arXiv research

Improved accuracy in community detection with vertex labels.

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

A variation of the preferential attachment random graph model of Barabási and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones one-by-one. At every step, the incoming vertex is randomly assigned a label, which represents a commun…

Graph Lie algebras have infinite prolongation if they have a vertex of degree one.

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

Graph neural networks often assume vertex labels are independent, but we show this is rarely true and propose a method to improve predictions.

Given a 2-crossing minimal chart $Γ$, a minimal chart with two crossings, set $α=\min\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$, and $β=\max\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$. In this paper we study the structure of a neighbourhood of $Γ_α\cupΓ_β$, and p…

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…

Suppose that one particular block in a stochastic block model is of interest, but block labels are only observed for a few of the vertices in the network. Utilizing a graph realized from the model and the observed block labels, the vertex nomination task is to order the vertices with unobserved block labels into a rank…

A labeled oriented graph (LOG) is an oriented graph with a labeling function from the edge set into the vertex set. The complexity of a LOG is the minimal cardinality of an initial set $S$ of vertices such that every vertex can be reached successively from $S$ only using edges with labels in $S$ or already visited vert…

Study sharpens threshold for matching correlated graphs without labels.

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…

A scalable graph-based SSL method for large-scale data with few labels.

While many multiple graph inference methodologies operate under the implicit assumption that an explicit vertex correspondence is known across the vertex sets of the graphs, in practice these correspondences may only be partially or errorfully known. Herein, we provide an information theoretic foundation for understand…

New tests detect asphericity in complex pairs, simplifying previous proofs.

Power of network tests degrades when vertices are misaligned.

A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex contraction). Such discretization together with non-negative factorization techniques c…

Method analyzes large-scale network data to detect communication pattern shifts.

We investigate minimal charts with loops, a simple closed curve consisting of edges of label $m$ containing exactly one white vertex. We shall show that there does not exist any loop in a minimal chart with exactly seven white vertices in this paper.

Efficiently updates vertex representations for dynamic graphs using random walks.

Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a ``nomination list'' such that, with high probability, vertices from the interesting b…

Solves a 45-year-old Poincaré Conjecture using geometrization of 3-manifolds.

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 …

New algorithm recovers labels from noisy categorical data.

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…

Graph-based method predicts edge flows from partial measurements.

A new algorithm tackles graph-based contextual bandits with efficient regret bounds.

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed t…

Algorithm predicts graph label changes online with cluster specialists.

Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We develop operations on their associated labeled graphs that will effectively construct from a single vertex all graphs that represent $1$-connected $2$-stratifolds. We describe an i…

New algorithm finds corrupted vertices in graphs with few queries.

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…

Vertex distortion detects if a knot is unknot.

A federated method for feature selection in multi-label data.

The paper finds and visualizes unique geometric polyhedra and tori with few vertices.

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

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 …

New maps on the plane with specific symmetry properties identified.

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

Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in correlated Erdős-Rényi graphs. However, very little is known about the existence of e…

Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The success of neural embeddings has prompted significant amounts of research into appli…

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

Defines formal vertex laws related to Lie conformal algebras.

Study Type $C$ skein modules using $Sp(2n)$ webs and construct transparent elements.

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the …

New relations for vertex polynomial in graphs of any degree.

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

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