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