مقایسهٔ روش‌ها

	Inertia (Within-Cluster Sum of Squares)	روش آرنج
حوزه	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM
سال پیدایش	1967	1953
پدیدآور	Stuart Lloyd, James MacQueen	Robert Thorndike
نوع	Clustering quality metric	Heuristic optimization criterion
منبع بنیادین	Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137.	Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics.
نام‌های دیگر	WCSS, within-cluster sum of squares, cluster cohesion	elbow analysis, knee detection
مرتبط	5	5
خلاصه	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.	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.