40 citations · 90 across the 18 of their papers we have counts for
5 papers · 1 filter
K-groups: A Generalization of K-means Clustering
Songzi Li, Maria L. Rizzo
We propose a new class of distribution-based clustering algorithms, called k-groups, based on energy distance between samples. The energy distance clustering criterion assigns obse…
-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this survey paper, we give an overview of our recent works on the study of the -entropy for the heat equation associated with the Witten Laplacian on super-Ricci flows and th…
Hamilton differential Harnack inequality and -entropy for Witten Laplacian on Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the $…
On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows
Songzi Li, Xiang-Dong Li
In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation associated with the time depe…
-entropy, super Perelman Ricci flows and -Ricci solitons
Songzi Li, Xiang-Dong Li
In this paper, we prove the characterization of the -super Perelman Ricci flows by various functional inequalities and gradient estimate for the heat semigroup generat…