手法を比較

	ガウス混合モデル	階層的クラスタリング	主成分分析
分野	機械学習	機械学習	機械学習
系統	Machine learning	Machine learning	Machine learning
提唱年	1977	1963	2002
提唱者	Dempster, Laird & Rubin (EM algorithm)	Ward, J. H.	Jolliffe, I.T. (textbook); Pearson & Hotelling (origins)
種類	Probabilistic (soft) clustering — mixture model	Unsupervised clustering (agglomerative)	Unsupervised dimensionality reduction
原典	Dempster, A.P., Laird, N.M. & Rubin, D.B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society: Series B, 39(1), 1–22.	Ward, J. H. (1963). Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association, 58(301), 236–244.	Jolliffe, I.T. (2002). Principal Component Analysis (2nd ed.). Springer.
別名	Gaussian Karışım Modeli (GMM Kümeleme), GMM, GMM clustering, mixture of Gaussians	Hiyerarşik Kümeleme, hiyerarşik kümeleme, agglomerative clustering, hierarchical agglomerative clustering	Temel Bileşenler Analizi (PCA), PCA, principal components analysis, Karhunen-Loève transform
関連	4	4	3
概要	A Gaussian Mixture Model is a probabilistic clustering method that models the data as a weighted mixture of several Gaussian distributions, fitted with the Expectation–Maximization algorithm formalized by Dempster, Laird & Rubin in 1977. It is a generalization of K-means in which each cluster can take its own shape, size, and orientation.	Hierarchical clustering is an unsupervised method that groups observations into nested clusters and draws the result as a dendrogram, so the number of clusters need not be fixed in advance. Its agglomerative form rests on the objective-function grouping criterion introduced by Joe Ward in 1963.	Principal Component Analysis (PCA) is an unsupervised dimensionality-reduction method — given its modern textbook treatment by Ian Jolliffe (2002) — that compresses high-dimensional data into fewer dimensions while preserving the maximum possible variance. It re-expresses correlated variables as a small set of uncorrelated principal components ordered by how much of the data's variation each one captures.