So sánh phương pháp

	Chỉ số Calinski-Harabasz	Gap Statistic	Quán tính
Lĩnh vực	Đánh giá mô hình	Đánh giá mô hình	Đánh giá mô hình
Họ	MCDM	MCDM	MCDM
Năm ra đời	1974	2001	1967
Người khởi xướng	Tadeusz Calinski, Jerzy Harabasz	Robert Tibshirani, Guenther Walther, Trevor Hastie	Stuart Lloyd, James MacQueen
Loại	Cluster quality metric	Statistical criterion	Clustering quality metric
Công trình gốc	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.	Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137.
Tên gọi khác	variance ratio criterion, pseudo F-statistic, CH index	gap index, Tibshirani gap statistic	WCSS, within-cluster sum of squares, cluster cohesion
Liên quan	5	5	5
Tóm tắt	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.	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.