Extended multivariate comparison of 68 cluster validity indices. A review

Clustering is an unsupervised machine learning methodology widely used in several sciences to find groups of similar patterns in complex data. The results generated by clustering algorithms generally depend on user-defined input parameters such as the number of expected clusters, which can have a great impact on the homogeneity of the identified clusters. Clustering validity indices (CVIs) are an effective method for determining the optimal number of clusters that best fit the natural partition of a dataset. They do not require any underlying assumption nor a priori knowledge about the true dataset structure. Since 1965, many cluster validity indices have been proposed in the literature and used in several different applications. In this paper, the performance of 68 cluster validity indices was evaluated on 21 real-life research and simulated datasets. CVIs were compared on the same partition for each dataset, which was searched for by the k-means clustering algorithm. Multivariate chemometric methods were applied to disclose mutual relationships among the indices and to select those that are more effective in terms of accuracy and reliability.