A unified approach to pattern recognition
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.
scientific article; zbMATH DE number 3872721
scientific article