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	Metodo del Gomito	Indice di Calinski-Harabasz	Statistica del Gap	Inerzia
Campo	Valutazione dei modelli	Valutazione dei modelli	Valutazione dei modelli	Valutazione dei modelli
Famiglia	MCDM	MCDM	MCDM	MCDM
Anno di origine	1953	1974	2001	1967
Ideatore	Robert Thorndike	Tadeusz Calinski, Jerzy Harabasz	Robert Tibshirani, Guenther Walther, Trevor Hastie	Stuart Lloyd, James MacQueen
Tipo	Heuristic optimization criterion	Cluster quality metric	Statistical criterion	Clustering quality metric
Fonte seminale	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.	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.
Alias	elbow analysis, knee detection	variance ratio criterion, pseudo F-statistic, CH index	gap index, Tibshirani gap statistic	WCSS, within-cluster sum of squares, cluster cohesion
Correlati	5	5	5	5
Sintesi	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 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.