A notion of stability for k-means clustering

Thibaut Le Gouic (1, 2) , Quentin Paris (2, 3)

1 I2M - Institut de Mathématiques de Marseille
2 CS-HSE - Faculty of Computer Science [Moscow]
3 HDI Lab - International Laboratory of Stochastic Algorithms and High-Dimensional Inference

In this paper, we define and study a new notion of stability for the $k$-means clustering scheme building upon the notion of quantization of a probability measure. We connect this notion of stability to a geometric feature of the underlying distribution of the data, named absolute margin condition, inspired by recent works on the subject.

Mots clés: k-means; clustering; stability

Domaines: Statistiques [math.ST]; Apprentissage [cs.LG]

Thibaut Le Gouic, Quentin Paris. A notion of stability for k-means clustering. Electronic Journal of Statistics , 2018, 12 (2), pp.4239-4263. ⟨10.1214/18-EJS1500⟩. ⟨hal-01694318v2⟩