External Clustering Validation using ARI, NMI and FMI

Clustering validation is essential for assessing the quality of unsupervised learning results, yet individual external metrics often fail to provide a complete evaluation. This paper proposes a weighted aggregation of three widely used indices—Adjusted Rand Index (ARI), Normalized Mutual Information (NMI), and Fowlkes–Mallows Index (FMI)—to produce a single, interpretable quality score. The method assigns weights of 0.4, 0.3, and 0.3 to ARI, NMI, and FMI, respectively, to balance structural accuracy, information content, and precision–recall aspects. The framework was implemented using Python and evaluated on the Iris dataset, a benchmark with three well-separated classes. Experimental results show that the combined score achieves 0.6851, classified under the “Good Clustering” band, providing a more balanced and consistent assessment than individual metrics alone. This approach enables clearer interpretation of clustering performance and can be extended to larger, high-dimensional, and noisy datasets in future research.