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Applied Physics and Mathematics

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Network model of cluster analysis
Khachumov M.V.

The solution of geometric clustering based on algorithm of
modified artificial neural network with a different set of metrics
and methods of initial placement of the clusters is proposed. The
formulation of the problem of clustering is given. We consider the
structure of the network model with additional memory to store
the coefficients of the covariance matrix of the generalized metric.
We detail the general scheme of geometric clustering based on
the network model, which includes the initial placement of the
clusters, setting weights of the neural network, the calculation
of the covariance matrix and classification. Spherical (spatial)
cluster placement model is preferred because of its simplicity and
effectiveness. Traveling salesman problem proposed as a testing
ground for the analysis of the network model. An algorithm to
adjust the network model for solving the traveling salesman
problem is given. Experimental research is made and the basic
steps of the solution are graphically illustrated. The quality of
network solutions is compared with the best known solutions
of this problem for various cities. Evaluation of the results and
recommendations for the use of the generalized metric are given.
Keywords: Network model, cluster analysis, neural network,
generalized metric, the covariance matrix, the traveling salesman
problem, experiment, recommendations.

Contacts: Email: khmike@inbox.ru

Pp. 80-86.

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