手法を比較

	Gap Statistic	Calinski-Harabasz Index（キャリンスキー・ハラバス指数）	慣性
分野	モデル評価	モデル評価	モデル評価
系統	MCDM	MCDM	MCDM
提唱年	2001	1974	1967
提唱者	Robert Tibshirani, Guenther Walther, Trevor Hastie	Tadeusz Calinski, Jerzy Harabasz	Stuart Lloyd, James MacQueen
種類	Statistical criterion	Cluster quality metric	Clustering quality metric
原典	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.
別名	gap index, Tibshirani gap statistic	variance ratio criterion, pseudo F-statistic, CH index	WCSS, within-cluster sum of squares, cluster cohesion
関連	5	5	5
概要	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.