A New Clustering Accuracy Measure Based on Relative Distances and its Cross-Validation Using Dirichlet Distribution

We provide a new cluster accuracy measure which assesses the quality of a cluster partition for a data set with inherent clustering. The novel index is a non-linear combination of compactness and separability of the clustering under analysis. The unknown number of existing clusters is estimated using the distances of each data member to individual cluster-representatives, which are taken into account in a form that explains the relative position of the member in a cluster compared to all other clusters available in the partition. On this relative distances, we apply the Dirichlet distribution to cross-validate the efficacy of the proposed measure, which evaluates its consistency to produce answer for a new data set in the future with the same clustering structure. Its usefulness, wide range of applications and superiority are illustrated by means of several interesting case studies.