قارن الطرق

	طريقة الكوع (Elbow Method)	مؤشر كالينسكي-هاراباز	القصور الذاتي
المجال	تقييم النماذج	تقييم النماذج	تقييم النماذج
العائلة	MCDM	MCDM	MCDM
سنة النشأة	1953	1974	1967
صاحب الطريقة	Robert Thorndike	Tadeusz Calinski, Jerzy Harabasz	Stuart Lloyd, James MacQueen
النوع	Heuristic optimization criterion	Cluster quality metric	Clustering quality metric
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.	Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137.
الأسماء البديلة	elbow analysis, knee detection	variance ratio criterion, pseudo F-statistic, CH index	WCSS, within-cluster sum of squares, cluster cohesion
ذات صلة	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.	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.