Justine Langman's REU 2014 Web Page

About Me

Name: Justine Langman
Email: justinel (at) reu.dimacs.rutgers.edu
Office: CoRE 448
Home Institution: Rutgers University
Project: Brain connectivity and graph theory

About My Project

I am working with Thierno Amadou Diallo on a graph theoretical analysis of brain connectivity. Our mentor is Professor Urmi Ghosh-Dastidar from City Tech-CUNY. Professor Ghosh has been working on this research problem for several summers with other students.

We will be considering the structural connectivity of the brain by taking regions of interest (ROIs) as nodes and structural fibers as edges of a graph. We might consider analyzing differences in structural connectivity between sexes, or perhaps differences in connectivity between healthy and damaged brains.

Research Log

Week 1

The first week was mainly becoming more acquainted with graph theory in general, as well as to get a slight idea about where our research will be headed. 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.
  4. Sex differences in the strucutral connectome of the human brain, Ingalhalikar et. al.
  5. Discrete Mathematics & Mathematical Reasoning--Chapter 10: Graphs, Etassami.

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, Thierno 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 a lot more about spectral clustering algorithms, such as different types of algorithms and comparisons of their consistencies and limits when dealing with large sets of data. This gave me some ideas on how to vary our spectral clustering algorithm so as to better analyze our data. I would like to vary certain function parameters at different points in the algorithm and compare the results of spectral clustering on the data.

I 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. I also researched--from a more biological perspective--brain connectivity and ROIs in order to help us with our analysis.

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 started designing a program in Matlab that will allow us to vary some parameters in the spectral clustering algorithm. My goal is to make a very simple GUI by which a user can input their clustering requirements and possibly compare the output clusters as parameters are varied at different points in the algorithm.

Here are some additional papers I have referenced thus far:

  1. Complex network measure of brain connectivity: Uses and interpretations, Rubinov and Sporns, 2009.
  2. Cognitive relevance of the community structure of the human brain functional coactivation network, Crossley et. al., 2013.
  3. A Tutorial on Spectral Clustering, von Luxberg, 2007.
  4. Limits of Spectral Clustering, von Luxberg and Bousquet.
  5. The elusive concept of brain connectivity, Horwitz, 2003.

Week 5

We got the Matlab code to work for the large amount of data that we found, but we are having trouble visualizing our clusters and graph clearly in Matlab. Since there are so many nodes and connections, we do not have a way of really distinguishing the individual nodes and connections with Matlab visualization capabilities. We can print out our clusters, but we realized that the data we found is not indicative of which regions of interest or voxels are being referenced. I also looked into more about how our data, in the form of a similarity matrix, was constructed, for example, the meaning behind the Jaccard index.

Week 6

I do not think my GUI idea will work in Matlab, so I started trying to rewrite some of our algorithm in Java since this language is more intuitive for me. Some things I am interested in exploring at this point:

  1. A recursively defined clustering algorithm. Right now our algorithm can only deal with creating 2 clusters from the data.
  2. A way to determine the number of clusters the data points "naturally" take based on the types of networks, e.g. small-world, random, etc.
  3. Some sort of transform which can turn ROI data into a voxel interpretation. From reading opinions of neuroscientists, a voxel-based approach really seems to be a lot more objective and should be eventually more useful than ROI analysis for neuroscience.

I also worked on a report for which my mentor was asking. Thierno and I were also invited to present our final paper at the MAA Mathfest, so I worked on finalizing the abstract for our presentation.

Week 7

We presented our research this week to other DIMACS students and researchers, so Thierno and I worked on our presentation for that. I also ran our bi-clustering algorithm recursively. I want to compare the results of doing that versus doing a k-clustering algorithm. I think the latter should give more natural results. (Is it worth measuring some sort of "deviation" of a a bi-clustering algorithm recursed k times versus a k-clustering algorithm?)

Week 8

I researched other means that have been used in determining brain connectivity. Thierno and I should compare the results of spectral clustering on our data with the results of other methods and algorithms run on the same data. Furthermore, it will be necessary to get feedback on our results from neuroscientists (because of concerns I addressed in previous weeks) to see if this is a valid method of brain data analysis. I think an analysis of network types, as I wrote above, is a viable strategy for estimating the efficacy of our algorithm, but I am not sure what measures we should use to do this. We programmed some standard connectivity measures to be produced by our original Matlab code, so we have to compare these measures across methods and algorithms.

Week 9

This week is spent writing our final reports for the DIMACS REU 2014. I will probably also be working on a subtly different paper for the MAA Mathfest for next week if I go to present our research.

To go back to the REU website:
  • The REU Website