Return to Colloquia & Seminar listing
Multivariate Topological Data Analysis
Colloquium| Speaker: | Peter Kim, University of Guelph, Canada |
| Location: | 1147 MSB |
| Start time: | Tue, May 10 2011, 3:10PM |
Description
We examine the estimation of a signal embedded in white noise on
a compact manifold. A sharp asymptotic minimax bound is determined under
the sup-norm risk over Holder classes of functions and generalizes similar
results available for spheres in various dimensions. The estimation allows
for the development of a statistical Morse theory using the level sets of
the estimated function and together with the sup-norm bound allows the
bounding of the Hausdorff distance in a persistence diagram in computational
algebraic topology. An application to MRI brain scans in an autism study will
be discussed.