We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…
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48 results for “graph matrices”
Random projections help in representing sparse graphs efficiently.
problem Efficiently representing sparse graphs of varying sizes and vertex sets.
method Random projection of adjacency matrices to retain graph functionality and properties.
result Random projections can accurately represent graphs of different sizes and vertex sets in the same space.
New nodal domain theorems for symmetric matrices via signed graphs.
problem Establish nodal domain theorems for symmetric matrices.
method Explore signed graph structure to define nodal domains for any function.
result Improved lower bound estimates for the number of strong nodal domains.
A polynomial time iterative algorithm for matching Gaussian matrices with non-vanishing correlationcs.DS
Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.
problem Matching vertices in two correlated Erdős-Rényi graphs.
method Iterative matching algorithm for correlated Gaussian Wigner matrices.
result First polynomial time algorithm for graph matching with arbitrarily small constant correlation.
New matrix reveals cluster info in sparse directed graphs.
problem Analyzing cluster information in directed graphs.
method Proposed complex non-backtracking matrix integrating Hermitian adjacency matrix and non-backtracking matrix properties.
result The complex non-backtracking matrix holds cluster information, especially for sparse directed graphs.
Extends graph encoder embedding to weighted graphs and matrices.
problem Classifying vertices in various graph types efficiently.
method Graph encoder embedding applied to weighted graphs, distance matrices, and kernel matrices.
result The method achieves asymptotic normality, enabling optimal classification.
π-GNN learns soft permutations for graph representations, improving graph classification and regression.
problem Limitations of MPNNs in graph neural networks.
method Proposes π-GNN, which learns a soft permutation matrix for each graph, projecting graphs into a common vector space.
result π-GNN achieves performance competitive with state-of-the-art models on graph classification and regression tasks.
The paper studies matrix normalization and graph balancing using a new functional and gradient descent.
problem Matrix normalization and graph balancing.
method A new functional called the non-normal energy, and gradient descent.
result Gradient descent of the non-normal energy converges to balanced graphs and preserves spectra and realness of weights.
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
Study uses graph Laplacians to analyze surface links.
problem Analyzing virtual genus of surface links.
method Laplacian matrices of weighted graphs in surfaces are used to define invariants.
result Obtained information about virtual genus.
New curvature tensor and matrices for connection graphs derived from Bakry-Émery curvature.
problem Deriving Buser-type bounds on eigenvalues of connection Laplacians.
method Reformulation of Bakry-Émery curvature through curvature matrices and tensor representations.
result Extension of curvature matrices to connection graphs, addressing eigenfunction challenges.
Bayesian Inference of Transition Matrices from Incomplete Graph Data with a Topological Priorstat.ME
Bayesian method infers transition matrices from incomplete graph data with topological constraints.
problem Inference of transition matrices from incomplete graph data with topological constraints.
method Bayesian approach using repeated interactions and a topological prior.
result Higher accuracy in inferring transition probabilities, improving downstream tasks.
Paper introduces a taxonomy of reduction matrices for more efficient graph coarsening.
problem Efficiently reducing graph size while preserving important information.
method Introduces a more general notion of reduction matrix, not necessarily the pseudo-inverse of the lifting matrix.
result Reducing the Restricted Spectral Approximation (RSA) by modifying the reduction matrix.
Survey on strong convergence in random matrices and its applications.
problem Understanding convergence of random matrices to operators.
method Analysis of operator norms of noncommutative polynomials.
result New insights and applications in random graphs, geometry, and operator algebras.
Graph alignment problem solved with convex relaxations for correlated matrices.
problem Recovering hidden vertex permutations from correlated Gaussian matrices.
method Convex relaxations of the quadratic assignment problem over doubly stochastic matrices.
result The solution of the convex relaxation concentrates around the ground-truth permutation matrix for certain correlation parameters.
Completing correlation matricesq-fin.MF
A method to complete incomplete correlation matrices using maximum entropy.
problem Incomplete correlation matrices in financial applications.
method Maximizing entropy of the distribution described by the matrix, constructing a chordal graph.
result A proper correlation matrix can be constructed for large models involving multiple currencies.
Constructing fast approximate eigenspaces with application to the fast graph Fourier transformscs.LG
Efficiently approximates eigenspaces for symmetric and general matrices.
problem Fast computation of eigenspaces for large matrices.
method Factor eigenspaces into fundamental components using transformations, solve minimization problems, and iteratively update.
result Improved computational efficiency for eigenspace approximation.
Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithmstat.ML
Paper tackles robust graph matching in dense graphs with AMP type algorithm.
problem Matching recovery between correlated Gaussian Wigner matrices with adversarial perturbations.
method Approximate Message Passing (AMP) type iterative algorithm with time-dependent matrix multiplication.
result Algorithm succeeds in polynomial time for non-vanishing correlation and small perturbations.
Proposes a new graph representation method using tensor products.
problem Dynamic graph representation and theoretical properties.
method Bind-and-sum approach in hyperdimensional computing (HDC), tensor product as binding operation.
result Memory vs. size analysis of graph representation size scaling.
In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure …
Graph clustering method uses templates to match vertices and outperforms classical methods.
problem Graph clustering with additional structural information.
method Formulates graph clustering as template matching, using orthonormal matrices for embedding.
result Method outperforms classical methods, especially for challenging cases.
Graph energy helps detect communities in networks better than traditional methods.
problem Detecting communities in sparse networks where traditional methods fail.
method Using graph energy based on the full spectrum of adjacency matrices.
result The difference in graph energy between a planted partition model and an Erdős--Rényi network has a distinct transition at the detectability threshold.
Bayesian graph learning improves graph representation accuracy.
problem Inaccurate graph construction from noisy data.
method Non-parametric Bayesian graph model for posterior inference of graph adjacency matrices.
result Model scales well to large graphs and improves node classification, link prediction, and recommendation tasks.
We propose a fast general projection-free metric learning framework, where the minimization objective is a convex differentiable function of the metric matrix , and resides in the set of generalized graph Laplacian matrices for con…
Joint Embedding of Graphsstat.AP
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the jo…
A network community detection method with integration of data from multiple layers and node attributesphysics.soc-ph
A method for community detection in multilayer networks using data matrices.
problem Community detection in multilayer networks with various node attributes.
method Data matrix representation and regular decomposition method extension for compression.
result Method identifies community structures well-aligned with real-world network hierarchies.
New centrality-based graph shift operators improve graph neural networks.
problem Improving graph neural networks by enhancing graph shift operators.
method Proposed Centrality Graph Shift Operators (CGSOs) using global centrality metrics.
result CGSOs lead to improved performance in graph neural networks on real-world datasets.
Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one…
The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. Firs…
Graph neural networks have become increasingly popular in recent years due to their ability to naturally encode relational input data and their ability to scale to large graphs by operating on a sparse representation of graph adjacency matrices. As we look to scale up these models using custom hardware, a natural assum…
Study of discrete period matrices on embedded graphs, relating to Riemann surfaces.
problem Understanding discrete conformal structures on surfaces via period matrices.
method Combinatorial interpretation of period matrices, using homological quasi-trees and Laplacian determinants.
result Derived a combinatorial analogue of the Weil-Petersson potential and related it to homological quasi-trees.
BAM model learns graph structure from data with robustness across linear and non-linear dependencies.
problem Detecting dependencies in datasets for graph structure learning.
method Proposes BAM, a neural network model using structural equation models and Chebyshev polynomials for training, with bilinear attention mechanism.
result Demonstrates robust generalizability and superior performance in graph estimation.
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 connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the datas…
Conjugate gradient methods improve efficiency for high-dimensional GLMMs.
problem Efficiency bottleneck in computing high-dimensional GLMM precision matrices.
method Combining spectral analysis and random graph theory with conjugate gradient methods.
result CG-based methods achieve linear scaling in cost with model parameters and observations.
Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistencystat.ML
Paper proves conditions for estimating precision matrices with Laplacian constraints.
problem Estimating high-dimensional precision matrices with Laplacian constraints.
method Minimizing Stein's loss with conditions on graph connectivity and Laplacian constraints.
result High-dimensional consistency achieved with Laplacian constraints, independent of graph structure.
New algorithms reduce communication in GNN training.
problem Higher communication costs in GNNs due to sparse connectivity.
method Parallel algorithms for sparse-dense matrix multiplication.
result Asymptotic reduction in communication compared to previous methods.
Unified framework for graph coarsening using node features and graph matrices.
problem Dimensionality reduction of large graphs while preserving node features.
method Optimization-based framework that unifies graph learning and dimensionality reduction.
result The learned coarsened graph is ε-similar to the original graph, where ε is a small positive number.
In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, …
On meandric permutationsmath.AT
We found a way to code meanders and show they are idempotent.
problem Understanding and coding meandric permutations.
method We established a bijection between meanders and Gauss diagrams, and used this to construct matrices that are idempotent.
result Meandric permutations are idempotent over the field GF(2).
Origin-destination (OD) matrices are often used in urban planning, where a city is partitioned into regions and an element (i, j) in an OD matrix records the cost (e.g., travel time, fuel consumption, or travel speed) from region i to region j. In this paper, we partition a day into multiple intervals, e.g., 96 15-min …
We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the -prediction error and the -risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can estimate a high-dim…
The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.
problem Understanding the spectral properties of mesh matrices of graphs.
method Definition and study of mesh matrices, introduction of mesh Laplacian, derivation of characteristic polynomial formulas.
result Mesh Laplacian eigenvalues are all real and greater than or equal to 1, with a smallest positive eigenvalue estimated.
GLFA improves latent factor analysis by incorporating graph structures for HiDS matrices.
problem Accurate representation learning on high-dimensional and sparse matrices.
method GLFA incorporates a graph to identify hidden high-order interactions and uses a recurrent LFA structure to improve representation learning.
result GLFA outperforms state-of-the-art models in predicting missing data of HiDS matrices.
MXGNet tackles visual reasoning tasks using graph neural networks.
problem Abstract reasoning, especially in the visual domain, is challenging for AI.
method Combines object-level representations, graph neural networks, and multiplex graphs.
result Achieves state-of-the-art accuracy on Euler Diagram Syllogisms and outperforms state-of-the-art models on RPM datasets.
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 may not have a solution.
Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for spa…
The paper tackles learning varying DAG structures based on contextual features.
problem Learning a single DAG for the entire population from observational data.
method A neural network that maps contextual features to a weighted adjacency matrix of a DAG, with a projection layer to ensure acyclicity.
result The new approach can recover context-specific DAGs where existing methods fail.