The paper investigates why GNNs struggle to generalize from small to large graphs.
problem Challenges in graph neural networks' ability to generalize across different graph sizes.
method Identified and studied the effect of local structure on size generalization; proposed a novel SSL task.
result GNNs can converge to non-generalizing solutions when there is a discrepancy in local structure.
This work investigates how GCNs should handle local structure discrepancies in testing nodes.
problem GCNs assume homophily but real graphs often have discrepancies in local structure.
method Using causal graph analysis, the study intervenes the graph structure to assess the local structure's impact on predictions.
result The method effectively enhances GCN predictions by eliminating local structure discrepancies.
Estimates manifold dimension using local graph structure.
problem Estimating the intrinsic dimension of manifolds from data.
method Regression on local PCA coordinates, focusing on local graph structure.
result Proposed QE and TLS estimators outperform existing methods.
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.
The spatial convolution layer which is widely used in the Graph Neural Networks (GNNs) aggregates the feature vector of each node with the feature vectors of its neighboring nodes. The GNN is not aware of the locations of the nodes in the global structure of the graph and when the local structures corresponding to diff…
Localized signal representation on graph bundles using Fourier analysis.
problem Representing signals on graph bundles with twists.
method Partition of unity and product factorization over the base graph.
result Lifted bases for signal spaces of graph bundle components.
Proposes methods for local clustering in attributed graphs.
problem Finding a single cluster concentrated on a specific region in a graph.
method Introduces Graph Unimodality (GU) and Attribute Unimodality (AU) measures, and LOCLU algorithm to optimize Compactness score.
result Local cluster detected by LOCLU concentrates on the region of interest and exhibits unimodal data distribution.
Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to …
In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex grid structures, and define a new vertex convolution operation by adopting a set of…
A new framework explains GNN predictions by simulating graph structure and feature changes.
problem Lack of transparency in GNN predictions hinders understanding.
method TraP2 framework using a three-layer architecture: Translation, Perturbation, and Paraphrase layers.
result TraP2 achieves 10.2% higher explanation accuracy than state-of-the-art methods.
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.
Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node features and have been proven to improve the performance of many graph related tasks…
Paper proposes a new method for joint feature selection and graph learning.
problem Previous methods suffer from neglecting joint formulation and lack of graph learning.
method Formulates multi-view feature selection with orthogonal decomposition, incorporates cross-space locality preservation, and uses a unified objective function for simultaneous learning.
result Demonstrates superior performance in multi-view feature selection and graph learning tasks.
We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions.…
Proposes a new graph kernel framework using regularized Wasserstein distances.
problem Learning optimal transport distances for graph kernels.
method Introduces Regularized Wasserstein (RW) discrepancy with two regularization terms.
result Empirically validated method outperforms state-of-the-art methods.
GNNs may be limited by graph topology, affecting their learning outcomes.
problem Understanding how graph topology influences GNN behavior and performance.
method Investigating the interaction between local topological features and GNN message-passing schemes.
result Locally similar neighborhoods can lead to consistent node representations, affecting GNN performance.
Optimal Reeb graphs identified for polygon decomposition.
problem Investigating the topological structure of planar polygon decomposition.
method Using oriented Reeb graphs with a marked vertex for height functions.
result Described all possible optimal Reeb graphs for specific polygon configurations.
GraphSTONE uses topic models to capture graph structures, improving GCN performance.
problem GCNs focus too much on node features and not enough on graph structures.
method GraphSTONE employs topic models of graphs to capture structural topics, which guide the aggregation of node features.
result GraphSTONE outperforms GCNs in performance, efficiency, and interpretability.
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.
It is not until recently that graph neural networks (GNNs) are adopted to perform graph representation learning, among which, those based on the aggregation of features within the neighborhood of a node achieved great success. However, despite such achievements, GNNs illustrate defects in identifying some common struct…
Proposes SimPool for graph pooling using structural similarity features.
problem Challenges in graph pooling due to lack of spatial locality.
method Integrates structural similarity features with a revised pooling layer to propose SimPool.
result SimPool produces node cluster assignments resembling CNN's locality preserving pooling.
GraphLIME explains GNN models by selecting key features locally.
problem Explaining the effectiveness of GNN models is challenging due to complex nonlinear transformations.
method GraphLIME uses HSIC Lasso for nonlinear feature selection in GNN models.
result GraphLIME provides more descriptive explanations than existing methods.
CaLoNet integrates spatial and local correlations for multivariate time series classification.
problem Ignoring spatial and local correlations in multivariate time series classification.
method Model spatial correlations using causality modeling, extract local correlations, integrate into graph neural network.
result Competitive performance compared to state-of-the-art methods on UEA datasets.
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.
Learning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis and data mining. Recent GNN algorithms are based on neural message passing, which enables GNNs to integrate loc…
New graph convolution captures local features on non-Euclidean grids.
problem Capturing local features on irregular, coarse non-Euclidean grids.
method Low-rank learnable local filters in graph convolutions.
result Proves more expressive than previous spectral graph convolution methods.
A framework for federated graph classification over non-IID graphs.
problem Training graph mining models collaboratively across different domains with non-IID graphs.
method Graph Clusters Federated Learning (GCFL) framework, dynamically finding clusters based on GNN gradients, and a gradient sequence-based clustering mechanism (GCFL+).
result Demonstrated effectiveness of GCFL+ in reducing structure and feature heterogeneity among graphs.
New research limits what GNNs can compute and generalizes their performance.
problem Limits of GNNs in computing graph properties and generalization bounds.
method Novel graph-theoretic formalism and data-dependent generalization bounds.
result Proves GNNs can't compute certain graph properties and provides tighter generalization bounds.
Learning network representations is a fundamental task for many graph applications such as link prediction, node classification, graph clustering, and graph visualization. Many real-world networks are interpreted as dynamic networks and evolve over time. Most existing graph embedding algorithms were developed for stati…
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.
Sharp bounds on diameter and eigenvalues for amply regular graphs.
problem Finding bounds for amply regular graphs' diameter and eigenvalues.
method New ideas relating discrete Ricci curvature to local matching properties, including a novel construction of a regular bipartite graph.
result Sharp diameter and eigenvalue bounds for amply regular graphs.
New methods identify local clusters in graphs with few labels.
problem Identifying specific substructures in large graphs without additional structural information.
method Random sampling, diffusion, and overlap analysis of local clusters.
result Proves the correctness of the proposed methods and achieves state-of-the-art results.
Proposes a graph learning framework for clustering and semi-supervised classification.
problem Graph-based clustering and semi-supervised classification techniques have shown impressive performance but lack explicit cluster structure.
method Uses self-expressiveness of samples for global structure and adaptive neighbor approach for local structure. Incorporates rank constraint to ensure optimal performance.
result The proposed method achieves better performance than state-of-the-art methods in clustering and semi-supervised classification.
Novel TRI-GNN framework improves graph classification robustness.
problem Graph neural networks suffer from over-smoothing and vulnerability to graph perturbations.
method Integrates higher-order graph information via persistent homology and local graph structure learning.
result TRI-GNN outperforms state-of-the-art baselines on node classification tasks.
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 …
Paper proposes LCP for structural encodings, outperforming existing methods.
problem Improving Graph Neural Networks performance through effective structural encodings.
method Geometric perspective, Local Curvature Profiles (LCP) for structural encodings, combining with global positional encodings, comparing with rewiring techniques.
result LCP significantly outperforms existing structural encodings and combining LCP with global positional encodings improves performance.
node2coords learns interpretable graph node representations robust to graph perturbations.
problem Need representations that capture graph structure and are robust to perturbations.
method Proposes a graph representation learning algorithm using Wasserstein barycenters.
result Learned representations are interpretable and stable to graph perturbations.
Symmetric TSP is structurally equivalent to a constrained Group Steiner Tree Problem.
problem Finding the shortest tour in a symmetric TSP.
method Structural equivalence between symmetric TSP and constrained Group Steiner Tree Problem.
result Maximizing net weight in the cGSTP is equivalent to minimizing the TSP tour length.
New method for estimating local structure around target nodes in DAGs.
problem Challenges in learning causal DAG structures in high-dimensional settings.
method Constraint-based method for estimating local structure around multiple target nodes.
result Consistency results for estimating local neighborhood structure of target nodes.
We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that a top-down sensing procedure can identify these partitions, and hence the activa…
In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation o…
We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the pres…
We call a singularity of a presymplectic form ω removable in its graph if its graph extends to a smooth Dirac structure over the singularity. An example for this is the symplectic form of a magnetic monopole. A criterion for the removability of singularities is given in terms of regularizing functions for pure spinor…
Enhances graph neural networks with structural message-passing for better generalization.
problem Limited representation power and inability to learn basic graph topological properties.
method Proposes a framework that includes a one-hot encoding of nodes and parametrized message and update functions ensuring permutation equivariance.
result Achieves state-of-the-art results on molecular graph regression on the ZINC dataset.
Proposes a method to identify causal relationships using background knowledge.
problem Identifying causal relationships in the presence of background knowledge.
method Learning local structure using all types of causal background knowledge (direct, non-ancestral, ancestral). Criteria for identifying causal relationships based on local structure.
result Effective and efficient method for local structure learning and causal relationship identification.
Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query…
A new hybrid GNN framework tackles oversmoothing in graph data.
problem Oversmoothing in graph convolutional networks limits their expressive power and generalization.
method Combines traditional GCN filters with band-pass filters defined via geometric scattering and introduces an attention framework.
result Improves expressive power and generalization of graph convolutional networks.
We extend Jendrol' and Skupień's results about the local structure of maps on the 2-sphere: In this paper we show that if a polyhedral map G on a surface $\M$ of Euler characteristic $χ(\M) \le 0$ has more than $126|χ(\M)|$ vertices, then G has a vertex with "nearly" non-negative combinatorial curvature. As a corol…