Random Walks and Diffusion on Simplicial Complexes: From Coverage Verification to a Simplicial Page Rank
Tuesday, October 29, 2013 - 2:00pm - 2:50pm
In this talk I will show how tools from algebraic topology, specifically homology and cohomology theory, can be used to study a range of problems in sensor networks from distributed, location-free coverage verification to distributed estimation based on pairwise relative measurements. I will show that finding sparse homology generators correspond to location of coverage holes, even when coordinates are not available. Furthermore, I will show that sparse cohomology generators can be used to detect outliers when one needs to aggregate noisy relative measurements for distributed estimation. Next, I will show how Hodge Theory and combinatorial Laplacians can be used to define random walks and Dirichlet problems on simplicial complexes, resulting in introduction of a simplciial Page Rank for measuring importance of higher order cells.