In this project the student will inquiries hypergraphs and generalizes the spectral graph theory to this setting. This project is well balanced between theory and application as the student will develop tools theoretically and use them in learning problems.
The students will start by defining a gradient operator on hypergraphs and his associated divergence. From this two operators, a Laplacian and a Fourier transform will emerge. From there, general filterbanks such as wavelets can be defined on hypergraphs. Tools like the TV-denoising will also be used.
As a second part, the student will implement his tool in Matlab with the help of the GSPBox. To test if this extension works better than other algorithm, a classification problem will be defined on different datasets including USPS.
This work might lead to a publication and is a soft introduction to the world of research.
What are you going to learn: Spectral graph theory, methodology
Theory: 4/5 Application: 4/5
Reading: Learning with Hypergraphs: Clustering, Classification, and Embedding