方法对比

	Calinski-Harabasz指数	“手肘法”	惯性
领域	模型评估	模型评估	模型评估
方法族	MCDM	MCDM	MCDM
起源年份	1974	1953	1967
提出者	Tadeusz Calinski, Jerzy Harabasz	Robert Thorndike	Stuart Lloyd, James MacQueen
类型	Cluster quality metric	Heuristic optimization criterion	Clustering quality metric
开创性文献	Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1-27.	Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics.	Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129-137.
别名	variance ratio criterion, pseudo F-statistic, CH index	elbow analysis, knee detection	WCSS, within-cluster sum of squares, cluster cohesion
相关	5	5	5
摘要	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 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.	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.