Enhances graph comparison by incorporating edge features using Fused Gromov-Wasserstein distance.
problem Graph distances overlook edge attributes, limiting their effectiveness.
method Introduced Fused Gromov-Wasserstein distance for graph comparison with edge features. Proposed algorithms for distance and barycenter computation.
result Empirically validated the effectiveness of the novel distance in graph learning tasks.
Estimates the first non-zero eigenvalue using Ricci curvature on graph edges.
problem Estimating the first non-zero eigenvalue of the Laplacian on graph edges.
method Defining edge distance, studying coarse Ricci curvature, and using Jost-Horak's Laplacian definition.
result Obtained an estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature for a regular graph.
SWRLDA improves LDA for multi-class classification with edge classes.
problem LDA's vulnerability to edge classes causing biased mean and large distances.
method Self-weighted robust LDA with l21-norm distance criterion.
result SWRLDA outperforms other methods on synthetic and real-world datasets.
The paper develops formulas for hyperbolic simplices based on edge lengths.
problem Understanding the geometry of hyperbolic simplices using only edge lengths.
method Develops geometric formulas for hyperbolic simplices based on edge lengths.
result Distance and projection formulas in hyperbolic simplices.
This note demonstrates how both the concept of distance and the concept of holonomy can be constructed from a suitable network with directed edges (and no lengths). The number of different edge types depends on the signature of the metric and the dimension of the holonomy group. If the holonomy group is of dimension on…
An efficient method to compute a single linkage dendrogram.
problem Computing a single linkage dendrogram efficiently.
method Form an edge-weighted graph, calculate MST, recursively split longest edge.
result Efficiently determine vertices of subtrees without additional cost.
HighwayGraph models long-distance node relations in GNNs with improved performance.
problem Limited-layer information propagation in GNNs hinders long-distance node relation modeling.
method Proposes two solutions: implicit and explicit modeling of long-distance node relations using shallow GNN architectures and a self-training framework.
result HighwayGraph achieves consistent and significant improvements over four GNNs on three benchmark datasets.
The complex of curves C(Sg) of a closed orientable surface of genus g≥2 is the simplicial complex having its vertices, C0(Sg), are isotopy classes of essential curves in Sg. Two vertices co-bound an edge of the 1-skeleton, C1(Sg), if there are disjoint representative…
New polyhedron example disproves Durer's conjecture.
problem Durer's conjecture on unfolding convex polyhedra.
method Constructing a specific polyhedron with pseudo-edge graph.
result Example polyhedron disproves conjecture.
New bounds for average graph distance using curvature and centrality.
problem Finding bounds for average graph distance.
method Using weighted average Ollivier curvature with edge betweenness centrality.
result Equality in bounds achieved for specific reflective graphs.
New curvature concept preserves graph distances under operations.
problem Preserving graph distances under graph operations.
method Characterization of distance matrix and its null space.
result Linear system Dx=1 may not have a solution. Study shows effective resistance distance yields more accurate network barycenter than Hamming distance.
problem Identifying the best metric for computing the Fréchet mean network.
method Compared the effectiveness of Hamming distance and effective resistance distance in capturing network topology.
result Effective resistance distance produces a more accurate Fréchet mean network.
Study calculates site-specific Gordian distances between graph embeddings.
problem Determining the minimal number of crossing changes between graph embeddings.
method Covering space theory for proofs.
result Site-specific Gordian distances between Milnor links and trivial links are determined.
A new discrete formula connects vertex and edge distributions on graphs.
problem Optimal transport on graphs with mixed vertex and edge distributions.
method Discrete transport equation and Benamou-Brenier formulation.
result Classification of all Wasserstein-1 geodesics on graphs.
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The technique is applied to intensity SAR d…
We calculate the Chern-Simons invariants of the twist knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of the twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present the concrete formulae and calc…
The ropelength of a space curve is usually defined as the quotient of its length by its thickness: the radius of the largest embedded tube around the knot. This idea was extended to space polygons by Eric Rawdon, who gave a definition of ropelength in terms of doubly-critical self-distances (local minima of the distanc…
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.
New model allows for high edge probability with nodes needing similarities in at least one area.
problem Overly restrictive Euclidean embedding for modern networks.
method Introduced Latent Channel Networks model and EM algorithm.
result Allows for high edge probability with nodes needing similarities in at least one area.
We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models. We show that the KL divergence is bounded below by a constant when the graphs differ by at least one edge; this is essentially the tighte…
Paper estimates non-causal graphical models using covariance extension and transportation distance.
problem Estimating non-causal graphical models with smoothing relations.
method Proposes a covariance extension problem and uses transportation distance to minimize error with white noise.
result Solution is a double-sided autoregressive non-causal graphical model.
Efficiently learns tree-structured Ising models with minimal samples.
problem Learning tree-structured Ising models efficiently and accurately.
method Plug-in estimator for mutual information using the Chow-Liu algorithm.
result Proper learning of tree-structured Ising models with O(nlnn/ε2) samples. This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The technique is applied to intensity Synthetic Apertur…
New distances for causal graphs improve evaluation of learned structures.
problem Difficulty in evaluating graphs learned by causal discovery algorithms.
method Developed a framework for causal distances, including new reachability algorithms.
result Improved distances are faster and more scalable than existing methods.
This paper introduces a new method for SAR imagery region discrimination using geodesic distances.
problem Region discrimination in monopolarized SAR imagery.
method Geodesic distance between GI0 models. result Advantages of using geodesic distance over stochastic distances.
Federated learning struggles with non-IID data, but a strategy improves model accuracy.
problem Federated learning accuracy drops significantly with non-IID data.
method Identified weight divergence as the cause, quantified by EMD, and proposed a solution of sharing a subset of globally shared data.
result Accuracy can be increased by 30% for CIFAR-10 with only 5% globally shared data.
New measures assess differences in causal graphs' separations.
problem Evaluating causal discovery algorithms' output.
method Proposes new distance measures capturing causal graphs' separations.
result Proposed distances assess differences in causal graphs' separations.
Enhances community detection in correlated networks with node attributes.
problem Community detection in multiple networks with correlated node attributes and edges.
method Introduced the correlated Contextual Stochastic Block Model (CSBM), developed a two-step matching procedure.
result Algorithm recovers exact node correspondence, enabling enhanced community detection.
A new SBM for non-negative zero-inflated edge weights in networks.
problem Modeling international trading networks with non-negative zero-inflated edge weights.
method Restricted Tweedie distribution and nodal information accounting.
result Efficient two-step algorithm for estimating covariate effects.
This paper approximates 1-Wasserstein distance using tree-based embedding.
problem Computational inefficiency of estimating 1-Wasserstein distance.
method L1-regularized approach to learn tree weights, using shortest path distance as a linear model.
result Tree-Wasserstein distance (TWD) approximates 1-Wasserstein distance efficiently.
The paper proves the existence of a unique circle packing on hyperbolic surfaces.
problem Proving the existence of a unique inversive distance circle packing on hyperbolic polyhedral surfaces.
method Deforming the surface by discrete Ricci flow, doing surgery by edge flipping, and using a variational principle of a convex Ricci potential.
result There exists a unique inversive distance circle packing that is discrete conformal to the original one.
Improved financial network predictability using LLM for edge filtering.
problem Spurious edges in financial networks from textual similarity.
method Two-stage framework: sparse candidate graph + LLM edge classification.
result LLM-based edge filtering improves Sharpe ratio and reduces drawdown.
This paper presents two approaches for filter design based on stochastic distances for intensity speckle reduction. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are used to compute the filtered value. The tests stem from stochastic divergences …
Topology helps estimate chromatic numbers of random graphs on spheres.
problem Estimating chromatic numbers of random graphs on spheres.
method Topology, specifically connectivity of Lóvasz's neighborhood complex.
result Connectivity bound is useful in dimensions 1 and 2, but generally poor.
Algorithm reconstructs vertex positions in random geometric graphs with improved accuracy.
problem Reconstructing vertex positions in random geometric graphs with high accuracy.
method Hybrid of graph distances and short-range estimates based on common neighbors.
result Algorithm reconstructs vertex positions with error of O(nβ), improving over previous results. New method distills cloud models into edge-friendly ones.
problem Cloud-to-edge model compression with limited data exchange.
method Two-step workflow of deprivatization and distillation.
result Outperforms previous state-of-the-art approaches on various benchmarks.
Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of dru…
Framework uses Minimax distances for unsupervised feature extraction.
problem Extracting features from unlabeled data.
method Develops a framework for computing Minimax distances and embedding them into a vector space.
result Minimax distances effectively capture underlying patterns and structures in data.
Graph attention improves node classification by distinguishing important edges.
problem Node classification in graph-based learning models.
method Theoretical analysis of graph attention networks for node classification.
result Graph attention can perfectly classify nodes in an 'easy' regime but fails in a 'hard' regime.
The paper proposes a method to learn representations from dendrograms.
problem Learning representations from dendrograms for machine learning applications.
method Develops a generalized framework for different distance measures and level functions, using embedding and aggregation techniques.
result Demonstrates the effectiveness of the method via numerical studies.
Improved molecular property prediction using updated neural message passing.
problem Predicting properties of molecules and materials accurately.
method Extended neural message passing model with edge update network.
result Superior prediction of formation energies and other properties on multiple datasets.
A new graph kernel uses Wasserstein distance for better graph comparison.
problem Graph kernels often discard valuable information and struggle with continuous attributes.
method Proposes a novel graph kernel using Wasserstein distance for node feature vector distributions.
result Improves prediction performance on graph classification tasks.
MRA-BGCN improves traffic forecasting accuracy through complex graph interactions.
problem Challenging traffic forecasting due to spatial-temporal dependency and uncertainty.
method Proposes MRA-BGCN, a deep learning model that uses bicomponent graph convolution and multi-range attention.
result MRA-BGCN achieves state-of-the-art results on real-world traffic 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.
New method for embedding large networks without attributes, achieving state-of-the-art performance.
problem Learning embeddings from large-scale networks without domain-dependent attributes.
method Use predefined local encodings based on node degree frequencies at different distances.
result Inductive network embeddings generalize well across unseen or distant regions in the network.
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a distance or similarity metric on the points, then look for highly connected subgra…
Proves existence of unique circle packings on polyhedral surfaces.
problem Existence of unique circle packings on polyhedral surfaces with specified discrete curvature.
method Constructs diffeomorphism between fiber bundles, uses discrete Ricci flow and edge flipping.
result Proves existence of unique inversive distance circle packings.
Method approximates Wasserstein distance between 2D histograms using min cost flow.
problem Computing Wasserstein distance between 2D histograms efficiently.
method Transforms the problem into an uncapacitated min cost flow problem.
result Approximates optimal solution with reduced network size O(n).