A Bayesian Framework for Persistent Homology

Maroulas, Vasileios; Nasrin, Farzana; Oballe, Christopher

doi:10.1137/19m1268719

Cited by 32 publications

(31 citation statements)

References 56 publications

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“…First, the molecular homological features, which measure the connectedness, proximity, and the empty space among the atoms, are computed and stored. These homological features are summarized in a persistence diagram (PD) [46][47][48][49][50][51][52][53][54][55][56][57][58] . A PD encodes molecular features such as bonds and rings.…”

Section: Resultsmentioning

confidence: 99%

Representation of molecular structures with persistent homology for machine learning applications in chemistry

et al. 2020

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Machine learning and high-throughput computational screening have been valuable tools in accelerated first-principles screening for the discovery of the next generation of functionalized molecules and materials. The application of machine learning for chemical applications requires the conversion of molecular structures to a machine-readable format known as a molecular representation. The choice of such representations impacts the performance and outcomes of chemical machine learning methods. Herein, we present a new concise molecular representation derived from persistent homology, an applied branch of mathematics. We have demonstrated its applicability in a high-throughput computational screening of a large molecular database (GDB-9) with more than 133,000 organic molecules. Our target is to identify novel molecules that selectively interact with CO 2. The methodology and performance of the novel molecular fingerprinting method is presented and the new chemicallydriven persistence image representation is used to screen the GDB-9 database to suggest molecules and/or functional groups with enhanced properties.

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Section: Resultsmentioning

confidence: 99%

Representation of molecular structures with persistent homology for machine learning applications in chemistry

et al. 2020

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“…These homological features are summarized in a persistence diagram (PD). [60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78] A PD encodes molecular features such as bonds and rings. The PDs can then be vectorized into a persistence image 79 (PI) for use as a molecular representation.…”

Section: Methodsmentioning

confidence: 99%

Representation of Molecular Structures with Persistent Homology Leads to the Discovery of Molecular Groups with Enhanced CO2 Binding

Townsend¹,

Micucci²,

Hymel³

et al. 2020

Preprint

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<p>Developing alternative strategies for efficient separation of CO2 and N2 is of general interest for the reduction of anthropogenic carbon emissions. In recent years, machine learning and high-throughput computational screening have been valuable tools in accelerated first-principles screening for the discovery of the next generation of functionalized molecules and materials. The application of machine learning for chemical applications requires the conversion of molecular structures to a machine-readable format known as a molecular representation. The choice of such representations impacts the performance and outcomes of chemical machine learning methods. Herein, we present a new concise and size-consistent molecular representation derived from persistent homology,an applied branch of mathematics. We have demonstrated its applicability in a high-throughput computational screening of a large molecular database (GDB-9) with more than 133,000 organic molecules. Our target is to identify novel molecules that selectively interact with CO2. The methodology and performance of the novel molecular fingerprinting method is presented and the new chemically-driven persistence image representation is used to screen the GDB-9 database to suggest molecules and/or functional groups with enhanced properties.</p>

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“…2 (b) and (c) as yellow regions. Posterior: With the above model characterization, the posterior intensity which explicitly show the update of the prior has the following form [22]:…”

Section: The Bayesian Modelmentioning

confidence: 99%

“…where C x|y , µ x|y and σ x|y are weights, mean and variance of the posterior intensity respectively, corresponding to the second part of (1), and these are pertinent updates of the prior parameters [22].…”

Section: A Conjugate Family Of Priors For Eeg Signalsmentioning

confidence: 99%

Bayesian Topological Learning for Brain State Classification

Nasrin¹,

Oballe²,

Boothe

et al. 2019

2019 18th IEEE International Conference on Machine Learning and Applications (ICMLA)

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Investigation of human brain states through electroencephalograph (EEG) signals is a crucial step in humanmachine communications. However, classifying and analyzing EEG signals are challenging due to their noisy, nonlinear and nonstationary nature. Current methodologies for analyzing these signals often fall short because they have several regularity assumptions baked in. This work provides an effective, flexible and noise-resilient scheme to analyze EEG by extracting pertinent information while abiding by the 3N (noisy, nonlinear and nonstationary) nature of data. We implement a topological tool, namely persistent homology, that tracks the evolution of topological features over time intervals and incorporates individual's expectations as prior knowledge by means of a Bayesian framework to compute posterior distributions. Relying on these posterior distributions, we apply Bayes factor classification to noisy EEG measurements. The performance of this Bayesian classification scheme is then compared with other existing methods for EEG signals.

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A Bayesian Framework for Persistent Homology

Cited by 32 publications

References 56 publications

Representation of molecular structures with persistent homology for machine learning applications in chemistry

Representation of molecular structures with persistent homology for machine learning applications in chemistry

Representation of Molecular Structures with Persistent Homology Leads to the Discovery of Molecular Groups with Enhanced CO2 Binding

Bayesian Topological Learning for Brain State Classification

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