The Problem of Pattern Recognition in Arrays of Interconnected Objects. Statement of the Recognition Problem and Basic Assumptions

A Problem of Pattern Recognition in Arrays of Interrelated Objects. Recognition Algorithm

“…As shown in [7], the Markov model (2) of the prior hidden field X of classes defines its onesided property (3) in the form of conditional probability distributions on the set of values of the variable x t ∈ X relative to any variable x r ∈ X 0 (t) from the Markov neighborhood of x t . Thus, for each pair of roots (r, t) ∈ G connected by the edge in the tree G, the pair of conditional probability distributions q t (x t |x r ) and q r (x r |x t ) is formally always defined.…”

“…Then, on replacing the designations in (4), according to the corollary of Theorem 3 from [7], the posterior hidden sequence of the classes X = X N 1 = (x 1 , . .…”

“…Expression (4) represents the result of Theorem 3 in [7]. According to the corollary of Theorem 3 in [7], the recognition algorithm of linearly ordered objects, which is given in the Appendix, at once follows from the recognition algorithm of the general form.…”

“…In the first part of the given work [7], the problem of pattern recognition in the arrays of interrelated objects was considered. A probabilistic approach was suggested, which relies on the representation of the array T of interrelated objects t ∈ T by a two-component random field (X, Y ) with both a hidden component X = (x t , t ∈ T ) to be restored, which contains information on m classes x t ∈ X = {1, .…”

“…with the same tree graph G of adjacency and conditional probability distributions, each of which is defined for the element t ∈ T by a requisite part Y + t of the observable field Y , whose elements form a subtree with the root in y t (Theorem 3 in [7]):…”