Сравнение методов

	Статистика разрыва (Gap Statistic)	Индекс Дэвиса-Болдина	Инерция
Область	Оценка моделей	Оценка моделей	Оценка моделей
Семейство	MCDM	MCDM	MCDM
Год появления	2001	1979	1967
Автор метода	Robert Tibshirani, Guenther Walther, Trevor Hastie	David L. Davies, Donald W. Bouldin	Stuart Lloyd, James MacQueen
Тип	Statistical criterion	Cluster quality metric	Clustering quality metric
Основополагающий источник	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.	Davies, D. L., & Bouldin, D. W. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1(2), 224-227.	Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137.
Другие названия	gap index, Tibshirani gap statistic	DBI, Davies Bouldin index	WCSS, within-cluster sum of squares, cluster cohesion
Связанные	5	5	5
Сводка	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 Davies-Bouldin Index, introduced by Davies and Bouldin in 1979, is a metric for evaluating clustering quality based on the average similarity between each cluster and its most similar neighboring cluster. Lower values indicate better clustering, with a minimum of 0 representing perfectly separated, non-overlapping 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.