This thesis explores GNNs, categorizing them into local and global approaches.
problem Understanding the convergence of global GNNs and connecting local and global approaches.
method Categorization of GNNs into local and global, study of Invariant Graph Networks, connecting local and global approaches, and using local MPNN for graph coarsening.
result Established a connection between local and global GNN approaches.
New graph kernel scales well with graph size and number, achieving state-of-the-art performance.
problem Graph kernels lose structure information when representing graphs.
method Proposes a positive-definite global alignment graph kernel using random features and random graph embeddings.
result Achieves quasi-linear scalability with respect to graph size and number.
Graph products inherit Morse local-to-global property from their components.
problem Generalizing local-to-global property to graph products of infinite groups.
method Generalizing maximization procedure for relatively hierarchically hyperbolic groups and showing stable embeddings.
result Graph products of infinite Morse local-to-global groups have the Morse local-to-global property.
Model forecasts global stock market volatility using dynamic graphs and all trading days.
problem Enhance forecasting accuracy and practical utility in global stock market volatility.
method Spatial-temporal graph neural network architecture to capture volatility spillover effect.
result Forecasting performance surpasses baseline models in all scenarios.
Global graph structure improves GNN performance.
problem Limited graph structure in GNNs leads to indistinguishable node embeddings.
method Empirically tested the impact of global graph information on GNN performance.
result Global information can significantly improve GNN performance by more than 5%.
Graph Signal Processing improves stock market volatility forecasting.
problem Forecasting realized volatility in a global stock market context.
method Integrating Graph Signal Processing into the HAR model.
result The proposed model outperforms HAR-type benchmarks.
Graph neural networks (GNNs) have shown great power in learning on attributed graphs. However, it is still a challenge for GNNs to utilize information faraway from the source node. Moreover, general GNNs require graph attributes as input, so they cannot be appled to plain graphs. In the paper, we propose new models nam…
COMRECGC finds common recourse for global counterfactual explanations in GNNs.
problem Finding common recourse for global counterfactual explanations in GNNs.
method Formalized the common recourse explanation problem and designed COMRECGC algorithm.
result COMRECGC outperforms strong baselines on four real-world graph datasets.
New spectral conditions ensure graph rigidity and global rigidity in the Euclidean plane.
problem Ensuring graph rigidity and global rigidity in the Euclidean plane.
method Improving algebraic connectivity bounds for graph rigidity and global rigidity.
result Every 6-connected graph is rigid and globally rigid if its algebraic connectivity exceeds specific thresholds.
This paper learns graph node representations using global context prediction.
problem Efficiently learning useful node representations from unlabeled graph data.
method Randomly selects node pairs, trains a neural net to predict contextual positions.
result Our approach outperforms many unsupervised methods and sometimes supervised ones.
The monitoring of large dynamic networks is a major chal- lenge for a wide range of application. The complexity stems from properties of the underlying graphs, in which slight local changes can lead to sizable variations of global prop- erties, e.g., under certain conditions, a single link cut that may be overlooked du…
Poisson learning doesn't solve graph semi-supervised learning issues.
problem Global information loss in graph-based semi-supervised learning.
method Poisson learning is Laplace regularization with thresholding.
result Poisson learning cannot overcome the global information loss problem.
Deep learning predicts drug prescriptions across global health records.
problem Predicting drug prescriptions in chronic disease patients.
method Adaptive cross-global attention graph kernel network with support vector machine.
result Model outperforms current methods in accuracy and interpretability.
We introduce and study the conical curvature-dimension condition, CCD(K,N), for graphs. We show that CCD(K,N) provides necessary and sufficient conditions for the underlying graph to satisfy a sharp global Poincaré inequality which in turn translates to a sharp lower bound for the first eigenvalues of these graphs.…
Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take global graph propertiesinto account may not scale well to large graph databases.…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by m-separation on such graphs are compositional graphoids. We focus in particular on the subclass of rib…
Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs. In general, the gradient estimate in the present paper is independent of our previous one. As applications, i…
We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains λ-Scale calculus, therefore in particular untyped lambda calculus. Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.
Paper proposes G-CRD to improve GNNs by preserving global graph topology.
problem Improving lightweight GNNs for robust performance on large-scale real-world graphs.
method Introduces Graph Contrastive Representation Distillation (G-CRD) using contrastive learning.
result G-CRD consistently boosts GNN performance and robustness, outperforming existing methods.
Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…
We present an equivalent criterion for the global existence of Euler's multiplier for an integrable one-form taking into account the corresponding codim-1-foliation. In particular, the impact of inseparable leaves is considered. Here, we suppose that the foliation can be reduced to a graph; we also discuss obstructions…
Quantum computing improves graph neural network aggregation.
problem Limitations of classical GNNs in processing global graph features.
method Quantum computer-generated aggregation weights for graph neural networks.
result Quantum-enhanced GNN performs similarly to classical models on standard datasets.
Graph cuts find global optima for Potts models in slight perturbations.
problem Finding optimal solutions in Potts models with graph cuts.
method α-expansion algorithm for MAP inference, with certification for perturbations.
result All local minima are global minima in slight perturbations, and solutions are close to original.
Paper presents a novel approach for global feature aggregation in Graph Neural Networks.
problem Graphs lack a straightforward way to perform non-local feature aggregation like images and texts.
method Utilizes Latent Fixed Data Structure (LFDS) to aggregate feature vectors from local extraction.
result Proposed methods achieve competitive or better results with linear computational complexity.
Study shows how discrete graph curvature relates to manifold curvature.
problem Relating discrete graph curvature to intrinsic manifold curvature.
method Continuum limits of Ollivier's Ricci curvature on data clouds.
result Random geometric graphs inherit global curvature properties of manifolds.
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density function over a measurable space. Furthermore, we analyze the connection between th…
Study neural architectures on learned latent graphs using Schrödinger dynamics.
problem Understanding neural architectures on learned latent graphs.
method Optimizes over stratified moduli space of weighted graphs with Kähler-Hessian metric.
result Multilayer stationary networks are equivalent to global stationary problems on supra-graphs.
This paper improves GNNs' generalization by adding a Low-Rank Global Attention module.
problem Improving the generalization power of Graph Neural Networks (GNNs).
method Incorporating a Low-Rank Global Attention (LRGA) module into GNNs.
result Augmenting GNNs with LRGA aligns them with a powerful graph isomorphism test, 2-Folklore Weisfeiler-Lehman (2-FWL).
Graph embedding method captures both local and global network structure.
problem Representing and analyzing complex graph networks.
method Spectral embedding based on a generalized graph Laplacian.
result Significant improvement in data analysis tasks.
Graph neural networks help assess how global changes affect plant-pollinator networks.
problem Interpreting GNN results to understand how global changes impact plant-pollinator networks.
method Simulation study and application on Spipoll dataset to assess effects of global changes on pollination networks.
result GNNs can detect interactive effects between covariates and plant genera on pollination network connectivity.
Study detects anomalies in financial markets using GNN and nonextensive entropy.
problem Detecting anomalies in global financial markets with many correlated assets.
method Used Graph Neural Networks (GNN) with nonextensive entropy to measure uncertainty.
result Anomalies are statistically different for nonextensive entropy parameters before, during, and after a crisis.
Structure inference is an important task for network data processing and analysis in data science. In recent years, quite a few approaches have been developed to learn the graph structure underlying a set of observations captured in a data space. Although real-world data is often acquired in settings where relationship…
We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than 2π along a time-like graph Γ. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient …
We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in score or rating-based cardinal data. From raw ranking data, we construc…
A new method detects financial fraud using graph transformers.
problem Detecting fraudulent transactions in financial data.
method Spatial-Temporal-Aware Graph Transformer (STA-GT) integrating GNNs and transformers.
result STA-GT outperforms general GNN models on financial fraud detection.
GNNRank uses neural networks to learn global rankings from competition match data.
problem Learning global rankings from pairwise comparisons in directed graphs.
method Proposes GNNRank, a trainable GNN-based framework with digraph embedding and new objectives.
result GNNRank achieves competitive and superior performance compared to baselines.
CTGCN learns dynamic graph embeddings preserving both local and global graph structure.
problem Learning node representations for evolving graphs while preserving both local and global graph structure.
method CTGCN uses k-core based temporal graph convolutional network to learn dynamic graph embeddings.
result CTGCN outperforms existing methods in link prediction and structural role classification.
A new framework for knowledge graph embedding using sheaves.
problem Learning representations for entities and relations in knowledge graphs.
method Using cellular sheaves to describe knowledge graph embeddings with consistency constraints.
result A generalized framework for reasoning about knowledge graph embedding models.
We describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce another object, relating t…
We study two global structural properties of a graph Γ, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erdös--Rényi random graph model G(n,p), proving a sharp threshold for a random graph to have the AS property asymptotically almost surely, and giving f…
Semi-supervised learning on graph structured data has received significant attention with the recent introduction of Graph Convolution Networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian regularization framework, GCNs perform an implicit Laplacian type regularization to …
MaGNet integrates local and global graph information for interpretable results.
problem Lack of interpretability and inability to learn varying-order representations in GNNs.
method Model-agnostic Graph Neural Network (MaGNet) framework integrating estimation and interpretation models.
result MaGNet effectively integrates information of various orders and provides meaningful, interpretable results.
The paper investigates how Global Self-attention improves GCNs.
problem Improving expressive power and addressing overfitting in GCNs.
method Applying Global Self-attention mechanism over graph features.
result GSA mechanism enhances expressive power and mitigates overfitting and over-smoothing in GCNs.
New research shows hyperbolic embeddings are useful for global consistency tasks in graphs.
problem The usefulness of hyperbolic representations in graph learning tasks.
method Computed hyperbolic embeddings for node classification and link prediction tasks, addressing optimization issues at zero curvature.
result Hyperbolic embeddings are more effective for tasks requiring global consistency, while Euclidean models are superior for other tasks.
The paper solves curvature problems on graphs using a special flow.
problem Solving curvature problems on finite graphs.
method Defined the Calabi flow for a specific curvature type and established its global existence and convergence.
result The solution to the Calabi flow exists globally and converges under certain conditions.
A reinforcement learning algorithm improves graph construction for robustness.
problem Improving graph construction for specific objectives.
method Reinforcement learning and graph neural networks.
result The approach outperforms existing methods in robustness.
Develops a novel global pooling framework using optimal transport.
problem Sub-optimal performance in global pooling operations.
method Regularized Optimal Transport (ROT) for generalized global pooling.
result ROTP layers can improve performance in various machine learning scenarios.
Proposes MGMN for end-to-end graph similarity learning.
problem Lack of cross-level interactions in graph similarity learning.
method Multi-level graph matching network (MGMN) combining node-graph matching and siamese graph neural networks.
result MGMN outperforms state-of-the-art models on graph-graph classification and regression tasks.