Nicolas Garcia Trillos
Ph.D., Carnegie Mellon, 2015
I received my bachelor's degree in mathematics from Los Andes University in Bogotá, Colombia, in 2010. I finished my Ph.D in mathematics at Carnegie Mellon University in 2015.
My research lies at the intersection of calculus of variations, geometric measure theory, optimal transportation and the applications of these areas to problems that arise from data analysis, machine learning and statistics. In particular, my research focuses on the study of the convergence of solutions of minimization problems in random geometric graphs, to solutions of analogous minimization problems in the continuum. The minimization problems of interest are those connected to important tasks in machine learning like clustering, dimensionality reduction, and classification.
N. Garcia Trillos and D. Slepcev. On the rate of convergence of empirical measures in ∞-transportation distance. To appear in Canadian Journal of Mathematics.
N. Garcıa Trillos and D. Slepcev. Continuum limit of total variation on point clouds.
X. Bresson, N. Garcıa Trillos, T. Laurent, D. Slepcev and J. von Brecht. Consistency of and ratio graph cuts. Preprint.
N. Garcıa Trillos, D. Slepcev. A variational approach to the consistency of spectral clustering. Preprint.