## Student Applied Math Seminar

•  Remy Liu, MSU
•  Understanding dataset characteristics via diffusion on graph
•  09/26/2022
•  1:00 PM - 2:00 PM
•  C117 Wells Hall (Virtual Meeting Link)
•  Craig Gross (grosscra@msu.edu)

Classical graph signal processing provides powerful techniques for understanding and modifying graph signals from the spectral domain, but they come with high computational costs. More recently, diffusion on graphs has been sought as an alternative approach to modifying graph signals; it is much more computationally efficient and is easy to interpret from the spatial perspective. Here, we present two different studies utilizing diffusion wavelets on a graph to filter graph signals for downstream analysis. In the first study, we aim to understand how and what is being utilized by Graph Neural Networks to achieve graph-related tasks. We do so by observing the performance difference between using the filtered graph and the original graph. We demonstrate that some image datasets, such as CIFAR and MNIST, rely on low-frequency signals; on the contrary, heterophilic datasets, such as WebKB, rely more heavily on high-frequency signals. In the second study on computational biology using gene interaction networks and gene expression data, we observe similar results where different frequency bands perform differently in a task-specific manner. In summary, our studies demonstrate the practical usage of graph diffusion to modify graph signals, leading to improved downstream prediction performance and a better understanding of the graph datasets' characteristics. $\\$ This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

## Contact

Department of Mathematics
Michigan State University