Algorithm for determining the optimum number of clusters on the basis of the Kohonen neural network

Abstract

The article discusses the possibilities of using artificial intelligence systems to solve clustering problems. The value of the optimality criterion for various combinations of the number of clusters and the number of neurons of the output network layer is determined. Self-organizing maps (SOM, Self Organizing Maps), developed by T. Kohonen and representing a powerful tool combining two important paradigms of data analysis - clustering and projecting, visualization of multidimensional data on a plane are considered. An example of the location of cluster nuclei after training the Kohonen neural network for different values of the number of neurons in the source layer is given. Comparing the speed of modern computers with the speed of the Kohonen neural network, with other types of neural networks, allows you to conduct a large number of network exercises in a short time, so you can use one of many methods to determine the maximum value of the function. The results of experimental studies to determine the criterion of optimality are presented in the article for different combinations of the number of clusters and the number of neurons in the original layer of the network. According to the method at the initial stage, a set of input vectors is formed, each of which includes three values. A general sequence of actions is formulated to calculate the optimal number of neurons in the output layer of the Kohonen network. The methodology presented in the article is a further development of teaching methods without a teacher. The technique proposed in the article avoids the need to specify the number of outputs of the Kohonen neural network and can be widely used both in solving data mining problems and in recognizing new unknown classes and situations in different fields.