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	Gap Statistic	シルエット係数
分野	モデル評価	モデル評価
系統	MCDM	MCDM
提唱年	2001	1987
提唱者	Robert Tibshirani, Guenther Walther, Trevor Hastie	Peter Rousseeuw
種類	Statistical criterion	Cluster 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.	Rousseeuw, P. J. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53-65.
別名	gap index, Tibshirani gap statistic	silhouette coefficient, silhouette index
関連	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 Silhouette Coefficient, introduced by Peter Rousseeuw in 1987, is a metric that measures how similar an object is to its own cluster compared to other clusters. It ranges from -1 to 1, where values close to 1 indicate well-separated and cohesive clusters, values near 0 suggest overlapping clusters, and negative values indicate misclustered points.