Adapting the right measures for K-means clustering

Clustering validation is a long standing challenge in the clustering literature. While many validation measures have been developed for evaluating the performance of clustering algorithms, these measures often provide inconsistent information about the clustering performance and the best suitable measures to use in practice remain unknown. This paper thus fills this crucial void by giving an organized study of 16 external validation measures for K-means clustering. Specifically, we first introduce the importance of measure normalization in the evaluation of the clustering performance on data with imbalanced class distributions. We also provide normalization solutions for several measures. In addition, we summarize the major properties of these external measures. These properties can serve as the guidance for the selection of validation measures in different application scenarios. Finally, we reveal the interrelationships among these external measures. By mathematical transformation, we show that some validation measures are equivalent. Also, some measures have consistent validation performances. Most importantly, we provide a guide line to select the most suitable validation measures for K-means clustering.