قارن الطرق

	مؤشر دن (Dunn Index)	مؤشر ديفيز-بولدن	إحصاءة الفجوة (Gap Statistic)	القصور الذاتي
المجال	تقييم النماذج	تقييم النماذج	تقييم النماذج	تقييم النماذج
العائلة	MCDM	MCDM	MCDM	MCDM
سنة النشأة	1974	1979	2001	1967
صاحب الطريقة	Joseph C. Dunn	David L. Davies, Donald W. Bouldin	Robert Tibshirani, Guenther Walther, Trevor Hastie	Stuart Lloyd, James MacQueen
النوع	Cluster quality metric	Cluster quality metric	Statistical criterion	Clustering quality metric
المصدر التأسيسي	Dunn, J. C. (1974). Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4(1), 95-104.	Davies, D. L., & Bouldin, D. W. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1(2), 224-227.	Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2), 411-423.	Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137.
الأسماء البديلة	Dunn's index, separation coefficient	DBI, Davies Bouldin index	gap index, Tibshirani gap statistic	WCSS, within-cluster sum of squares, cluster cohesion
ذات صلة	5	5	5	5
الملخص	The Dunn Index, introduced by Joseph C. Dunn in 1974, is a metric that captures cluster quality by measuring the ratio of the minimum between-cluster distance to the maximum within-cluster diameter. Higher values indicate well-separated and compact clusters, with better clustering quality.	The Davies-Bouldin Index, introduced by Davies and Bouldin in 1979, is a metric for evaluating clustering quality based on the average similarity between each cluster and its most similar neighboring cluster. Lower values indicate better clustering, with a minimum of 0 representing perfectly separated, non-overlapping clusters.	The Gap Statistic, developed by Tibshirani, Walther, and Hastie in 2001, is a principled statistical method for determining the optimal number of clusters in a dataset. It compares the observed within-cluster sum of squares to the expected value under a null hypothesis of no clustering structure, providing a theoretically grounded approach to cluster number selection.	Inertia, also called Within-Cluster Sum of Squares (WCSS), is a measure of cluster cohesion that quantifies how tightly points are grouped around their cluster centroids. Lower values indicate more compact, cohesive clusters. Inertia is the primary objective function for k-means clustering and has been a fundamental metric since the method's introduction.