方法对比

	正则化 K-均值聚类	K-means聚类	正则化高斯混合模型
领域	机器学习	机器学习	机器学习
方法族	Machine learning	Machine learning	Machine learning
起源年份	2010	1967 (formalized 1982)	2000s–2010s
提出者	Witten, D. M. & Tibshirani, R. (sparse k-means formulation)	MacQueen, J. B.; Lloyd, S. P.	Fraley, C. & Raftery, A. E. (regularization formalized); sklearn team (practical reg_covar parameter)
类型	Regularized unsupervised clustering	Partitional clustering	Probabilistic clustering with regularization
开创性文献	Witten, D. M., & Tibshirani, R. (2010). A framework for feature selection in clustering. Journal of the American Statistical Association, 105(490), 713–726.	Lloyd, S. P. (1982). Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2), 129–137.	Fraley, C. & Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97(458), 611–631.
别名	sparse k-means, penalized k-means, regularized clustering, constrained k-means	k-means clustering, Lloyd's algorithm, k-means partitioning, hard k-means	Regularized GMM, GMM with covariance regularization, stabilized Gaussian mixture model, penalized GMM
相关	2	4	5
摘要	Regularized k-means extends standard k-means by adding a penalty term — most commonly an L1 (lasso-type) or L2 constraint — to the objective function. This discourages degenerate cluster solutions and, in the sparse variant introduced by Witten and Tibshirani (2010), simultaneously selects the features that drive cluster separation, making it especially valuable in high-dimensional settings where many features are irrelevant.	K-means is a classic unsupervised partitional clustering algorithm that divides a dataset into K non-overlapping groups by iteratively assigning each observation to its nearest centroid and updating centroids as the mean of their assigned points. It is one of the most widely used exploratory tools in machine learning and data analysis.	A Regularized Gaussian Mixture Model (GMM) adds a small positive constant to the diagonal of each component covariance matrix during the Expectation-Maximization algorithm, preventing singular or near-singular matrices that cause numerical failures when the data are sparse, high-dimensional, or contain near-duplicate observations.