arXiv research

From computational geometry comes the notion of a Gabriel graph of a point set in the plane. The Gabriel graph consists of those edges connecting two points of the point set such that the circle whose diameter is the edge does not contain any point of the point set in its interior. We define a generalization of the Gab…

Flexible per-class regularization improves binary classifiers.

Unified approach to multiclass classification using Gabriel graphs.

In this paper we give an extension of the Cartier-Gabriel-Kostant structure theorem to Hopf algebroids.

Reprint of a 1989 paper including minor corrections of misprints. Added comments (11 pages) about later related papers in the literature concerning comparison of Gabriel-Zisman calculus of (right) fractions and the use of generalized morphims in the sense of Haefliger-Skandalis-Hilsum for inverting differentiable equiv…

Suppose that $θ_1,θ_2,\dots,θ_n$ are positive numbers and $n\ge 3$. Does there exist a sphere with a spherical metric with $n$ conical singularities of angles $2πθ_1,2πθ_2,\dots,2πθ_n$? A sufficient condition was obtained by Gabriele Mondello and Dmitri Panov (arXiv:1505.01994). We show that it is also necessary when w…

Extends distribution algebra concept to Lie groupoids.

The paper shows how MMD metrizes weak convergence for certain kernels.

Let $(\mathcal{M}, Q)$ be a dg manifold. The space of vector fields with shifted degrees $(\mathcal{X}(\mathcal{M})[-1], L_Q)$ is a Lie algebra object in the homology category $\mathrm{H}((C^{\infty}_{\mathcal{M}},Q)\mathrm{-}\mathbf{mod})$ of dg modules over $(\mathcal{M},Q)$, the Atiyah class $α_{\mathcal{M}}$ being …

A new machine learning method calculates failure probability efficiently and accurately.

Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.

Proposes MGMN for end-to-end graph similarity learning.

The paper explores graphons of line graphs from sparse finite graphs.

MxPool learns graph features from diverse graphs using a hierarchical structure.

Study the geometry of graph product extension graphs.

Graph neural network learns graph distances effectively.

Quasi-transitive graphs quasi-isometric to planar graphs can be upgraded to Cayley graphs.

Customized-GNN generates model-specific for each graph.

Graph embedding leaks sensitive graph properties and subgraphs.

Characterizes graphs with leveled embeddings and introduces new graph invariants.

The paper shows conflict graphs of Petersen family graphs are mostly unbalanced.

Two new methods improve graph embedding without needing a complete graph structure.

We define a pseudo-inverse for line graphs using linear integer programming.

Develops method to create non-Abelian Ricci-flat graphs via bundles.

New method uses graph generative models for graph classification.

MathNet uses wavelets for graph representation and learning.

Unified framework for graph coarsening using node features and graph matrices.

A fast graph embedding method for large graphs.

Quadratic bounds found for graph dimensions.

Study classifies Halin graphs with positive curvature.

PSimGNN partitions graphs into subgraphs for efficient graph similarity computation.

We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform. Different from graph Fourier transform, graph wavelet transform can be obtained …

This paper develops graph theory for racks and quasigroups.

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and con…

We introduce a novel approach to graph-level representation learning, which is to embed an entire graph into a vector space where the embeddings of two graphs preserve their graph-graph proximity. Our approach, UGRAPHEMB, is a general framework that provides a novel means to performing graph-level embedding in a comple…

Graph Cascades rewire graphs to improve structure-aware learning.

CTGCN learns dynamic graph embeddings preserving both local and global graph structure.

The dominant graph neural networks (GNNs) over-rely on the graph links, several serious performance problems with which have been witnessed already, e.g., suspended animation problem and over-smoothing problem. What's more, the inherently inter-connected nature precludes parallelization within the graph, which becomes …

Graphs can be fooled by small edge changes, but this work protects them.

The study bounds the effective diameter of graphs with positive Ollivier curvature.

SpeqNets improve graph neural networks by scaling and adapting to graph sparsity.

Paper converts graph learning to lifelong learning.

Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the laten…

Proves Bochner's identity on graphs using a new auxiliary graph.

AgraSSt assesses graph generators using Stein operators and kernel discrepancies.

Proposes a graph pooling method leveraging node proximity for hierarchical graph representation learning.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampli…

Graph comparison ties to Alexandrov's theorems.