Graph-Informed Neural Networks for Regressions on Graph-Structured Data

Berrone, Stefano; Santa, Francesco Della; Mastropietro, Antonio; Pieraccini, Sandra; Vaccarino, Francesco

doi:10.3390/math10050786

Cited by 7 publications

(3 citation statements)

References 45 publications

(62 reference statements)

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“…Traditional methods to solve this problem are mostly based on graph Laplacian regularization [20,21]. Recently, GNNs have emerged as promising approaches for semisupervised node classification [22][23][24][25], which are briefly introduced below.…”

Section: Semi-supervised Node Classificationmentioning

confidence: 99%

Robust Graph Neural Networks via Ensemble Learning

Sun

et al. 2022

Mathematics

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Graph neural networks (GNNs) have demonstrated a remarkable ability in the task of semi-supervised node classification. However, most existing GNNs suffer from the nonrobustness issues, which poses a great challenge for applying GNNs into sensitive scenarios. Some researchers concentrate on constructing an ensemble model to mitigate the nonrobustness issues. Nevertheless, these methods ignore the interaction among base models, leading to similar graph representations. Moreover, due to the deterministic propagation applied in most existing GNNs, each node highly relies on its neighbors, leaving the nodes to be sensitive to perturbations. Therefore, in this paper, we propose a novel framework of graph ensemble learning based on knowledge passing (called GEL) to address the above issues. In order to achieve interaction, we consider the predictions of prior models as knowledge to obtain more reliable predictions. Moreover, we design a multilayer DropNode propagation strategy to reduce each node’s dependence on particular neighbors. This strategy also empowers each node to aggregate information from diverse neighbors, alleviating oversmoothing issues. We conduct experiments on three benchmark datasets, including Cora, Citeseer, and Pubmed. GEL outperforms GCN by more than 5% in terms of accuracy across all three datasets and also performs better than other state-of-the-art baselines. Extensive experimental results also show that the GEL alleviates the nonrobustness and oversmoothing issues.

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Section: Semi-supervised Node Classificationmentioning

confidence: 99%

Robust Graph Neural Networks via Ensemble Learning

Sun

et al. 2022

Mathematics

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“…Graph models 9 – 18 are arguably the most widely used tools for molecular representations in molecular dynamics simulation, coarse-grained models, elastic network models, QSAR/QSPR, graph neural networks, etc. In general, a molecule (or a molecular complex) is modeled as a graph with each vertex representing an atom, an amino acid, a domain, or an entire molecule, and edge representing covalent-bond, non-covalent-bond, or more general interaction.…”

Section: Introductionmentioning

confidence: 99%

Persistent Dirac for molecular representation

Wee

Bianconi

Xia

2023

Sci Rep

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Molecular representations are of fundamental importance for the modeling and analysing molecular systems. The successes in drug design and materials discovery have been greatly contributed by molecular representation models. In this paper, we present a computational framework for molecular representation that is mathematically rigorous and based on the persistent Dirac operator. The properties of the discrete weighted and unweighted Dirac matrix are systematically discussed, and the biological meanings of both homological and non-homological eigenvectors are studied. We also evaluate the impact of various weighting schemes on the weighted Dirac matrix. Additionally, a set of physical persistent attributes that characterize the persistence and variation of spectrum properties of Dirac matrices during a filtration process is proposed to be molecular fingerprints. Our persistent attributes are used to classify molecular configurations of nine different types of organic-inorganic halide perovskites. The combination of persistent attributes with gradient boosting tree model has achieved great success in molecular solvation free energy prediction. The results show that our model is effective in characterizing the molecular structures, demonstrating the power of our molecular representation and featurization approach.

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“…Graph models [9][10][11][12][13][14][15][16][17][18] are arguably the most widely used tools for molecular representations in molecular dynamics simulation, coarse-grained models, elastic network models, QSAR/QSPR, graph neural networks, etc. In general, a molecule (or a molecular complex) is modeled as a graph with each vertex representing an atom, an amino acid, a domain, or an entire molecule, and edge representing covalent-bond, non-covalent-bond, or more general interaction.…”

Section: Introductionmentioning

confidence: 99%

Persistent Dirac for molecular representation

Wee¹,

Bianconi²,

Xia³

2023

Preprint

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Molecular representations are of fundamental importance for the modeling and analysis of molecular systems. Representation models and in general approaches based on topological data analysis (TDA) have demonstrated great success in various steps of drug design and materials discovery.Here we develop a mathematically rigorous computational framework for molecular representation based on the persistent Dirac operator. The properties of the spectrum of the discrete weighted and unweighted Dirac matrices are systemically discussed and used to demonstrate the geometric and topological properties of both non-homology and homology eigenvectors of real molecular structures. This allows us to asses the influence of weighting schemes on the information encoded in the Dirac eigenspectrum. A series of physical persistent attributes, which characterize the spectrum of the Dirac matrices across a filtration, are proposed and used as efficient molecular fingerprints. Finally, our persistent Dirac-based model is used for clustering molecular configurations from nine types of organic-inorganic halide perovskites. We found that our model can cluster the structures very well, demonstrating the representation and featurization power of the current approach.

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Graph-Informed Neural Networks for Regressions on Graph-Structured Data

Cited by 7 publications

References 45 publications

Robust Graph Neural Networks via Ensemble Learning

Robust Graph Neural Networks via Ensemble Learning

Persistent Dirac for molecular representation

Persistent Dirac for molecular representation

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