GAP uses deep learning to efficiently partition graphs.
problem Graph partitioning to minimize edge cut.
method Deep learning approach with a differentiable loss function.
result GAP achieves competitive partitions and generalizes to unseen graphs.
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48 results for “Graph partitioning”
In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graph partitions. The two types of measures, graph-aware and set parti…
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…
A scalable method for graph partitioning and matching using Gromov-Wasserstein discrepancy.
problem Graph partitioning and matching for large-scale graphs.
method Recursive -partition mechanism with proximal gradient algorithm.
result Achieves a trade-off between accuracy and efficiency.
New method improves nearest neighbor search using neural networks and graph partitioning.
problem Efficient nearest neighbor search in high-dimensional spaces.
method Developed a new framework for space partitioning using neural networks and graph partitioning.
result Neural LSH partitions outperform existing methods on standard benchmarks.
FairGP uses graph partitioning to make Graph Transformers fair and scalable.
problem Fairness issues in Graph Transformers, especially against sensitive features.
method Graph partitioning to minimize the influence of higher-order nodes and optimize attention mechanisms.
result FairGP improves fairness in Graph Transformers while reducing computational complexity.
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …
We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for …
We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally propagating information between the subgraphs. To efficiently partition graphs, we …
Min-cut clustering, based on minimizing one of two heuristic cost-functions proposed by Shi and Malik, has spawned tremendous research, both analytic and algorithmic, in the graph partitioning and image segmentation communities over the last decade. It is however unclear if these heuristics can be derived from a more g…
Unified framework for differentiable graph partitioning with probabilistic cuts.
problem Lack of general guarantees and principled gradients in prior probabilistic relaxations of graph cuts.
method Unified probabilistic framework covering a wide class of cuts, including Normalized Cut, with tight analytic upper bounds.
result Rigorous, numerically stable foundation for scalable, differentiable graph partitioning.
PSimGNN partitions graphs into subgraphs for efficient graph similarity computation.
problem Efficiently compute graph similarity scores for large graphs.
method Graph partitioning followed by subgraph-level and node-level comparisons using a graph neural network.
result PSimGNN outperforms state-of-the-art methods in graph similarity computation tasks.
A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.
problem Capturing super-dyadic interactions in k-uniform hypergraphs.
method Tensor-based representation and tensor eigenvalue decomposition for capturing interactions.
result Improved min-cut solution on 2-uniform hypergraphs (graphs) compared to standard spectral partitioning.
Improved spectral clustering via Gromov-Wasserstein Learning.
problem Optimizing graph partitioning performance.
method Bridge spectral clustering and GWL, using heat kernel for stable node correspondences.
result Improved graph partitioning results without compromising theoretical guarantees.
This paper proposes a method to learn graph representations by partitioning edges into communities.
problem Graph neural networks ignore how edges are formed, leading to suboptimal representation learning.
method Introduces a generative model to partition edges into community-specific weighted edges, then uses these for GNN-based inference and classification.
result The method learns discriminative representations for both node-level and graph-level classification tasks.
A new method learns graph compression from data.
problem Graphs lack ordering, making conventional compression algorithms ineffective.
method Partition and Code framework: decompose, learn, encode.
result PnC achieves compression gains that grow with graph size.
We classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices. For graphs in these families, we verify a conjecture presented in Adams' "The Knot Book": If a vertex is remo…
This study proposes a graph partitioning method to improve spatial prediction models.
problem Improving interpretability of spatial prediction models in industries.
method Graph partitioning problem to minimize within-segment variances, formulated as mixed-integer quadratic programming.
result Approximation scheme efficiently identifies spatial segments, improving computational efficiency.
Graph-partitioning-based DCRNN improves traffic forecasting for large highways.
problem Challenges in accurately forecasting traffic on large highway networks.
method Graph-partitioning method to decompose large networks into smaller, independent networks.
result Demonstrated improved traffic forecasting on a large California highway network.
PASCO speeds up graph clustering for large graphs.
problem Efficiently clustering large graphs with many communities.
method Overlay method combining coarsening and parallel clustering.
result PASCO accelerates clustering with improved efficiency and quality.
Enhances robustness of multi-view clustering via partition fusion.
problem Dealing with noises and inconsistency in multi-view data.
method Generates multiple partitions, integrates them, and co-evolves graph learning, partition generation, and view weight learning.
result Empirical results verify the effectiveness and robustness of the proposed approach.
We find the minimal number of links in an embedding of any complete -partite graph on 7 vertices (including , which has at least 21 links). We give either exact values or upper and lower bounds for the minimal number of links for all complete -partite graphs on 8 vertices. We also look at larger complete bip…
Let φ(G) be the minimum conductance of an undirected graph G, and let 0=λ_1 <= λ_2 <=... <= λ_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, φ(G) = O(k) λ_2 / \sqrt{λ_k}, and this performance guarantee is achieved by the spectral partitioning algorithm. …
Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph accor…
New method for distributed online learning with communication constraints reduces joint regret.
problem Joint regret minimization in a distributed online learning setting with communication constraints.
method Adaptive graph partitioning and comparator-adaptive online convex optimization with delayed gradient information.
result Optimal graph partition selection for adversarial activations and gradients reduces joint regret.
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified and a novel rearrangement algorithm is proposed, which we show is strictly decreas…
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is demonstrated to efficiently solve eigenvalue problems for graph Laplacians that appear in spectral clustering. For static graph partitioning, 10-20 iterations of LOBPCG without preconditioning result in ~10x error reduction, enough to achieve 100% corr…
Improved taxi demand-supply forecasts using graph-based LSTM.
problem Accurate taxi demand-supply forecasting with complex spatial and temporal patterns.
method Investigated impact of spatial partitioning techniques (Voronoi vs. Geohash) on LSTM network performance.
result GraphLSTM offers competitive performance against ConvLSTM, at lower complexity, across real-world data sets.
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph part…
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary pot…
Graphs can model interactions between vertices, but how well depends on graph structure.
problem Lack of formal characterization of GNNs' ability to model interactions between vertices.
method Formalized interaction strength using separation rank and quantified it for different partitions of vertices.
result GNNs' ability to model interactions is primarily determined by the partition's walk index.
We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that a top-down sensing procedure can identify these partitions, and hence the activa…
Develops a new weighted Laplacian method for graph problems.
problem Graph partitioning and balanced minimum cut problems.
method Weighted Laplacian method based on graph theory and PDEs.
result Established equivalence relations among graph problems.
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise naturally when working with factor graphs. Belief propagation is a widely deplo…
New spectral clustering method using LASSO regularization for robust graph partitioning.
problem Lack of theoretical guarantees for spectral clustering on general graph models.
method 1-spectral clustering on a new random model with LASSO regularization.
result Effective and robust to small noise perturbations, validated by simulations and real data.
Improved spectral clustering algorithm for better performance.
problem Improving the performance of spectral clustering algorithms.
method Developed a new performance guarantee under a weaker assumption and evaluated using a different spectral embedding map.
result Better performance guarantee under a weaker assumption and evaluation of a new spectral embedding map.
A new algorithm reduces CI tests for causal graph recovery.
problem Exponential CI tests limit causal discovery algorithms.
method CCPG (Causal Consistent Partition Graph) with polynomial CI tests.
result CCPG efficiently recovers causal graph with polynomial tests.
SON-GOKU uses graph coloring to improve multi-task learning by partitioning tasks into compatible groups.
problem Gradient interference between conflicting multi-task learning objectives slows convergence and model performance.
method SON-GOKU computes gradient interference, constructs an interference graph, and applies greedy graph-coloring to partition tasks.
result SON-GOKU consistently outperforms baselines and state-of-the-art multi-task optimizers on six datasets.
A new algorithm efficiently partitions images without seeds or thresholds.
problem Efficiently partitioning images without explicit seeds or thresholds.
method Mutex Watershed algorithm that incorporates both attractive and repulsive cues.
result Determines optimal segments without seeds or thresholds, solving NP-hard problem.
We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods to get algorithms for calculating partition functions in these families. These …
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We prove that certain decompositions lead to a theoretically optimal condition number.…
The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph, they are not in th…
Efficient algorithm for matching graphs with community structure.
problem Graph matching between correlated stochastic block models with constant correlation.
method Partition trees rooted from each vertex, comparing edge statistics to different communities.
result First low-order polynomial-time algorithm achieving exact matching with high probability in dense graphs.
Consistent spectral clustering with fairness constraints on representation graphs.
problem Finding balanced clusters in similarity graphs with fairness constraints.
method Developed variants of unnormalized and normalized spectral clustering for fair planted partitions.
result Consistency results for constrained spectral clustering under fair planted partitions.
Graph Unlearningcs.LG
GraphEraser improves unlearning efficiency for graph data.
problem Improving unlearning efficiency for graph data.
method Two novel graph partition algorithms and a learning-based aggregation method.
result Achieves up to 35.94× unlearning time improvement on large datasets.
We give a Conway-Gordon type formula for invariants of knots and links in a spatial complete four-partite graph in terms of the square of the linking number and the second coefficient of the Conway polynomial. As an application, we show that every rectilinear spatial contains a nontrivial Ha…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data since they tend to emphasize cut sizes over cut values. We propose a graph partit…
Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploi…