Порівняння методів

	Гаусова сумішева модель	DBSCAN	Ієрархічна кластеризація	Метод головних компонент	UMAP
Галузь	Машинне навчання	Машинне навчання	Машинне навчання	Машинне навчання	Машинне навчання
Родина	Machine learning	Machine learning	Machine learning	Machine learning	Machine learning
Рік появи	1977	1996	1963	2002	2018
Автор методу	Dempster, Laird & Rubin (EM algorithm)	Ester, M., Kriegel, H.-P., Sander, J. & Xu, X.	Ward, J. H.	Jolliffe, I.T. (textbook); Pearson & Hotelling (origins)	McInnes, L.; Healy, J.; Melville, J.
Тип	Probabilistic (soft) clustering — mixture model	Density-based clustering algorithm	Unsupervised clustering (agglomerative)	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.	Ester, M., Kriegel, H.-P., Sander, J. & Xu, X. (1996). A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. Proceedings of the 2nd KDD, 226–231.	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.
Інші назви	Gaussian Karışım Modeli (GMM Kümeleme), GMM, GMM clustering, mixture of Gaussians	DBSCAN Kümeleme, density-based clustering, density-based spatial clustering	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
Пов'язані	4	3	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.	DBSCAN is a density-based clustering algorithm, introduced by Ester, Kriegel, Sander and Xu in 1996, that groups together points lying in dense regions and flags points in sparse regions as noise. It is effective on noisy data and on clusters of irregular, non-spherical shapes.	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.