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.
Proposes CAL to learn causal adjacency for better spatiotemporal prediction.
Graphs represent knot adjacency for n crossings.
Random projections help in representing sparse graphs efficiently.
New matrix reveals cluster info in sparse directed graphs.
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links…
A scalable method to learn causal graphs from large data.
For graphs generated from stochastic blockmodels, adjacency spectral embedding is asymptotically consistent. Further, adjacency spectral embedding composed with universally consistent classifiers is universally consistent to achieve the Bayes error. However when the graph contains private or sensitive information, trea…
Two new methods improve graph embedding without needing a complete graph structure.
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency structure on the half-edges around each vertex, and an embedding of a *-graph is…
Sharp threshold found for Frechet mean of inhomogeneous graphs.
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We…
New centrality-based graph shift operators improve graph neural networks.
AutoLL uses neural networks to automatically reorder graph nodes for linear layouts.
A graph's winding numbers around two non-adjacent vertices differ by ±1.
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the modularity matrix, and we derive the error of the approximation. There is also a comp…
Improved bipartite link prediction using 2-hop paths.
We study real nonsingular projective cubic fourfolds up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in the middle homology. Moreover, we provide a graph whose vertices represent the equivale…
Proposes a new graph representation method using tensor products.
The paper proposes DEA to make graph neural networks fairer in link prediction.
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connec…
This paper presents a methodology for image classification using Graph Neural Network (GNN) models. We transform the input images into region adjacency graphs (RAGs), in which regions are superpixels and edges connect neighboring superpixels. Our experiments suggest that Graph Attention Networks (GATs), which combine g…
We compute an approximate Fréchet mean for sets of sparse graphs.
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …
We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [bg], and hence give rise to weight systems. Among these weight systems are those associated with the Conway and HOMFLYPT polynomials. We extend these ideas to looking at a space o…
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs or learn task-driven adaptive graphs. In this paper, we propose Graph Learning Ne…
This paper studies the problem of learning causal structures from observational data. We reformulate the Structural Equation Model (SEM) with additive noises in a form parameterized by binary graph adjacency matrix and show that, if the original SEM is identifiable, then the binary adjacency matrix can be identified up…
Scharlemann and Thompson define the width of a 3-manifold M as a notion of complexity based on the topology of M. Their original definition had the property that the adjacency relation on handles gave a linear order on handles, but here we consider a more general definition due to Saito, Scharlemann and Schultens, in w…
Bayesian graph learning improves graph representation accuracy.
The paper computes an approximation to the sample Frechet mean of graph sets using spectral information.
Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which an embedding can be applied to observations not present in the training set. Appli…
Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine learning algorithms like classification, clustering, etc., over graph datasets. In…
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describ…
We study the gordian graph of all knots in : two knots are adjacent if they differ by a single crossing change. We prove that this graph contains isometrically an infinite countable tree with infinite valency, and that the complement of any finite subset is connected.
Graph-Relational Domain Adaptation (GRDA) adapts domains based on their graph structure.
New algorithms improve community detection and parameter estimation for PABM.
SPARC tackles cold-start nodes in graphs by using spectral embeddings.
New method handles structural uncertainty in graphs better than existing models.
The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding…
The study examines convergence of stochastic processes on large graphs and adjacency matrices.
BiGG model efficiently generates sparse graphs with reduced complexity.
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show that these weight systems are related to the weight systems induced by the Conway a…
Many popular dimensionality reduction procedures have out-of-sample extensions, which allow a practitioner to apply a learned embedding to observations not seen in the initial training sample. In this work, we consider the problem of obtaining an out-of-sample extension for the adjacency spectral embedding, a procedure…
This paper characterizes and explains the disagreement between two graph embedding methods.
Spectral clustering for geometric graphs achieves strong consistency in community recovery.
Paper explores embedding methods for detecting pseudo-cliques in random graphs, showing limitations and potential.
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the …
This paper improves GNN robustness by aligning feature and adjacency matrix learning.