4 papers · 1 filter
Exact Topological Compliance: Generating Persistence-Equivalent Graphs
Mattie Ji, Indradyumna Roy, Vikas Garg
Persistent homology summarizes the topological evolution of a graph as persistence diagrams (PDs). Generating graphs whose topology matches a target descriptor is increasingly impo…
Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cells
Mattie Ji, Indradyumna Roy, Vikas Garg
Persistent homology (PH) encodes global information, such as cycles, and is thus increasingly integrated into graph neural networks (GNNs). PH methods in GNNs typically traverse an…
On topological descriptors for graph products
Mattie Ji, Amauri H. Souza, Vikas Garg
Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (bo…
Graph Persistence goes Spectral
Mattie Ji, Amauri H. Souza, Vikas Garg
Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hiera…