مقایسهٔ روش‌ها

	روش آرنج	شاخص دیویس-بولدین	آماره شکاف	Inertia (Within-Cluster Sum of Squares)
حوزه	ارزیابی مدل	ارزیابی مدل	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM	MCDM	MCDM
سال پیدایش	1953	1979	2001	1967
پدیدآور	Robert Thorndike	David L. Davies, Donald W. Bouldin	Robert Tibshirani, Guenther Walther, Trevor Hastie	Stuart Lloyd, James MacQueen
نوع	Heuristic optimization criterion	Cluster quality metric	Statistical criterion	Clustering quality metric
منبع بنیادین	Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics.	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.
نام‌های دیگر	elbow analysis, knee detection	DBI, Davies Bouldin index	gap index, Tibshirani gap statistic	WCSS, within-cluster sum of squares, cluster cohesion
مرتبط	5	5	5	5
خلاصه	The Elbow Method is a heuristic for selecting the optimal number of clusters in partitional clustering. Introduced by Robert Thorndike in 1953, it involves fitting clustering models for increasing numbers of clusters and plotting the within-cluster sum of squares (WCSS) against the number of clusters. The 'elbow' occurs where the rate of WCSS decrease sharply changes, suggesting an optimal cluster count.	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.