A unified approach to pattern recognition
type: Item
instance of: scholarly article
title: A unified approach to pattern recognition
zbMATH Open document ID: 0547.68086
DOI: 10.1016/0031-3203(84)90056-6
author: Lev Goldfarb
published in: Pattern Recognition
publication date: 1984-01-01T00:00:00Z
review text: A new approach to pattern recognition is proposed [for a fuller exposition of the approach see Progress in Machine Intell. and Pattern Recognition, Vol. 2, 236-397 (1985)]. No restrictions on the form of pattern representation are imposed. The pattern classification problem is formulated in a metric (or even pseudometric) space. Since the ``syntactic'', or ``structural'', problems can be approached from the metric point of view (by means of various distances on strings, trees, etc.), these problems can be solved within the proposed framework. The new approach is based on Schoenberg-Frechet's result about isometric embedding of a finite metric space in a pseudoeuclidean vector space [\textit{I. J. Schoenberg}, Ann. Math., II. Ser. 36, 724-732 (1935; Zbl 0012.30703)], and an algorithm following from it. The embedding algorithm constructs a distance preserving vector representation of a finite metric space (representing a training sample) in a pseudoeuclidean vector space. The representation is unique up to a motion of the vector space, and so any legitimate decision algorithm in the constructed pseudoeuclidean space should be invariant with respect to the group of motions. The concept of a generalized covariance matrix is introduced. It is shown that most of the classical ``geometric'' algorithms can be adapted to pseudoeuclidean vector spaces. The method of abstract orthogonal projection is proposed for an efficient on-line vector representation of an input pattern. The training sample is assumed to be an \(\epsilon\)-net of the distribution support. In summary, the proposed approach translates the original metric problem into one in a vector space of a minimum dimension.
Mathematics Subject Classification ID: 68T10
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 3872721
zbMATH Keywords: vector approach
zbMATH Keywords: structural approach
zbMATH Keywords: pattern recognition
zbMATH Keywords: pattern classification
zbMATH Keywords: isometric embedding
zbMATH Keywords: metric space
zbMATH Keywords: pseudoeuclidean vector space
zbMATH Keywords: vector representation
zbMATH Keywords: motion
zbMATH Keywords: generalized covariance matrix
zbMATH Keywords: abstract orthogonal projection
zbMATH Keywords: training sample
MaRDI profile type: Publication
full work available at URL: 0031-3203(84)90056-6
OpenAlex ID: W2076523907
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description: scientific article; zbMATH DE number 3872721