ARGEW improves node embeddings for weighted homophilous graphs by emphasizing strong edge weights.
problem Lack of accurate node embeddings for weighted homophilous graphs.
method ARGEW (Augmentation of Random walks by Graph Edge Weights) augments random walks by emphasizing nodes with larger edge weights.
result ARGEW produces embeddings where node pairs with strong edge weights have closer embeddings.
Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge, the extent to which the edge is embedded in a surrounding structure, and the age…
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…
Paper proposes efficient weight updates for edge nodes with minimal communication.
problem Inefficient and resource-intensive full weight updates for edge nodes.
method Deep partial updating, selecting a subset of weights to update.
result Achieves similar performance with fewer weight updates.
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership information. In particular, we introduce a edge weight distribution matrix to the s…
Study of Ricci flow on trees, focusing on edge weights and curvatures.
problem Understanding the evolution of metrics on trees under Ricci flow.
method Continuous-time Ricci flow based on Lin-Lu-Yau Ollivier Ricci curvature.
result Ricci flow converges to zero curvature on edge weights of positive normalized values in caterpillar trees.
Paper uses GNN and conformal prediction for accurate edge weight prediction.
problem Predicting edge weights on graphs for various applications.
method Graph Neural Network (GNN) with conformal prediction and error reweighting.
result Our method provides better coverage and efficiency than baselines.
The paper predicts edge weights in weighted directed networks using metric geometry.
problem Predicting edge weights in weighted directed networks.
method Introducing new types of weighted directed networks (AWDNs), constructing metrics, and proposing modified kNN and SVM methods.
result The proposed methods outperform traditional approaches in predicting edge weights.
Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale …
New algorithm detects communities in weighted networks, improving on binary ones.
problem Few methods exist for detecting communities in weighted networks.
method Pseudo-likelihood approach for weighted stochastic block model.
result The method is consistent and works well for both homogeneous and heterogeneous networks.
Constructs weight 1/2 multiplier systems for a specific group and relates to geometric edge paths.
problem Constructing weight 1/2 multiplier systems for a specific group.
method Defines an eta function and Rademacher symbol, relates to geometric edge paths in a triangulation of the upper half plane.
result Relates weight 1/2 multiplier systems to geometric edge paths.
We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation, which we solve using a Bayesian approach. We introduce a variational algorithm that …
A new SBM for non-negative zero-inflated edge weights in networks.
problem Modeling international trading networks with non-negative zero-inflated edge weights.
method Restricted Tweedie distribution and nodal information accounting.
result Efficient two-step algorithm for estimating covariate effects.
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex wei…
New method clusters hypergraphs using weighted random walks and Laplacians.
problem Clustering hypergraph data with edge-dependent weights.
method Random walks with edge-dependent vertex weights, constructing hypergraph Laplacians for clustering.
result Proposed methods outperform existing hypergraph clustering algorithms.
SWRLDA improves LDA for multi-class classification with edge classes.
problem LDA's vulnerability to edge classes causing biased mean and large distances.
method Self-weighted robust LDA with l21-norm distance criterion.
result SWRLDA outperforms other methods on synthetic and real-world datasets.
The paper proposes a novel Kernelized image segmentation scheme for noisy images that utilizes the concept of Smallest Univalue Segment Assimilating Nucleus (SUSAN) and incorporates spatial constraints by computing circular colour map induced weights. Fuzzy damping coefficients are obtained for each nucleus or center p…
Federated learning technique improves convergence speed with communication delays.
problem Communication delays between edge nodes and aggregator in federated learning.
method Developed FedDelAvg, a technique that generalizes federated averaging to incorporate a weighting between current local model and delayed global model.
result FedDelAvg achieves a significant improvement in convergence speed, especially when optimizing the weighting scheme to account for delays.
Paper tackles dense subgraph discovery with noisy feedback.
problem Discover dense subgraphs in edge-weighted graphs with noisy feedback.
method Proposes polynomial-time and scalable algorithms for dense subgraph discovery.
result Polynomial-time algorithm obtains nearly-optimal solution with high probability.
The paper proves ML estimators are strongly consistent for identifying edge weights in BAR models.
problem Identifying edge weights in Bernoulli Autoregressive (BAR) models.
method Maximum Likelihood (ML) estimation for two variants of BAR models.
result ML estimators are strongly consistent for edge weight identification.
A new model for detecting overlapping communities in weighted networks.
problem Community detection in overlapping weighted networks with mixed membership and edge weights.
method Mixed membership distribution-free (MMDF) model with an efficient spectral algorithm and fuzzy weighted modularity.
result The MMDF model can estimate community memberships and evaluate community quality for weighted networks.
A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local "richness" of the cyclic structure. In this paper, we introduce renewal non-backtrac…
New framework for dense weighted networks with community-specific patterns.
problem Dense networks with varying edge weights across communities.
method Proposes a new model with functions mapping node characteristics to edge weights, requiring few parameters.
result Developed a bootstrap methodology for generating new networks.
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of dif…
Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing such data is that inference at the individual edge level is not particularly biolog…
This work estimates edge weights of edge-reinforced random walks using observed data.
problem Statistical estimation of edge weights in edge-reinforced random walks.
method Proposes an estimator based on the generalized method of moments using the magic formula and hyperbolic Gaussian structure.
result Analyzes the sample complexity of the proposed estimator.
Graph Neural Networks (GNNs) have been widely studied for graph data representation and learning. However, existing GNNs generally conduct context-aware learning on node feature representation only which usually ignores the learning of edge (weight) representation. In this paper, we propose a novel unified GNN model, n…
Flow on weighted graphs sharpens Bakry-Émery curvature.
problem Sharp curvature in weighted graphs.
method Bakry-Émery curvature flow on mixed weighted graphs.
result Limits of curvature flow are curvature sharp.
We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an n node multilayer neural net that has degree at most nγ for some γ<1 and each edge has a random edge weight in [−1,1]. Our algorithm learns {\em …
Let X be an infinite Riemann surface equipped with its conformal hyperbolic metric such that the action of the covering group π1(X) on X~ is of the first kind-i.e., the surface X is equal to its convex core. We first prove that any geodesic lamination on X is nowhere dense. Given a fixed geodesic pant…
We address the problem of computing a single linkage dendrogram. A possible approach is to: (i) Form an edge weighted graph G over the data, with edge weights reflecting dissimilarities. (ii) Calculate the MST T of G. (iii) Break the longest edge of T thereby splitting it into subtrees TL, TR. (iv) Apply …
BiTAT improves neural network quantization for edge devices by focusing on weight dependencies and disentangling them.
problem Performance degradation of compact neural networks under extreme quantization.
method Task-dependent Aggregated Transformation (BiTAT) method that orthonormalizes weights and progressively quantizes them.
result BiTAT effectively preserves model performance on ImageNet and CIFAR-100 with compact backbones.
Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there are many other applications in which only \emph{multi}-way similarity measures ar…
New test detects differences in heterogeneous datasets.
problem Detecting differences between two samples with unknown heterogeneity.
method Developed a nonparametric testing procedure that handles latent heterogeneity through a composite null.
result The test accurately detects differences in the presence of unknown heterogeneity.
Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.
problem Finding optimal discrete harmonic maps between hyperbolic surfaces.
method Minimizing Dirichlet energy over all possible hyperbolic structures and realizations within a fixed homotopy class.
result At the optimal hyperbolic structure, the discrete harmonic map and edge weights are induced from a weighted Delaunay decomposition.
Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on vertices and edges. In this work, we propose a Gaussian-induced convolution (GIC) fra…
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
New model detects communities in networks with signed, continuous weights.
problem Detect communities in networks with signed, continuous weights.
method Heterogeneous Block Covariance Model (HBCM) with variational EM algorithm.
result Provable consistent estimates of group memberships.
A new model clusters network nodes based on relative edge weights.
problem Clustering networks ignores node capacities, leading to biased results.
method Proposes a Dirichlet stochastic block model for composition-weighted networks.
result Validated on simulated and real-world networks, showing improved clustering accuracy.
While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools. Here we study the problem of classification of networks with labeled nodes, motiv…
Paper studies weighted Fermat-Frechet problem for simplex edge lengths.
problem Finding optimal edge lengths for simplex deformations.
method Isometric embedding techniques for K-Space. result New variational method to solve weighted Fermat-Frechet problem.
A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces a second Laplacian matrix such that a principal minor is an Ale…
The (torsion) complexity of a finite edge-weighted graph is defined to be the order of the torsion subgroup of the abelian group presented by its Laplacian matrix. When G is d-periodic (i.e., G has a free action of the rank-d free abelian group by graph automorphisms, with finite quotient) the Mahler measure of its Lap…
Study reconstructs hidden perfect matchings in random graphs with specific edge weights.
problem Reconstructing hidden perfect matchings in random weighted bipartite graphs.
method Analyzes the maximum likelihood estimator for matching reconstruction under different probability distributions of edge weights.
result Sharp threshold and infinite-order phase transition in reconstruction error for different probability distributions.
Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links modify the graph neighborhoods, which critically affects the performance of GCNs in semi-supervised learning (SSL) tasks. Aiming at robustifying GCNs conditi…
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
problem Optimal model structure reconstruction from weighted colored graph adjacency matrix.
method Uses prize-collecting Steiner tree algorithm to reconstruct minimum spanning tree.
result Demonstrates the effectiveness of the prize-collecting Steiner tree algorithm for model structure reconstruction.
Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As real-world graphs are often incomplete and noisy, treating them as ground-truth inform…