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

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arxiv 2406.07100 v3 pith:Y7QYIXLI submitted 2024-06-11 cs.LG cs.AImath.AT

Soham Mukherjee , Shreyas N. Samaga , Cheng Xin , Steve Oudot , Tamal K. Dey This is my paper · ORCID
classification cs.LGcs.AImath.AT
keywords parameterpersistenced-grilend-to-endframeworkgrillearningtopological
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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.

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  1. Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent

    math.AT 2024-12 conditional novelty 7.0 of 10

    A gradient-descent method selects small sets of intervals that approximate full generalized persistence diagram domains, reducing computation time severalfold with comparable classification accuracy.

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