Welcome to the world of manifold regression! In part 2 we will apply manifold regression to a case study involving fMRI brain imaging data. See part 1 for an introduction to these models.
If you want to skip past the data preparation steps, and go right into the manifold regression, click here
Getting Data
First, we need a set of data to work from. There are many great fMRI imaging datasets available on the OpenNeuro website.
Welcome to the world of manifold regression! In part 1 we will introduce the basic concepts, overview the theory behind regression on manifolds, develop an intuition for these models, and discuss their applications. See part 2 for a step by step statistical analysis applying these models.
What is regression? We will consider regular linear regression (RLR) as an analogy to help understand manifold regression. In RLR, we consider pairs of observations \((x,y)\), with \(x\) the independent variable, and \(y\) the dependent variable.