Research

My research focuses on machine learning, signal processing, and network science, with an emphasis on learning over graphs and manifolds. I explore the theoretical foundations and practical implementations of scalable algorithms for large, non-Euclidean datasets. My work is organized into the following areas:

Graphon Signal Processing and Transferability

I investigate signal processing and learning on graphons, which can be thought as both limits of very large graphs and graph generative models. By modeling large graphs as samples from graphons, my work formalizes the transferability of graph neural networks (GNNs) by analyzing their continuity on convergent graph sequences. This includes early formulations of graphon signal processing and the development of graphon neural networks for efficient learning of transferable GNN models for large graphs. Most of this work was done together with my dear collaborator Prof. Luiz Chamon.

GNN transferability pipeline

Key publications:

Manifold Signal Processing and Manifold Neural Networks

With my dear collaborator Dr. Zhiyang Wang, I also study signal processing on manifolds, which can be seen as the limit objcts geometric graphs. This includes defining convolutional filters on submanifolds of Euclidean space, studying their stability, and developing manifold neural networks. Applications range from image classification on image manifolds to geometric machine learning on “any-data” manifolds motivated by the manifold hypothesis.

Example of a data manifold for image classification

Key publications: