A0899
Title: Geometric inference via graph Laplacians
Authors: Dena Asta - The Ohio State University (United States) [presenting]
Abstract: Networks can be encoded in terms of their graph Laplacians, matrices that intuitively describe the information flow on a network. When those networks are generated from a geometric space X in a certain sense, an intuitive assumption for social networks, then those graph Laplacians are directly approximating some vital information on the space X. Some recent work will be described in inferring the complete geometric structure of X from graph Laplacians under some mild smoothness assumptions on X - an estimator for intrinsic distances in X between the sample points. The key idea underlying this sort of geometric inference is to regard graph Laplacians not merely as linear operators but as linear operators satisfying a specific approximate "product rule" for second derivatives.
