Modification of CHF and BIC coefficients for Evaluation of Clustering with Mixed Type Variables

Cluster analysis is a multivariate statistical method, which is used to classify objects. It is used in many areas, such as the classification of customers or respondents in various marketing surveys. Individual objects are characterized by different variables. Variables can be quantitative and qualitative. Depending on the type of variables it is necessary to select the appropriate method of measuring distances of objects and clusters. There are many ways how to measure these distances and it is not clearly defined how to choose specific measure in different conditions. Depending on the extent of distances and the method chosen may arise different clusters, and thus different results. For this reason, it is necessary to evaluate the clustering result. The evaluation should analyze the numbers of clusters and different clustering methods. There are many coefficients for evaluate results of clustering. In the current literature are defined in particular coefficients, which are used for the quantitative variables. For variables of mixed types (a combination of qualitative and quantitative) are coefficients described only in a very limited extent. The aim of this paper is to analyze the modified coefficients CHF and BIC on real data sets in case of mixed types variables.