مقایسهٔ روش‌ها

	مدل آمیخته گوسی	خوشه‌بندی سلسله‌مراتبی	تحلیل مؤلفه‌های اصلی	یو-مپ
حوزه	یادگیری ماشین	یادگیری ماشین	یادگیری ماشین	یادگیری ماشین
خانواده	Machine learning	Machine learning	Machine learning	Machine learning
سال پیدایش	1977	1963	2002	2018
پدیدآور	Dempster, Laird & Rubin (EM algorithm)	Ward, J. H.	Jolliffe, I.T. (textbook); Pearson & Hotelling (origins)	McInnes, L.; Healy, J.; Melville, J.
نوع	Probabilistic (soft) clustering — mixture model	Unsupervised clustering (agglomerative)	Unsupervised dimensionality reduction	Nonlinear manifold-learning dimension reduction
منبع بنیادین	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.	McInnes, L., Healy, J. & Melville, J. (2018). UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction. arXiv:1802.03426.
نام‌های دیگر	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	UMAP (Uniform Manifold Approximation and Projection), uniform manifold approximation and projection, manifold dimension reduction
مرتبط	4	4	3	5
خلاصه	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.	UMAP (Uniform Manifold Approximation and Projection) is a fast, scalable nonlinear dimension-reduction method grounded in manifold-learning theory, introduced by McInnes, Healy and Melville in 2018. It compresses high-dimensional data into a low-dimensional embedding for visualisation and downstream analysis.