# 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.

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:

57Q05

Keywords: