122 citations · 349 across the 22 of their papers we have counts for
6 papers · 1 filter
Consistency of Cheeger and Ratio Graph Cuts
Nicolas Garcia Trillos, Dejan Slepcev, James von Brecht +2
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measu…
Average-distance problem for parameterized curves
Xin Yang Lu, Dejan Slepčev
We consider approximating a measure by a parameterized curve subject to length penalization. That is for a given finite positive compactly supported measure , for and…
On the rate of convergence of empirical measures in -transportation distance
Nicolás García Trillos, Dejan Slepčev
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the -transportation distance between the measur…
Nonlocal-interaction equations on uniformly prox-regular sets
José A. Carrillo, Dejan Slepčev, Lijiang Wu
We study the well-posedness of a class of nonlocal-interaction equations on general domains , including nonconvex ones. We show that under mild assumptions o…
Existence of Ground States of Nonlocal-Interaction Energies
Robert Simione, Dejan Slepčev, Ihsan Topaloglu
We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp co…
Continuum limit of total variation on point clouds
Nicolás García Trillos, Dejan Slepčev
We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the…