Graph neural network learns graph distances effectively.
problem Maintaining graph distance metric properties.
method GRAPH-BERT based semi-supervised distance metric learning.
result GB-DISTANCE outperforms existing methods.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
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48 results for “metric graph”
Two metrics on graph spaces compared to Weil-Petersson.
problem Comparing metrics on graph spaces.
method Two Riemannian metrics on a moduli space of metric graphs.
result Comparison of geometric features with Weil-Petersson metric.
The aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and explicitly allow infinite graphs. Motivated by the general form of a Laplacian on …
The study combines graph-minors and metric spaces, answering some questions and conjectures.
problem Whether geodesic metric spaces without a fat minor are quasi-isometric to graphs without minor.
method Combining graph-minors and coarse geometry, answering affirmatively for small .
result Affirmative answer for small in the problem statement.
Graph kernels for metric graphs using tropical algebra.
problem Comparing graphs representing different metric spaces.
method Purely based on geometry and topology, invariant under edge subdivision.
result Capture complementary geometric and topological information.
No Einstein metrics found on extended graph 4-manifolds.
problem Finding Einstein metrics on extended graph 4-manifolds.
method Defined and analyzed extended graph 4-manifolds as per [FLS15].
result Extended graph 4-manifolds do not support Einstein metrics.
Paper studies metric ribbon graphs and provides a recursion for their volumes.
problem Calculating volumes of combinatorial moduli spaces of directed metric ribbon graphs.
method Decomposes directed ribbon graphs into simpler graphs with one vertex, proving a canonical recursion scheme for volumes.
result Explicit recursion for volumes of four-valent metric ribbon graphs provided.
New metrics improve uncertainty estimation on graph data.
problem Current GNNs focus only on nodewise scores, limiting uncertainty estimation.
method Proposed edgewise metrics for uncertainty estimation on graphs.
result GNN models with structured prediction perform better in uncertainty estimation.
New transportation metric for graph data outperforms existing methods.
problem Computing distances between structured objects like graphs.
method Fused Gromov-Wasserstein (FGW) metric that considers both structure and features.
result FGW outperforms graph kernels and deep graph networks in graph classification.
GRNF embeds graphs into vectors preserving distances.
problem Representing graph data in a vector space while preserving distances.
method Graph Random Neural Features (GRNF) using graph neural networks.
result GRNF preserves graph metric structure and distances.
New metric assesses hierarchical clustering quality.
problem Evaluate the quality of hierarchical graph clustering.
method Proposes a novel metric based on dendrogram reconstruction.
result Optimal graph representation leads to regular dendrograms.
PolyGraph Discrepancy improves graph generative model evaluation.
problem Inability of existing metrics to provide an absolute performance measure and comparability across different graph descriptors.
method Approximates Jensen-Shannon distance using binary classifiers trained to distinguish between real and generated graphs.
result PGD provides a more robust and insightful evaluation compared to MMD metrics.
Graph comparison ties to Alexandrov's theorems.
problem Graph comparison conditions on metric spaces.
method Proof of Alexandrov's implications from graph comparisons.
result Complete description of graphs with trivial comparisons.
A new metric assesses causal graphs using node permutations to detect inconsistencies.
problem Quantifying the goodness of causal graphs and distinguishing them from random graphs.
method Constructing a baseline through node permutations and comparing inconsistencies.
result The proposed metric can distinguish between true and wrong causal graphs.
Generative modeling on metric graphs using neural optimal transport
problem Deep generative modeling for continuous probability distributions on metric graphs
method Embedding graph into smooth ambient space, solving entropic Kantorovich problem, projecting back onto graph
result Generator is graph-supported
Subgraph Entropymath.GT
Metric graphs have subgraphs with entropy at least λ.
problem Finding subgraphs with high entropy in metric graphs.
method Proving existence of subgraphs with entropy at least λ for graphs of rank r with entropy 1.
result Metric graphs have subgraphs with entropy at least λ.
New definition of naturally reductive Finsler manifolds using geodesic graphs.
problem Defining naturally reductive Finsler manifolds using geodesic graphs.
method Proposed a new geometrical definition using geodesic graphs and constructed examples of Finsler metrics.
result Explicit examples of Finsler naturally reductive metrics constructed.
The paper extends graph metrics to include new points and distances.
problem Extending graph metrics to include new points and distances.
method Proves properties of floppy graph metrics and introduces new metrics.
result For certain conditions, adding new points and distances results in a full metric.
Nonexistence results for semilinear parabolic and hyperbolic inequalities on metric graphs
problem Nonexistence of solutions to semilinear parabolic and hyperbolic inequalities on metric graphs
method Construction of a new pseudo-metric and space-time test functions
result All solutions must be identically zero
A new metric based on hitting probabilities for directed graphs and Markov chains.
problem Lack of metrics specifically adapted to asymmetric structure of directed graphs and Markov chains.
method Metric based on hitting probabilities, insensitive to shortest and average walk distances.
result New structural theory of directed graphs and utility for various applications.
Machine learning predicts graph layouts and metrics.
problem Selecting a good graph layout method is subjective and computationally expensive.
method Uses graph kernels to compute topological similarity and estimate layout aesthetics.
result Estimation is faster and more accurate than actual layout calculations.
Graph Laplace operators uniquely identify metrics and densities on manifolds.
problem Identifying Riemannian metrics and sampling densities from graph Laplace operators.
method Analyzing intrinsic and extrinsic graph Laplace operators on compact Riemannian manifolds.
result Graph Laplace operators uniquely determine metrics and densities under certain conditions.
The paper compares PINN methods for solving drift-diffusion equations on metric graphs.
problem Solving drift-diffusion equations on metric graphs using machine learning.
method Comparison of physics-informed neural networks (PINNs) for solving drift-diffusion equations on metric graphs.
result PINNs offer a flexible and versatile tool for solving parameter identification or optimization problems on metric graphs.
Incomplete pressure metric on bordered surface Teichmüller space proved.
problem Incompleteness of pressure metric on Teichmüller space of bordered surfaces.
method Using moduli space of metric graphs and fat graphs associated to bordered surfaces.
result Pressure metric is not a constant multiple of Weil-Petersson metric.
IGML learns discriminative metrics for graph classification.
problem Defining an appropriate distance metric for graph data.
method Supervised distance metric learning in a subgraph-based feature space with sparsity-inducing penalty.
result IGML identifies important subgraphs for graph classification.
Develops new metrics for graph similarity based on random walks.
problem Defining similarity between vertices in unweighted graphs.
method Random walks and stochastic calculus on graphs.
result Laplace transformed hitting time (LTHT) is a robust alternative to expected hitting time.
GWCA analyzes cross-graph correlations for movie retrieval.
problem Cross heterogeneous graph comparison in movie retrieval.
method Spectral graph filtering, Wasserstein metric learning, generalized eigenvalue decomposition.
result Surprise consistency in learning processes and closed-form solution.
New method uses contrastively trained GNNs for more reliable graph model evaluation.
problem Need effective methods to evaluate Graph Generative Models.
method Use representations from contrastively trained Graph Neural Networks (GNNs) for evaluation.
result Contrastively trained GNNs provide more reliable evaluation metrics than traditional or GNN-based approaches.
Paper proves no nontrivial solutions to certain elliptic equations on graphs.
problem Proving nonexistence of solutions to semilinear elliptic equations on metric graphs.
method Constructed a modified distance function and introduced test functions to show nonexistence under volume growth conditions.
result No nontrivial solutions exist for the equations under suitable conditions.
GSimCNN predicts graph similarity using CNNs, outperforming existing methods.
problem Challenging pairwise graph similarity computation due to NP-hardness.
method Graph Edit Distance (GED) as core metric, GSimCNN (Convolutional Neural Networks).
result State-of-the-art performance on graph similarity search.
Graph ConvNet improves classification by leveraging label graph structure.
problem Ignoring label graph structure in multi-class classification leads to suboptimal performance.
method Proposes a GCN-based neural network classifier that incorporates the graph structure of labels.
result The proposed model outperforms baseline methods in terms of graph-theoretic metrics.
Metrics for quandlesmath.GT
Study metrics on quandles, a knot theory algebraic system.
problem Investigate metrics on quandles, a knot theory algebraic system.
method Investigate graph structures and metric spaces induced by the actions of the inner and displacement groups on quandles.
result Show that the metric space associated with the displacement group for generalized Alexander quandles is quasi-isometric to the displacement group with a word metric.
Graph scattering transforms are stable to metric perturbations of network topology.
problem Stability of graph data representations under metric perturbations.
method Extending scattering transforms to network data using multiresolution graph wavelets and graph convolutions.
result Graph scattering transforms are stable to metric perturbations of the underlying network topology.
The paper proves that certain spaces are injective and Helly graphs.
problem Understanding the structure of certain geometric and algebraic spaces.
method Building Helly graphs and injective metric spaces from lattices.
result The natural piecewise metric on Euclidean buildings and Deligne complexes is injective.
Geodesic graphs for special Finsler metrics on spheres are studied.
problem Characterizing geodesic orbit Finsler metrics on spheres.
method Explicit constructions and group extensions.
result Not all projective spaces admit invariant Finsler metrics.
Extends canonical measures to metric graphs and proves a generalized Kazhdan's theorem.
problem Understanding limiting measures on metric graphs and their relation to hyperbolic measures.
method Introducing hyperbolic measures on universal covers of metric graphs and proving a generalized Kazhdan's theorem.
result All limiting measures on metric graphs satisfy a Gauss-Bonnet formula, interpreted as a trace formula.
This paper tightens the generalization error bound for graph embedding in non-Euclidean spaces.
problem High generalization error in non-Euclidean graph embedding, preventing practical applications.
method Novel upper bound of graph embedding's generalization error using local Rademacher complexity.
result The new bound is tighter and faster, allowing better performance in non-Euclidean spaces.
Paper determines Assouad-Nagata dimension for all minor-closed metrics.
problem Understanding the Assouad-Nagata dimension of minor-closed metrics.
method Using edge-weighted graphs and edge-deletion/contraction to model minor-closed metrics, determining their Assouad-Nagata dimension.
result Determined the Assouad-Nagata dimension for every minor-closed metric.
Lecture notes on group actions on injective spaces and Helly graphs.
problem Understanding group actions on specific metric spaces.
method Review of injective metric spaces and Helly graphs, elementary properties, constructions, and exercises.
result Presentation of various constructions of injective metric spaces and Helly graphs with interesting group actions.
New centrality-based graph shift operators improve graph neural networks.
problem Improving graph neural networks by enhancing graph shift operators.
method Proposed Centrality Graph Shift Operators (CGSOs) using global centrality metrics.
result CGSOs lead to improved performance in graph neural networks on real-world datasets.
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
problem Graph learning methods can be limited by information from distant vertices and path length constraints.
method Proposes a Graph Kernel based on LCS similarity and Wasserstein distance in a novel metric space.
result The new kernel emphasizes comparisons between similar paths and reduces information loss.
Optimizes ground metric on graphs for evolving density models.
problem Optimizing ground metric for evolving density models.
method Adaptive ground metric learning constrained to geodesic distances on graphs.
result Efficiently learned geodesic distances align with observed density evolution.
This paper evaluates metrics for graph generative models, addressing common pitfalls.
problem Evaluating and comparing graph generative models effectively.
method Systematic evaluation of MMD, analysis of synthetic and real graphs, practical recommendations.
result MMD can be problematic; practical solutions are provided.
Graph CNNs adapt to varying graph structures for better performance.
problem Fixed graph structures limit the performance of Graph CNNs on real data.
method Adaptive graph learning and distance metric learning for efficient graph construction.
result Adaptive Graph CNNs improve convergence speed and predictive accuracy on various graph datasets.
Application of Support Vector Machine Modeling and Graph Theory Metrics for Disease Classificationstat.ML
SVM with graph metrics improves diabetes prediction.
problem Improving disease classification accuracy using machine learning.
method Combining SVM modeling with graph theory metrics for disease prediction.
result SVM with graph metrics outperformed without, achieving ROC index of 75.6.
Surjectivity of Cannon-Thurston map proven for metric graph bundles.
problem Proving surjectivity of Cannon-Thurston map in metric graph bundles.
method Generalized Mj-Sardar's result to include more types of fibers.
result Continuous extension map between boundaries is surjective.
Develops framework for Bakry-Emery estimate on Dirichlet spaces.
problem Lack of Ricci curvature lower bounds in metric graphs.
method General framework on Dirichlet spaces for weak Bakry-Emery estimate.
result Establishes estimate in metric graphs where traditional curvature bounds are not applicable.
A new metric learning framework for signed graphs using Gershgorin disc alignment.
problem Learning Mahalanobis metrics from signed graphs efficiently.
method Proposes a fast metric learning framework using Gershgorin disc perfect alignment (GDPA) to circumvent full eigen-decomposition.
result Proves that Gershgorin disc left-ends of similarity transform are perfectly aligned at the smallest eigenvalue, enabling efficient optimization.