مقایسهٔ روش‌ها

	شاخص دان	شاخص کالینسکی-هاراباس	آماره شکاف
حوزه	ارزیابی مدل	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM	MCDM
سال پیدایش	1974	1974	2001
پدیدآور	Joseph C. Dunn	Tadeusz Calinski, Jerzy Harabasz	Robert Tibshirani, Guenther Walther, Trevor Hastie
نوع	Cluster quality metric	Cluster quality metric	Statistical criterion
منبع بنیادین	Dunn, J. C. (1974). Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4(1), 95-104.	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.
نام‌های دیگر	Dunn's index, separation coefficient	variance ratio criterion, pseudo F-statistic, CH index	gap index, Tibshirani gap statistic
مرتبط	5	5	5
خلاصه	The Dunn Index, introduced by Joseph C. Dunn in 1974, is a metric that captures cluster quality by measuring the ratio of the minimum between-cluster distance to the maximum within-cluster diameter. Higher values indicate well-separated and compact clusters, with better clustering quality.	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.