قارن الطرق

	طريقة الكوع (Elbow Method)	مؤشر كالينسكي-هاراباز	مؤشر ديفيز-بولدن	إحصاءة الفجوة (Gap Statistic)
المجال	تقييم النماذج	تقييم النماذج	تقييم النماذج	تقييم النماذج
العائلة	MCDM	MCDM	MCDM	MCDM
سنة النشأة	1953	1974	1979	2001
صاحب الطريقة	Robert Thorndike	Tadeusz Calinski, Jerzy Harabasz	David L. Davies, Donald W. Bouldin	Robert Tibshirani, Guenther Walther, Trevor Hastie
النوع	Heuristic optimization criterion	Cluster quality metric	Cluster quality metric	Statistical criterion
المصدر التأسيسي	Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics.	Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1-27.	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.
الأسماء البديلة	elbow analysis, knee detection	variance ratio criterion, pseudo F-statistic, CH index	DBI, Davies Bouldin index	gap index, Tibshirani gap statistic
ذات صلة	5	5	5	5
الملخص	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 Calinski-Harabasz Index, also called the Variance Ratio Criterion, was introduced by Calinski and Harabasz in 1974. It is a metric that measures the ratio of between-cluster variance to within-cluster variance, adjusted for the number of clusters and data points. Higher values indicate better-separated, more compact clusters.	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.