Порівняння методів

	Гаусова сумішева модель	Метод головних компонент	UMAP
Галузь	Машинне навчання	Машинне навчання	Машинне навчання
Родина	Machine learning	Machine learning	Machine learning
Рік появи	1977	2002	2018
Автор методу	Dempster, Laird & Rubin (EM algorithm)	Jolliffe, I.T. (textbook); Pearson & Hotelling (origins)	McInnes, L.; Healy, J.; Melville, J.
Тип	Probabilistic (soft) clustering — mixture model	Unsupervised dimensionality reduction	Nonlinear manifold-learning dimension reduction
Основоположне джерело	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.	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.
Інші назви	Gaussian Karışım Modeli (GMM Kümeleme), GMM, GMM clustering, mixture of Gaussians	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
Пов'язані	4	3	5
Підсумок	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.	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.