Instability of the Betti Sequence for Persistent Homology and a Stabilized Version of the Betti Sequence

Johnson, Megan; Jung, Jaehun

doi:10.48550/arxiv.2109.09218

Cited by 1 publication

(1 citation statement)

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“…If a given vectorization φ holds such a stability inequality for some d and , we call φ a stable vectorization [7]. Persistence Landscapes [13], Persistence Images [3], Stabilized Betti Curves [48] and several Persistence curves [25] are among well-known examples of stable vectorizations. Now, we are ready to prove the stability of MP Fingerprints given in Section 4.1 Let and be two graphs. Let φ be a stable SP vectorization with the stability equation for some 1 ≤ p φ ≤ ∞.…”

Section: Figurementioning

confidence: 99%

ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery

Demir

Coskunuzer²,

Segovia-Domínguez

et al. 2022

Preprint

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In computer-aided drug discovery (CADD), virtual screening (VS) is used for identifying the drug candidates that are most likely to bind to a molecular target in a large library of compounds. Most VS methods to date have focused on using canonical compound representations (e.g., SMILES strings, Morgan fingerprints) or generating alternative fingerprints of the compounds by training progressively more complex variational autoencoders (VAEs) and graph neural networks (GNNs). Although VAEs and GNNs led to significant improvements in VS performance, these methods suffer from reduced performance when scaling to large virtual compound datasets. The performance of these methods has shown only incremental improvements in the past few years. To address this problem, we developed a novel method using multiparameter persistence (MP) homology that produces topological fingerprints of the compounds as multidimensional vectors. Our primary contribution is framing the VS process as a new topology-based graph ranking problem by partitioning a compound into chemical substructures informed by the periodic properties of its atoms and extracting their persistent homology features at multiple resolution levels. We show that the margin loss fine-tuning of pretrained Triplet networks attains highly competitive results in differentiating between compounds in the embedding space and ranking their likelihood of becoming effective drug candidates. We further establish theoretical guarantees for the stability properties of our proposed MP signatures, and demonstrate that our models, enhanced by the MP signatures, outperform state-of-the-art methods on benchmark datasets by a wide and highly statistically significant margin (e.g., 93% gain for Cleves-Jain and 54% gain for DUD-E Diverse dataset).

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