General Information

Office: CoRE 434
E-mail: diallot@reu.dimacs.rugters.edu

Project Description

The study of brain connectivity using graph theory.


Weekly Log

Week 1

The first week was mainly introduction graph theory in general, as well as to get some guides from our mentor. We gave a PowerPoint Presentation on some basic graph theory concepts along with some more specific concepts that might be applicable to our resesarch.

These are the sources I consulted in my preliminary research:
  1. Graph theoretical analysis of complex networks in the brain, Stam & Reijneveld.
  2. Complex brain networks: graph theoretical analysis of structural and functional systems, Bullmore & Sporns.
  3. Weighted Graph Comparison Techniques for Brain Connectivity Analysis, Alper et. al.

Week 2

Professor Ghosh guided us through learning some more background about matrix representations of graphs, spectral theory and analysis. As a way to get our feet wet, Justine and I have been working to prove some theorems and lemmas which were not provided in certain relevant papers. Furthermore, we have started thinking about where and how we will get brain connectivity data--for example, how the edges of our graph, corresponding to structural fiber tracts in the brain, will be weighted.

Here are some papers and sources we referenced this week:
  1. The Normalized Laplacian Matrix and General Randić Index of Graphs, Cavers.
  2. A Tutorial in Connectome Analysis: Topological and Spatial Features of Brain Networks, Kaiser.
  3. Comparison of Spectral Methods Through the Adjacency Matrix and the Laplacian of a Graph, Zumstein - Download.
  4. Eigenvalues and Structures of Graphs, Butler - Download.
  5. Consistency of Spectral Clustering, von Luxburg, Belkin & Bousquet.

Week 3

This week I learned the basic of matlab, such as how to compule a code, how to plot a graph using the adjacency matrix. This gave me some ideas on how to vary our spectral clustering algorithm so as to better analyze our data.

Justine also was able to obtain some brain connectivity data and structural region of interest (ROI) data that we will use as input for our program that will run a spectral clustering algorithm.

Week 4

Professor Ghosh gave us some code written by past students. The code is for applying spectral clustering to competition graphs. We were able to play around with small amounts of data using this code in the hopes that when we have a large set of brain connectivity data the clustering algorithm will work.

I rewrote the code to make it useful to our project. i did modify the data we have and play with the modified code.

Here are some additional papers we have referenced thus far:

  1. Complex network measure of brain connectivity: Uses and interpretations, Rubinov and Sporns, 2009.
  2. A Tutorial on Spectral Clustering, von Luxberg, 2007.
  3. Limits of Spectral Clustering, von Luxberg and Bousquet.
  4. The elusive concept of brain connectivity, Horwitz, 2003.


Additional Information