Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy

• URL: http://arxiv.org/abs/2106.07501v2
• Date: Thu, 13 Jul 2023 05:51:09 GMT
• Title: Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy
• Authors: Zhicheng Guo, Jiaxuan Zhao, Licheng Jiao, Xu Liu
• Abstract summary: We propose a balanced coarsening scheme for multilevel hypergraph. An initial partitioning algorithm is designed to improve the quality of k-way hypergraph.
• Score: 40.93626211612559
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT algorithm, we generate a prior hypergraph under a relaxed balance constraint. With the prior hypergraph, we have defined the Wasserstein discrepancy to coordinate the optimal transport of coarsening process. And the optimal transport matrix is solved by Sinkhorn algorithm. Our coarsening scheme fully takes into account the minimization of connectivity metric (objective function). For the initial partitioning stage, we define a normalized cut function induced by Fiedler vector, which is theoretically proved to be a concave function. Thereby, a three-point algorithm is designed to find the best cut under the balance constraint.

Related papers

• A Sample Efficient Alternating Minimization-based Algorithm For Robust Phase Retrieval [56.67706781191521]
  In this work, we present a robust phase retrieval problem where the task is to recover an unknown signal. Our proposed oracle avoids the need for computationally spectral descent, using a simple gradient step and outliers.
  arXiv  Detail & Related papers  (2024-09-07T06:37:23Z)
• Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity [59.75300530380427]
  We consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds.
  arXiv  Detail & Related papers  (2024-06-28T02:56:22Z)
• Graph Cuts with Arbitrary Size Constraints Through Optimal Transport [18.338458637795263]
  We propose a new graph cut algorithm for partitioning graphs under arbitrary size constraints. We solve it using an accelerated proximal GD algorithm which guarantees global convergence to a critical point.
  arXiv  Detail & Related papers  (2024-02-07T10:33:09Z)
• Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization [39.352542703876104]
  This paper considers decentralized convex composite optimization over undirected and connected networks. A novel CTA (Combine-Then-Adapt)-based decentralized algorithm is proposed under uncoordinated network-independent constant stepsizes.
  arXiv  Detail & Related papers  (2023-02-07T03:50:38Z)
• Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model [6.681901523019242]
  We consider the community detection problem in random hypergraphs under the nonuniform hypergraph block model (HSBM) We provide a spectral algorithm that outputs a partition with at least a $gamma$ fraction of the vertices classified correctly, where $gammain depends on the signal-to-noise ratio (SNR) of the model. The theoretical analysis of our algorithm relies on the concentration and regularization of the adjacency matrix for non-uniform random hypergraphs, which can be of independent interest.
  arXiv  Detail & Related papers  (2021-12-22T05:38:33Z)
• Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation [71.27989298860481]
  We address the non- optimisation problem of finding a matrix on the Stiefel manifold that maximises a quadratic objective function. We propose a simple yet effective sparsity-promoting algorithm for finding the dominant eigenspace matrix.
  arXiv  Detail & Related papers  (2021-09-30T19:17:35Z)
• Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks [79.16773494166644]
  We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network. We design two optimal algorithms that attain these lower bounds. We corroborate the theoretical efficiency of these algorithms by performing an experimental comparison with existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-08T15:54:44Z)
• Hybrid Trilinear and Bilinear Programming for Aligning Partially Overlapping Point Sets [85.71360365315128]
  In many applications, we need algorithms which can align partially overlapping point sets are invariant to the corresponding corresponding RPM algorithm. We first show that the objective is a cubic bound function. We then utilize the convex envelopes of trilinear and bilinear monomial transformations to derive its lower bound. We next develop a branch-and-bound (BnB) algorithm which only branches over the transformation variables and runs efficiently.
  arXiv  Detail & Related papers  (2021-01-19T04:24:23Z)
• Hypergraph Partitioning using Tensor Eigenvalue Decomposition [19.01626581411011]
  We propose a novel approach for the partitioning of k-uniform hypergraphs. Most of the existing methods work by reducing the hypergraph to a graph followed by applying standard graph partitioning algorithms. We overcome this issue by utilizing the tensor-based representation of hypergraphs.
  arXiv  Detail & Related papers  (2020-11-16T01:55:43Z)
• S-ADDOPT: Decentralized stochastic first-order optimization over directed graphs [16.96562173221624]
  Decentralized convex optimization is proposed to minimize a sum of smooth and strongly cost functions when the functions are distributed over a directed network nodes. In particular, we propose thetextbftextttS-ADDOPT algorithm that assumes a first-order oracle at each node. For decaying step-sizes$mathcalO (1/k)$, we show thattextbfttS-ADDOPT reaches the exact solution subly at$mathcalO (1/k)$ and its convergence is networkally-independent
  arXiv  Detail & Related papers  (2020-05-15T21:14:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.