قارن الطرق

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