Topological Inference in fMRI / Dimension Reduction

Friday, October 4, 2013 - 1:30pm - 2:45pm
Lind 305
Jonathan Taylor (Stanford University)
In the first lecture, we will provide an overview of the various ways that topological information
is used in signal detection problems in functional MRI (fMRI) and other
imaging applications. The principal tool used involves computing the expected
number of critical points of various types of a smooth random field under
some predetermined null hypothesis. We will describe roughly
how some of these calculations can be carried out
using the so-called Gaussian Kinematic Formula.

In the second lecture, we will describe some typical dimension reduction
tools used in statistics and machine learning. Not surprisingly, many of these techniques
build on the SVD of some data-matrix. Topics covered will include
(generalized) PCA, sparse PCA, some ICA and, time permitting, matrix completion.
MSC Code: