D-GRIL: End-to-End Topological Learning with 2-parameter Persistence
This work provides an incremental improvement for researchers in topological data analysis and drug discovery by extending existing persistence methods to 2-parameters.
The paper tackles the problem of enhancing end-to-end topological learning by extending it from 1-parameter to 2-parameter persistence using a vectorization technique called GRIL, resulting in D-GRIL which is applied to learn bifiltration functions on graph datasets and bio-activity prediction in drug discovery.
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.