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…
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48 results for “weighted adjacency”
Method selects number of communities in weighted networks.
problem Selecting the number of communities in weighted networks.
method Proposes a novel weighted DCSBM and uses a sequential testing framework with spectral clustering and matrix scaling.
result Method is consistent in estimating the true number of communities under mild conditions.
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…
Due to a resource-constrained environment, network compression has become an important part of deep neural networks research. In this paper, we propose a new compression method, \textit{Inter-Layer Weight Prediction} (ILWP) and quantization method which quantize the predicted residuals between the weights in all convol…
Paper extends Cohen's method to compute Jones polynomial for certain braid subfamilies.
problem Computing Jones polynomial for specific knot families.
method Using weighted adjacency matrices and determinants for certain subfamilies of braid groups.
result Jones polynomial can be computed in polynomial time for certain subfamilies of braid groups.
New model for detecting communities in weighted bipartite networks.
problem Lack of models for weighted bipartite networks.
method Introducing Bipartite Distribution-Free model and its extension.
result Spectral algorithms for consistent estimation of node labels.
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.
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…
DFM model detects communities in weighted networks without distributional assumptions.
problem Challenges in community detection for weighted networks.
method Distribution-Free Model (DFM) for weighted networks, using spectral clustering.
result Spectral clustering yields consistent community detection under DFM.
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.
Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squ…
New method clusters weighted directed networks using motifs.
problem Clustering directed networks fails to consider higher-order structure and edge weights.
method Motif-based weighted spectral clustering with new matrix formulae.
result Scalable and effective clustering on large graphs and real-world data.
Dagma-DCE improves causal discovery with interpretable measures and open-source code.
problem Arbitrary proxy measures of causal strength in non-parametric causal discovery.
method Uses weighted adjacency matrices based on an interpretable measure of causal strength.
result Achieves state-of-the-art performance in simulated datasets.
New algorithm achieves strong consistency in binary non-uniform hypergraph classification.
problem Node classification on binary non-uniform hypergraphs with varying edge probabilities.
method Proposes a refinement algorithm using power iteration on weighted adjacency matrices.
result Proves optimality of the refinement algorithm, achieving strong consistency and IT lower bound.
PRESTO improves rare event prediction by shrinking towards proportional odds model.
problem Difficult to predict rare events due to class imbalance.
method PRESTO relaxes proportional odds model by estimating separate weights for transitions between categories, imposing L1 penalty to shrink towards proportional odds.
result PRESTO consistently estimates decision boundary weights under sparsity assumption, improving rare probability estimation.
Efficiently learns DAG structures without cycles.
problem Learning DAG structures efficiently with constraints.
method Proposes DAG-NoCurl, a two-step algorithm to find and project acyclic graphs.
result Significantly improves efficiency over existing methods, often by more than one order of magnitude.
A knot K is called Gordian adjacent to a knot L if there exists an unknotting sequence for L containing K. We provide a sufficient condition for Gordian adjacency of torus knots via the study of knots in the thickened torus. We also completely describe Gordian adjacency for torus knots of index 2 and 3 using Levine-Tri…
Paper determines 2-adjacent knots up to 12 crossings.
problem Identifying 2-adjacent knots with up to 12 crossings.
method Used Heegaard Floer d-invariants and Alexander polynomial to obstruct 2-adjacency.
result Proved conjectures about 2-adjacent knots by Ito and Kato.
Adjacency defined for three-manifolds, linking them to the 3-sphere.
problem Characterizing adjacency between three-manifolds and the 3-sphere.
method Introducing adjacency concept, using -component links and surgery slopes.
result Characterized adjacencies from three-manifolds to the 3-sphere.
Paper proves rigidity of Doyle spirals in hexagonal lattice circle packings.
problem Proving Doyle conjecture for hexagonal lattice circle packings.
method Using Liouville theorem of discrete harmonic functions based on logarithmic radii ratio observation.
result Proves rigidity of Doyle spirals in hexagonal lattice circle packings with bounded radii ratios.
Optimizes matching in weighted graphs with semi-bandit sampling.
problem Finding optimal pairings in weighted graphs with sequential sampling.
method Leverages rank-1 assumption on adjacency matrix to reduce sample complexity and regret.
result Achieves linear dependency in the number of vertices for sample complexity and regret.
Study reveals decurve flows in graph propagation models.
problem Limitations of traditional graph analysis and propagation mechanisms.
method Introduces Generalized Propagation Neural Networks (GPNNs) and Continuous Unified Ricci Curvature (CURC).
result Observation of decurve flow during training of graph neural networks, revealing propagation dynamics.
Proposes CAL to learn causal adjacency for better spatiotemporal prediction.
problem Suboptimal performance in spatiotemporal prediction due to out-of-distribution data.
method Causal Adjacency Learning (CAL) method to discover causal relations over graphs.
result Calculated causal adjacency matrix enhances prediction performance on out-of-distribution test data.
The paper introduces an adjacency constraint to improve goal-conditioned HRL.
problem Training inefficiency in goal-conditioned HRL due to large action space.
method Restricting the high-level action space to a k-step adjacent region of the current state.
result The adjacency constraint preserves optimal hierarchical policies and improves HRL performance.
This work identifies and mitigates topological bias in HGNNs using meta-weighting and debiasing.
problem Topological bias in HGNNs affects model performance on specific nodes.
method Meta-weighting adjacency matrix, PageRank projection, debiasing structure.
result The debiasing structure improves HGNNs' performance and debiasing.
Graphs represent knot adjacency for n crossings.
problem Understanding adjacency relationships between knots.
method Defined a new graph to represent -adjacency.
result Proved several results about the new graph .
Reconstruct spacetime from order and number of points.
problem Reconstruct spacetime from chronological relations and i.i.d. samples.
method Relaxing hypotheses of Gromov reconstruction theorem, using random adjacency matrices and chronological relations.
result Spacetime can be recovered by only knowing 'order' and 'number' of its points.
A knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any m (no larger than n) of them yields a projection of the unknot. We show that a non-trivial satellite knot K is n-adjacent to the unknot, for some n>0, if and only if it is n-adjacent to the un…
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…
S-SGD: Symmetrical Stochastic Gradient Descent with Weight Noise Injection for Reaching Flat Minimacs.LG
S-SGD adds symmetrical noise to weights to avoid sharp minima in deep learning.
problem SGD does not always converge to a flat minimum, leading to poor generalization.
method Symmetrical weight noise injection in SGD.
result S-SGD outperforms conventional SGD and weight-noise injection methods in large batch training.
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…
A knot is said to be Gordian adjacent to a knot if is an intermediate knot on an unknotting sequence of . We extend previous results on Gordian adjacency by showing sufficient conditions for Gordian adjacency between classes of positive braid knots through manipulations of braid words. In additio…
This paper presents an algorithm to construct a weighted adjacency matrix of a plane bipartite graph obtained from a pretzel knot diagram. The determinant of this matrix after evaluation is shown to be the Jones polynomial of the pretzel knot by way of perfect matchings (or dimers) of this graph. The weights are Tutte'…
A tiling of the sphere by triangles, squares, or hexagons is convex if every vertex has at most 6, 4, or 3 polygons adjacent to it, respectively. Assigning an appropriate weight to any tiling, our main result is explicit formulas for the weighted number of convex tilings with a given number of tiles. To prove these for…
We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised learning algorithms. When suitably scaled, graph Laplacians approach limiting cont…
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…
New model for detecting communities in weighted bipartite networks.
problem No model for community detection in overlapping bipartite weighted networks.
method Introduces BiMMDF model allowing any distribution with block structure.
result Efficient algorithm with theoretical guarantee of consistent estimation.
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
Novel Haar-Laplacian for directed graphs enhances spectral graph applications.
problem Lack of suitable Laplacian for directed graphs in spectral graph theory.
method Inspired by Haar-like transformation, introduces a Hermitian matrix preserving direction and weight.
result HaarNet outperforms in weight prediction and denoising on directed graphs.
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.
EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
problem Inaccurate and poorly designed calculation of high-order proximity in network embedding.
method EPINE redefines high-order proximity intuitively and proposes a scalable algorithm for accurate calculation.
result EPINE outperforms existing methods in network reconstruction, link prediction, and node classification.
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant operators, which include the edge Laplacian and the adjacency matrix on graphs. In the …
Graph Convolution Network (GCN) has been recognized as one of the most effective graph models for semi-supervised learning, but it extracts merely the first-order or few-order neighborhood information through information propagation, which suffers performance drop-off for deeper structure. Existing approaches that deal…
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.
Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embeddingstat.ML
LASE improves local network structure visualization by targeting locally low-dimensional regions.
problem Global spectral embedding fails to capture local geometric features in sparse, transitive networks.
method Local Adjacency Spectral Embedding (LASE) using weighted spectral decomposition.
result LASE reveals locally low-dimensional structure, improving local reconstruction and visualization.
The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank factorizations in order to approximately decompose and eventually invert such big…
New method for freezing sets in arbitrary dimensions.
problem Creating freezing sets for digital images in arbitrary dimensions.
method Using and adjacencies to obtain freezing sets in .
result Demonstrated freezing sets for digital images in arbitrary dimensions.