We have examined a class of optimal classification problems with an objective function based on a loss functional defined directly on the set of all subsets of the given set of objects without resorting to distance between objects.
A “fast” algorithm MATCHING was proposed for approximate solution of the optimal class fication problem. The algorithm is iterative, and the number of partitioning classes analyzed is roughly halved from iteration to iteration. The assignment problem is solved in each iteration.
Computer experiments have shown that in many cases (over 75% for problems of dimension from 4 to 15) a symmetric initial matrix in the assignment problem produces a symmetric optimal assignment.
The relative error of the proposed algorithm investigated for some model problems does not exceed 12% in most of the cases (Figs. 4 and 5) and, in general, depends on the dimension of the problem (n) and the location of k* on the interval [1, n], where k* is the number of classes in the optimal classification.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Yu. P. Rudnev and N. N. Kolesnik, “Principles of construction of a computer-aided system for planning, registration, and reporting in a personnel training institute,” Ekspress-Inf. NII Probl. VSh, Ser. Uprav., Ekonom., Prognoziro. Razvitiya VSh, No. 8, Moscow (1981).
V. A. Petrov, Batch Production and Computer-Aided On-Line Control [in Russian], Mashinostroenie, Leningrad (1975).
B. G. Mirkin, Analysis of Qualitative Attributes [in Russian], Statistika, Moscow (1976).
R. Duda and P. Hart, Pattern Recognition and Scene Analysis [Russian translation], Mir, Moscow (1976).
W. Churchman, R. Ackoff, and L. Arnoff, An Introduction to Operations Research [Russian translation], Nauka, Moscow (1968).
A. Kaufmann and R. Faure, Introduction to Operations Research, Academic Press, New York (1968).
H. Kuhn, “The Hungarian method for the assignment problem,” Naval Research Logistic Quarterly,2, 83–97 (1955).
L. Gilman and A. Rose, APL: An Interactive Approach [Russian translation], Mir, Moscow (1979).
I. I. Malashinin and A. I. Kononov, “Implementation of APL for ES computers,” Prikl. Inform., No. 1, 155–170 (1981).
Translated from Kibernetika, No. 6, pp. 90–95, November–December, 1988.
About this article
Cite this article
Kolesnik, N.N., Rudnev, Y.P. Algorithm for one classification problem. Cybern Syst Anal 24, 788–795 (1988). https://doi.org/10.1007/BF01079153
- Objective Function
- Operating System
- Artificial Intelligence
- Relative Error
- Approximate Solution