مقایسهٔ روش‌ها

	شاخص کالینسکی-هاراباس	شاخص دیویس-بولدین	شاخص دان	روش آرنج
حوزه	ارزیابی مدل	ارزیابی مدل	ارزیابی مدل	ارزیابی مدل
خانواده	MCDM	MCDM	MCDM	MCDM
سال پیدایش	1974	1979	1974	1953
پدیدآور	Tadeusz Calinski, Jerzy Harabasz	David L. Davies, Donald W. Bouldin	Joseph C. Dunn	Robert Thorndike
نوع	Cluster quality metric	Cluster quality metric	Cluster quality metric	Heuristic optimization criterion
منبع بنیادین	Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1-27.	Davies, D. L., & Bouldin, D. W. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1(2), 224-227.	Dunn, J. C. (1974). Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4(1), 95-104.	Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics.
نام‌های دیگر	variance ratio criterion, pseudo F-statistic, CH index	DBI, Davies Bouldin index	Dunn's index, separation coefficient	elbow analysis, knee detection
مرتبط	5	5	5	5
خلاصه	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 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.	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 Elbow Method is a heuristic for selecting the optimal number of clusters in partitional clustering. Introduced by Robert Thorndike in 1953, it involves fitting clustering models for increasing numbers of clusters and plotting the within-cluster sum of squares (WCSS) against the number of clusters. The 'elbow' occurs where the rate of WCSS decrease sharply changes, suggesting an optimal cluster count.