing the properties of “generalized density” is obtained. The analysis of the density properties along the axes of a metric configuration allowed us to formulate methods for calculating the topological neighborhoods of points and for finding the “grains” of metric condensations. The theoretical results point to a new plethora of algorithms for searching metric condensations − methods based on the “restoration” of the set (the condensation searched) using the data on the components of the projection of the set on the axes of the metric configuration. The only mandatory parameters of any algorithm of this family of algorithms are the metric itself and the distribution of σ, which characterizes the accuracy of the values of the metric.