Paper compares graph and set partition measures for graph clustering.
problem Comparing graph clustering methods using different similarity measures.
method Introduces graph-aware partition similarity measures and compares them with set partition measures.
result Graph-aware measures provide complementary information to set partition measures.
Better spectral partitioning of signed graphs using standard Laplacian.
problem Meaningless partitioning using signed Laplacian eigenvectors.
method Use standard graph Laplacian for spectral partitioning.
result Fiedler vector of standard Laplacian is easier to compute and more beneficial.
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.
A scalable method for graph partitioning and matching using Gromov-Wasserstein discrepancy.
problem Graph partitioning and matching for large-scale graphs.
method Recursive K-partition mechanism with proximal gradient algorithm. result Achieves a trade-off between accuracy and efficiency.
GPNNs improve semi-supervised classification on large graphs.
problem Handling large graphs for semi-supervised classification.
method Alternates local and global graph propagation with partitioning.
result GPNNs achieve similar performance with fewer steps than standard GNNs.
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 K4,4,1…
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…
Mean-field theory improves understanding of GNN in graph partitioning.
problem Understanding the performance and flexibility of GNN in graph partitioning.
method Developed a mean-field theory for a minimal GNN architecture.
result Good agreement between theory and numerical experiments.
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.
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.
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.
New graph-based preconditioners speed up optimization on graph data.
problem Optimizing functions on graph data structures.
method Construct combinatorial preconditioners from graph partitions.
result Provable optimal condition numbers for certain decompositions.
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.
New insights into belief propagation and Bethe approximation for factor graphs.
problem Understanding the correctness and efficiency of belief propagation and its relation to partition functions.
method Viewing factor graphs through the lens of polynomials and reformulating Bethe approximation as a polynomial optimization problem.
result For bipartite normal factor graphs, the Bethe approximation is a lower bound to the partition function under certain analytic conditions.
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. …
We find the minimal number of links in an embedding of any complete k-partite graph on 7 vertices (including K7, 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 k-partite graphs on 8 vertices. We also look at larger complete bip…
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…
LOBPCG speeds up spectral clustering for streaming graphs, reducing computation time and memory usage.
problem Efficiently partitioning large graphs in streaming environments.
method Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) for graph Laplacians.
result LOBPCG reduces computation time by 100-1000x for streaming graphs compared to static graph partitioning.
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.
New method for clustering imbalanced clusters.
problem Spectral clustering's sensitivity to imbalanced clusters.
method Proposes a graph partitioning problem with minimum size constraints to handle imbalanced cluster sizes.
result Demonstrates superiority of the proposed method through experiments.
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.
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…
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.
New method approximates partition function of graphical models using gauge functions and polynomials.
problem Computing the partition function of graphical models is computationally challenging.
method Combines gauge function technique with real stable polynomials to approximate partition function.
result Belief Propagation estimations in the sequence do not decrease and low-bound the partition function.
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.
The paper shows how discrete Dirichlet partitions converge to continuum partitions.
problem Consistency of Dirichlet partitions on graphs and domains.
method Variational formulation and Γ-convergence of discrete to continuum Dirichlet energies.
result Discrete Dirichlet energies Γ-converge to continuum Dirichlet energies.
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 …
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.