Evolutionary k-Means Clustering Method with Controlled Number of Clusters Applied to Determine the Typology of Polish Municipalities

Obtaining a method of grouping the data items in a number of categories, depending on the values of easy-to-interpret parameters, giving the ability to regulate to a certain degree the level of detail of data division (the number, size and location of detected clusters), became the impetus to develop the evolutionary k-means method and to examine its properties in conjunction with the test data, containing several important parameters of Polish municipalities. The method presented is based on the widely known k-means approach, which, in combination with the evolutionary algorithm and some easy-to-obtain information on grouped data, allows for obtaining an adaptive method of data clustering. In this method, the degree of detail in the distribution of data can be easily adjusted using one parameter, and, depending on the value of this parameter, the method produces more detailed or more coarse data clustering, involving more or less of the detected clusters. This key parameter depends on some geometric characteristics of clustered data. It is, of course, possible to generate different divisions using classical k-means, by simply specifying different numbers of clusters to be detected, but in connection with evolutionary method and some information about clustered data it is possible to do it more efficiently and with an additional interpretation for the results. The paper presents the evolutionary k-means method, the data considered and the obtained results, compared with the results generated by geographers.