Improved model for grouping nodes in bipartite networks.
problem Challenges in grouping nodes in bipartite graphs.
method Introduced DC-LBM and developed variational EM algorithm.
result Significantly enhanced performance on real-world data.
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48 results for “labeled bipartite graphs”
Bipartite graphs have been used to represent data relationships in many data-mining applications such as in E-commerce recommendation systems. Since learning in graph space is more complicated than in Euclidian space, recent studies have extensively utilized neural nets to effectively and efficiently embed a graph's no…
We consider matrix completion for recommender systems from the point of view of link prediction on graphs. Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges denoting observed ratings. Building on recent progress in deep learning on graph-structured data, we prop…
Constructs Lie algebras from labeled directed graphs and identifies properties of these algebras.
problem Constructing and analyzing Lie algebras from labeled directed graphs.
method Using labeled directed simple graphs to construct 2-step nilpotent Lie algebras, identifying ideals and subalgebras through special subgraphs, and proving isomorphisms based on label occurrences.
result Lie algebras depend only on the underlying undirected graph if all edges are labeled uniquely.
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.
New research finds six bipartite intrinsically knotted graphs with 23 edges.
problem Identifying intrinsically knotted bipartite graphs with 23 edges.
method Analyzing embeddings and graph minors to find minimal intrinsically knotted graphs.
result No minor minimal intrinsically knotted bipartite graph exists with 23 edges.
This work analyzes two methods for combining multiple binary labels in bipartite ranking.
problem Combining multiple binary labels for optimal bipartite ranking.
method Loss aggregation vs. label aggregation approaches.
result Label aggregation is preferable to loss aggregation due to label dictatorship issues.
New metrics found for 6k-dimensional manifolds with positive Ricci curvature.
problem Finding metrics of positive Ricci curvature on simply-connected manifolds.
method Using labeled bipartite graphs to describe certain manifolds and constructing metrics of positive Ricci curvature.
result Many new examples of 6k-dimensional manifolds with positive Ricci curvature.
Proves Khovanov homology has no torsion for bipartite circle graphs.
problem Proving properties of Khovanov homology for bipartite circle graphs.
method Proved homotopy equivalence of independence complexes to wedges of spheres.
result Extreme Khovanov homology has no torsion.
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…
Improved text summarization using belief propagation on weighted bipartite graphs.
problem Text summarization from a graph theory perspective.
method Generalized belief propagation algorithm for weighted bipartite graphs.
result Our algorithm outperforms greedy methods in text summarization tasks.
A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, and the 13 graphs obtained from by moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set incl…
GRAPE uses graph representation to handle missing data in feature imputation and label prediction.
problem Handling missing data in machine learning tasks.
method GRAPE uses a bipartite graph where observations and features are nodes, and observed feature values are edges. It formulates feature imputation as edge-level prediction and label prediction as node-level prediction, solving these with Graph Neural Networks.
result GRAPE achieves 20% lower mean absolute error for imputation and 10% lower for label prediction compared to state-of-the-art methods.
New method for matching bipartite and unipartite graphs without collapsing.
problem Matching between bipartite and unipartite networks without losing information.
method Formulated as an undirected graphical model, aligns graphs without collapsing.
result Consistent method with conditions for exact recovery of matching solution.
We define integral odd Khovanov homology of principally unimodular bipartite graph-links.
We present evidence in support of a conjecture that a bipartite graph with at least five vertices in each part and |E(G)| \geq 4 |V(G)| - 17 is intrinsically knotted. We prove the conjecture for graphs that have exactly five or exactly six vertices in one part. We also show that there is a constant C_n such that a bipa…
We characterize which automorphisms of an arbitrary complete bipartite graph can be induced by a homeomorphism of some embedding of the graph in .
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
problem Incorrect descriptions of realizable Gauss diagrams using parity conditions.
method Used bipartite graphs to describe realizable Gauss diagrams.
result Realizable Gauss diagrams can be accurately described using bipartite graphs.
The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular abstract graphs. This question has been answered for complete graphs; it is natu…
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…
We study the Thurston-Bennequin number of complete and complete bipartite Legendrian graphs. We define a new invariant called the total Thurston-Bennequin number of the graph. We show that this invariant is determined by the Thurston-Bennequin numbers of 3-cycles for complete graphs and by the Thurston-Bennequin number…
Improved bipartite link prediction using 2-hop paths.
problem Link prediction in bipartite networks without node attributes.
method Multiply reconstructed adjacency matrix with symmetrically normalized training adjacency matrix to form 2-hop paths.
result 2-hop paths improve link prediction performance.
New tests detect communities in dense bipartite graphs with high accuracy.
problem Detecting communities in dense bipartite graphs with high accuracy.
method Non-asymptotic upper and lower bounds, novel minimax-optimal tests, hard-thresholded nonlinear statistics.
result Non-asymptotic upper and lower bounds match for any configuration of graph sizes.
We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology by using the "Kauffman states" on a graph diagram.
The study proves conjecture for specific Artin groups.
problem Proving conjecture about Artin groups' properties.
method Analyzing Artin groups associated to triangle-free graphs and cones over square-free bipartite graphs.
result Proves conjecture for specific Artin groups.
We give an algorithmic computation for the height of Kauffman's clock lattice obtained from a knot diagram with two adjacent regions starred and without crossing information specified. We show that this lattice is more familiarly the graph of perfect matchings of a bipartite graph obtained from the knot diagram by over…
Temperley-Lieb algebras have been generalized to sl(3) web spaces. Since a cubic bipartite planar graph with suitable directions on edges is a web, the quantum sl(3) invariants naturally extend to all cubic bipartite planar graphs. First we completely classify them as a connected sum of primes webs. We also provide a m…
Proposes a graph-based method for active learning in regression.
problem Active learning for regression is understudied and faces challenges with noisy labels and parameter uncertainty.
method Formulates active regression as a bipartite graph optimization problem.
result Demonstrates the effectiveness of the proposed graph-based approach on benchmark data sets.
The interior polynomial is an invariant of bipartite graphs, and a part of the HOMFLY polynomial of a special alternating link coincides with the interior polynomial of the Seifert graph of the link. We extend the interior polynomial to signed bipartite graphs, and we show that, in the planar case, it is equal to a par…
The interior polynomial is an invariant of (signed) bipartite graphs, and the interior polynomial of a plane bipartite graph is equal to a part of the HOMFLY polynomial of a naturally associated link. The HOMFLY polynomial is a famous link invariant with many known properties. For example, the HOMFLY polynom…
Neural execution solves complex graph problems like bipartite matching.
problem Solving complex graph algorithms like maximum bipartite matching.
method Reduces bipartite matching to a flow problem and uses Ford-Fulkerson for maximum flow.
result Neural network achieves optimal matching almost 100% of the time.
We determine for which , the complete bipartite graph has an embedding in whose topological symmetry group is isomorphic to one of the polyhedral groups: , , or .
A quantum N-dimer modelmath.QA
Quantum model for knotted graphs from knot theory.
problem Constructing an isotopy invariant polynomial for knotted bipartite ribbon graphs.
method Applying quantum topology to construct an isotopy invariant polynomial.
result Computed the expected number of loops in the double dimer model.
Develops a new variational estimator for node popularity in bipartite networks.
problem Estimating node popularity in bipartite networks with varying patterns.
method Variational Expectation-Maximization (VEM) framework for the Two-Way Node Popularity Model (TNPM).
result The proposed method achieves superior estimation accuracy across different types of networks.
Graph neural networks speed up nonnegative matrix factorization.
problem Efficiently factorize nonnegative matrices for various applications.
method Developed a graph neural network that combines bipartite self-attention with ADMM updates.
result Significant acceleration achieved in nonnegative matrix factorization.
We present a discrete Morse-theoretic method for proving that a regular CW complex is homeomorphic to a sphere. We use this method to define bisimplices, the cells of a class of regular CW complexes we call bisimplicial complexes. The 1-skeleta of bisimplices are complete bipartite graphs making them suitable in constr…
PAC learning simplified as bipartite matching.
problem Efficiently solving PAC learning problems.
method Transductive learning and one-inclusion graphs.
result PAC learning can be reduced to bipartite matching.
Paper uses bipartite graph to forecast cross-market returns, revealing asymmetry.
problem Cross-market return predictability and asymmetry between U.S. and Chinese markets.
method Directed bipartite graph capturing time-ordered linkages, hypothesis testing for edge selection, regularized and ensemble machine learning models.
result U.S. returns predict Chinese intraday returns, but not vice versa, revealing asymmetry.
New method embeds bipartite graphs into vectors, overcoming nonlinear challenges.
problem Learning vector representations for bipartite graphs with nonparametric components.
method Semiparametric exponential family distribution, pseudo-likelihood objective, gradient descent.
result Gradient descent achieves linear convergence rate and robust to model misspecification.
The graph braid group of a complete bipartite graph is the fundamental group of a configuration space of points on the graph, which is a CAT(0) cube complex. We combine an analysis of the topology of links of vertices in this complex, the description of a hidden symmetry among the parameters, and known results from the…
Formula for weight system on complete bipartite graphs.
problem Computing values of weight system for chord diagrams.
method Chmutov-Varchenko recurrence relation, Hopf algebra projections.
result Computed values for chord diagrams with complete bipartite intersection graphs.
We study the Seifert surfaces of a link by relating the embeddings of graphs by using induced graphs. As applications, we prove that every link is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph , where all voltage assignments on the edges of $K_{2…
Let G be a connected bipartite graph with color classes E and V and root polytope Q. Regarding the hypergraph (V,E) induced by G, we prove that its interior polynomial is equivalent to the Ehrhart polynomial of Q, which in turn is equivalent to the h-vector of any triangulation of Q. It follows that the interior polyno…
This paper improves upper bounds on ribbonlength for certain alternating links.
problem Finding tighter bounds on the ribbonlength of alternating links.
method Proved a new upper bound for alternating links with bipartite dual graphs.
result Improved upper bounds on ribbonlength for specific links.
A novel approach for semi-supervised learning using regularized optimal transport.
problem Improving model performance with unlabeled data.
method Regularized optimal transport between empirical measures for affinity matrix construction, incremental label propagation, and certainty score.
result Surpasses state-of-the-art results on 12 benchmark datasets.
Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better served with specialized embedding techniques. We propose two embeddings for bip…
A strong interaction is known to exist between edge-colored graphs (which encode PL pseudo-manifolds of arbitrary dimension) and random tensor models (as a possible approach to the study of Quantum Gravity). The key tool is the {\it G-degree} of the involved graphs, which drives the {\it expansion} in the tensor …
In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights and the bias parameters that maximize the energy funct…