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math.ST2018★ 11 cited
Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendible geodesics
Adil Ahidar-Coutrix, Thibaut Le Gouic, Quentin Paris
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Ou…
math.ST2018★ 2 cited
A notion of stability for k-means clustering
Thibaut Le Gouic, Quentin Paris
In this paper, we define and study a new notion of stability for the -means clustering scheme building upon the notion of quantization of a probability measure. We connect this…