arXiv research

Enhances graph classification with multiple graphs.

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…

For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, w…

Improved graph embedding through refined linear transformation and community recovery.

Graph cross network improves graph classification accuracy.

Gaussian processes classify graphs using vertex and edge features.

Convolutional layers in graph neural networks are a fundamental type of layer which output a representation or embedding of each graph vertex. The representation typically encodes information about the vertex in question and its neighbourhood. If one wishes to perform a graph centric task, such as graph classification,…

Given a vertex of interest in a network $G_1$, the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network $G_2$. A vertex nomination scheme produces a list of the vertices in $G_2$, ranked according to how likely they are judged to be the corresponding vertex of …

This paper examines how graph topology affects adversarial attacks on vertex classification.

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This approach has been highly successful owing to the theory, methodology and software that …

Proposes methods to recover labels from shuffled networks using graph averages.

New methods cluster and test graphs without vertex correspondence.

The paper classifies palettes of Dehn colorings for spatial graphs.

DeepMap learns deep graph representations via CNNs, improving graph classification performance.

A normal pseudomanifold is a pseudomanifold in which the links of simplices are also pseudomanifolds. So, a normal 2-pseudomanifold triangulates a connected closed 2-manifold. But, normal $d$-pseudomanifolds form a broader class than triangulations of connected closed $d$-manifolds for $d \geq 3$. Here, we classify all…

An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised representation learning have been demonstrated to give the state-of-the-art perfor…

The paper introduces a method for detecting principal communities and embedding vertices.

We developed a convolution neural network (CNN) on semi-regular triangulated meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN, including convolution and down-sampling, are directly defined in a vertex domain. By exploiting the ordering property of semi-regular meshes, the convolution is defin…

Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the microscopic structure, such as the first- and second-order proximity of vertexes, while th…

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function $κ$, provided that the latent positions are i.i.d. from some distribution F. We then consider the exploitation task of vertex classi…

We present a deep learning approach for vertex reconstruction of neutrino-nucleus interaction events, a problem in the domain of high energy physics. In this approach, we combine both energy and timing data that are collected in the MINERvA detector to perform classification and regression tasks. We show that the resul…

A fast graph embedding method for large graphs.

New triangulations of quaternionic projective plane found with various symmetry groups.

The paper studies graph products of groups and recovers graph and vertex groups under certain conditions.

Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through an embedding method provides superior performance in many real-world applicatio…

New method for learning on heterogeneous graphs without meta-paths.

We consider the problem of vertex classification for graphs constructed from the latent position model. It was shown previously that the approach of embedding the graphs into some Euclidean space followed by classification in that space can yields a universally consistent vertex classifier. However, a major technical d…

A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.

Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We obtain a classification of $1$-connected $2$-stratifolds in terms of their associated labeled graphs and develop operations that will construct from a single vertex all graphs that…

Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. In earlier work a complete classification of semi-equivelar map of type $(3^5, 4)$ on the surface of Euler characteristic -1 was given. In the meantime Karabas an Nedela classified vertex transitive semi-equivelar maps on…

We study the meromorphic open-string vertex algebras and their modules over the two-dimensional Riemannian manifolds that are complete, connected, orientable, and of constant sectional curvature $K\neq 0$. Using the parallel tensors, we explicitly determine a basis for the meromorphic open-string vertex algebra, its mo…

Network representation learning (NRL) methods aim to map each vertex into a low dimensional space by preserving the local and global structure of a given network, and in recent years they have received a significant attention thanks to their success in several challenging problems. Although various approaches have been…

This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transit…

Vertex distortion detects if a knot is unknot.

The study finds the bounds of vertex orbits in maps derived from specific lattices.

634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations of octonionic projective plane.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Defines formal vertex laws related to Lie conformal algebras.

Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types $[p^3, 3]$ for $p \equiv 1$ (mod $6$), but there doesn't exist vertex-transitive map of such types. In particu…

The study examines vertices in curves with singular points in the Euclidean plane.

Vertex distortion measures how far lattice knots deviate from straight lines.

New method uses mosaics to study wild knots.

A message passing algorithm is derived for recovering communities within a graph generated by a variation of the Barabási-Albert preferential attachment model. The estimator is assumed to know the arrival times, or order of attachment, of the vertices. The derivation of the algorithm is based on belief propagation unde…

This article announces the completion of the classification of rank 4 locally projective polytopes and their quotients. There are seventeen universal locally projective polytopes (nine nondegenerate). Amongst their 441 quotients are a further four (nonuniversal) regular polytopes, and 152 nonregular but section regular…

We prove that there exists a geodesic trajectory on the dodecahedron from a vertex to itself that does not pass through any other vertex.

This paper investigates the problem of active learning for binary label prediction on a graph. We introduce a simple and label-efficient algorithm called S2 for this task. At each step, S2 selects the vertex to be labeled based on the structure of the graph and all previously gathered labels. Specifically, S2 queries f…

New proof for global rigidity of vertex scaling on polyhedral surfaces.

Proves a generalized Whitehead cut vertex lemma for tree groups.