قارن الطرق

	توسيع تجميع العناقيد القياسي k-means بإضافة حد جزائي	نموذج الخليط الغاوسي المنتظم
المجال	تعلم الآلة	تعلم الآلة
العائلة	Machine learning	Machine learning
سنة النشأة	2010	2000s–2010s
صاحب الطريقة	Witten, D. M. & Tibshirani, R. (sparse k-means formulation)	Fraley, C. & Raftery, A. E. (regularization formalized); sklearn team (practical reg_covar parameter)
النوع	Regularized unsupervised clustering	Probabilistic clustering with regularization
المصدر التأسيسي	Witten, D. M., & Tibshirani, R. (2010). A framework for feature selection in clustering. Journal of the American Statistical Association, 105(490), 713–726.	Fraley, C. & Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97(458), 611–631.
الأسماء البديلة	sparse k-means, penalized k-means, regularized clustering, constrained k-means	Regularized GMM, GMM with covariance regularization, stabilized Gaussian mixture model, penalized GMM
ذات صلة	2	5
الملخص	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.	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.