D-GRIL: End-to-End Topological Learning with 2-parameter Persistence

TL;DR

This paper introduces D-GRIL, an end-to-end topological learning framework utilizing 2-parameter persistence and the GRIL vectorization technique, demonstrating its effectiveness on graph datasets and bio-activity prediction tasks.

Contribution

It extends topological learning from 1-parameter to 2-parameter persistence by developing the D-GRIL method with a solid theoretical foundation.

Findings

D-GRIL successfully learns bifiltration functions on benchmark graph datasets.

The framework improves bio-activity prediction accuracy in drug discovery.

Theoretical differentiation of GRIL enhances understanding of 2-parameter persistence applications.

Abstract

End-to-end topological learning using 1-parameter persistence is well-known. We show that the framework can be enhanced using 2-parameter persistence by adopting a recently introduced 2-parameter persistence based vectorization technique called GRIL. We establish a theoretical foundation of differentiating GRIL producing D-GRIL. We show that D-GRIL can be used to learn a bifiltration function on standard benchmark graph datasets. Further, we exhibit that this framework can be applied in the context of bio-activity prediction in drug discovery.