Computing and Mathematical Sciences Colloquium

Monday February 13, 2017 4:00 PM

Variational Problems on Graphs and Their Continuum Limits

Speaker: Associate Professor Dejan SlepĨev, Department of Mathematical Sciences, Carnegie Mellon University
Location: Annenberg 105

I will discuss variational problems arising in machine learning and their limits as the number of data points goes to infinity. Consider point clouds obtained as random samples of an underlying "ground-truth" measure. Graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points. Many machine learning tasks, such as clustering and classification, can be posed as minimizing functionals on such graphs. We consider functionals involving graph cuts and graph laplacians and their limits as the number of data points goes to infinity. In particular we establish for what graph constructions the minimizers of discrete problems converge to a minimizer of a functional defined in the continuum setting. The talk is primarily based on joint work with Nicolas Garcia Trillos, as well as on works with Xavier Bresson, Moritz Gerlach, Matthias Hein, Thomas Laurent, James von Brecht and Matt Thorpe.

Series Computing and Mathematical Sciences Colloquium Series

Contact: Carmen Nemer-Sirois at (626) 395-4561 carmens@cms.caltech.edu