Download Algebraic Methods in Pattern Recognition: Course held at the by Juliusz Kulikowski PDF

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Extra info for Algebraic Methods in Pattern Recognition: Course held at the Department of Automation and Information July 1971

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W. ,). 6) \l=i An euclidean distance measure is rather preferable in the case of multi-stage components vectors: ~(z* ,z) 2 1/2. 7) in the case of the binary-components vectors the Hamming 1 s arid the euclidean distances are equivalent. A. Aizerman, E. M. I. Rosoneer [1, 3]. 8) v =i are some real coefficients. Then, the distance measure is defined as 38 Chap. 9) eCz*,z) = [K(z*,z*)+K(z,z)-2K (z*,z)] t/2. 12) g(z*,z) = (z*,z) 11t(z*) + v(z) - (z*,z) and a distance measure (proposed by J. Rogers and T.

Are automorphic to each other: the first relation describes a horizontal line-segment, while the seccnd one describes a verti~ cal line-segment. lled a 11 ro- tation 11 • It is also possible to define other kinds of isomorphisms like scale-changing etc. 14) is not an isomorphism of relations in the above-mentioned sense. Let us consider a more detailed general situation. 55 A Homomorphism of the Relations There are given two families of sets , with the relations Ru and Rv , correspondi ngly.

Rn k , because it can be very easily proved that the statistical dependence b~ tween the random variables is not a transitive property. ,x~n' are pairwise each other, they are sta- tistically dependent in common. Therefore, there exists a kind of relation between the relation Rn different from the P -rela tion: a T -relation can be defined as a relation consisting of all sequences of the relations

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