Quality Criteria for GMDH-based Clustering. Lyudmyla Sarycheva

Abstract. New external criteria of clustering quality estimation (GMDH-criteria) are proposed. The GMDH-criteria are based on splitting of initial sample X containing n clustered objects , in two not intersected equivalent subsamples A and B. Each subsample A for an object corresponds to a subsample B of the object. They form together the pair named a dipole. The GMDH-criteria generate minimum in area of underfitted clusterizations and allow to find clusterization of optimal complexity in a case of noisy data.

Keywords. Group Method of Data Handling (GMDH), external criteria of clustering quality estimation, modeling, clusterization.

References.
1. A.G. Ivakhnenko. Objective clusterization based on the theory of self-organizing of models // Automation, 1987.– no.5.–P.6-15. (In Russian)
2. A.G. Ivakhnenko. Method of series test (exhaustive search) of the clusterizations-candidates by criteria of a differential type // Pattern recognition, classification, prognosis. Mathematical methods and their application. Â. 2. – Moscow: Nauka, 1989. – P.126-158. (In Russian)
3. A.G. Ivakhnenko and V.S. Stepashko, Pomekhoustoychivost’ modelirovaniya (Noise Immunity of Modelling), Naukova dumka, Kiev, 1985.– 216 p.,  http://www.gmdh.net/articles/theory/bookNoiseIm.pdf
4. A.G. Ivakhnenko. Induktivnyi metod samoorganizatsii modelei slozhnykh sistem (Inductive Method of Complex Systems Models Self-Organization). – Kiev: Naukova Dumka, 1987. – 296 p.(In Russian),  http://www.gmdh.net/articles/theory/bookInductModel.pdf
5. A.G. Ivahnenko. Continuity and discretization. Exhaustive search methods of simulation and clusterization.. – Naukova dumka, Kiev, 1990. – 224 p. (In Russian)
6. V.S. Stepashko, Yu. L. Kocherga. Methods and criterion of problem solving of structural identification // Automation, 1985. – no.5. – P. 29–37. (In Russian)
7. A.G. Ivakhnenko and Yu. P. Yurachkovskiy, Modelirovaniye slozhnykh system po eksperimental’nym dannym (Modelling of Complex Systems for Experimental Data), Radio I Svyaz’, Moscow, 1987.– 120 p. (In Russian)