Probabilistic approach for comparing partitions

Abstract

The comparison of two partitions in Cluster Analysis can be performed using various classical coefficients (or indexes) in the context of three approaches (based, respectively, on the count of pairs, on the pairing of the classes and on the variation of information). However, different indexes usually highlight different peculiarities of the partitions to compare. Moreover, these coefficients may have different variation ranges or they do not vary in the predicted interval, but rather only in one of their subintervals. Furthermore, there is a great diversity of validation techniques capable of assisting in the choice of the best partitioning of the elements to be classified, but in general each one tends to favour a certain kind of algorithm. Thus, it is useful to find ways to compare the results obtained using different approaches. In order to assist this assessment, a probabilistic approach to comparing partitions is presented and exemplified. This approach, based on the VL (Validity Linkage) Similarity, has the advantage, among others, of standardizing the measurement scales in a unique probabilistic scale. In this work, the partitions obtained from the agglomerative hierarchical cluster analysis of a dataset in the field of teaching are evaluated using classical and probabilistic (of VL type) indexes, and the obtained results are compared.