مقایسهٔ روش‌ها

	روش آرنج	شاخص کالینسکی-هاراباس
حوزه	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM
سال پیدایش	1953	1974
پدیدآور	Robert Thorndike	Tadeusz Calinski, Jerzy Harabasz
نوع	Heuristic optimization criterion	Cluster 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.	Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1-27.
نام‌های دیگر	elbow analysis, knee detection	variance ratio criterion, pseudo F-statistic, CH index
مرتبط	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 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.