Given the competition graph G= (V, E) based on the Hudson river data sets with the node set (species) V, edge set E, and the weight matrix W (Wij= number of shared preys between ith and jth predators), it is possible to partition the competition graph G into two sub graphs GA and GB using the combination of Fiedler order and linkage-based refinements to minimize cut (A, B) while maximizing WA and WB at the same time.
Before I came to Dimacs Reu 2012, I met with my Mentor, Dr. Urmi Ghosh-Dastidar in order to know about the project I am going to work on. She gave me some paper that I had to read to have a better understanding of the project. On Monday, June 4, we went to the Core Building at 8:00 am to have breakfast together and to meet with Dr. Gene Fiorini the Dimacs Reu Director. Soon we went to the orientation to meet with the Dimacs Staff and to know each other also and the evening we had a social meeting. Finally we passed the most of our time to prepare our first presentation of our project which we did it on Friday, June 8, 2012.
On Monday, June 11, I met with my mentor, Dr. Urmi Ghosh-Dastidar in order to set up what we are going to do. She gave us some new papers and she asked us to write the problem we are solving through the Min-Max Cut, to read the Laplacian, Normalized Laplacians, Adjacency Matrix, the review of Symmetric Matrices and Alassane and I worked on them during the week.
I worked on the papers that my Mentor, Dr. Urmi Ghosh-Dastigar gave me. Alassane and I met with her on Wednesday and Friday to present our explanation of the Min-Max Cut and to talk about the data of our project.
On Monday, June 18, we went to in interesting trip to Watson Research Center, IBM to listen some great researchers who talked about their works like on Applied Mathematics to solve problems in real life, on cryptography and cryptanalysis with the issue of security, and the Watson project and his importance in researches and decisions making.
I worked the Hudson River data set and the related work on spectral partition to have a better understanding of them. I met with my mentor, Dr. Urmi Ghosh-Dastidar on Friday, June 29, to talk about the evolution of the Project and to give us instruction for the next week.
I tried to prove that minimizing Cut (A, B) is equivalent to solve the eigensystem (D-W)X=λX. I worked the linkage-based refinement to find out why this method can improve the quality of graph partitioning better than the Fiedler linear search order. On Friday, July 6, I met with Dr. Urmi Ghosh-Dastidar to discuss about what we did and what we are supposed to do for next week.
I started to work in the finalpresentation of our project. Alassane and I met with our mentor, Dr. Urmi Ghosh-Dastidar, on Wednesday to present the proof of why minimizing cut(A,B) is equivalent to solve the eigen-system (D-W)= λX , to talk about what we must do to finalize our project, and on Friday to work in the results of our project.
I met with my mentor Dr. Urmi Ghosh-Dastidar on Monday to work in the Matlab code to produce the outcome of our research. Alassane and I finalized the results of our project and the final power point presentation. We presented it on Thursday around 9:00 am and we worked in the final report.
This is the last week of the DIMACS REU 2012. I work on the report of my project which Alassane and I submit on Thursday, July 26, 2012. I will continue to work in my project in order to try to see if I can improve the results by finding a partition where the two subgraphs could have approximately the same number of nodes?