Bounded Projection Matrix Approximation with Applications to Community Detection

• URL: http://arxiv.org/abs/2305.15430v1
• Date: Sun, 21 May 2023 06:55:10 GMT
• Title: Bounded Projection Matrix Approximation with Applications to Community Detection
• Authors: Zheng Zhai, Hengchao Chen and Qiang Sun
• Abstract summary: We introduce a new differentiable convex penalty and derive an alternating direction method of multipliers (ADMM) algorithm. Numerical experiments demonstrate the superiority of our algorithm over its competitors.
• Score: 1.8876415010297891
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable convex penalty and derive an alternating direction method of multipliers (ADMM) algorithm. Theoretically, we establish the convergence properties of the proposed algorithm. Numerical experiments demonstrate the superiority of our algorithm over its competitors, such as the semi-definite relaxation method and spectral clustering.

Related papers

• Bregman-divergence-based Arimoto-Blahut algorithm [53.64687146666141]
  We generalize the Arimoto-Blahut algorithm to a general function defined over Bregman-divergence system. We propose a convex-optimization-free algorithm that can be applied to classical and quantum rate-distortion theory.
  arXiv  Detail & Related papers  (2024-08-10T06:16:24Z)
• Regularized Projection Matrix Approximation with Applications to Community Detection [1.3761665705201904]
  This paper introduces a regularized projection matrix approximation framework designed to recover cluster information from the affinity matrix. We investigate three distinct penalty functions, each specifically tailored to address bounded, positive, and sparse scenarios. Numerical experiments conducted on both synthetic and real-world datasets reveal that our regularized projection matrix approximation approach significantly outperforms state-of-the-art methods in clustering performance.
  arXiv  Detail & Related papers  (2024-05-26T15:18:22Z)
• Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms [63.03966552670014]
  We discuss the key related theoretical aspects, with a particular focus on the fairness properties of primal optima and associated risk allocations. The algorithms we provide allow for learning primals, optima for the dual representation and corresponding fair risk allocations.
  arXiv  Detail & Related papers  (2023-02-02T22:16:49Z)
• Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity [15.023842222803058]
  Current algorithms are designed using the block coordinate descent method or the proximal point algorithm. We propose a novel algorithm based on the two-metric projection method, incorporating a carefully designed search direction and variable partitioning scheme. Experimental results on synthetic and real-world datasets demonstrate that our proposed algorithm provides a significant improvement in computational efficiency compared to the state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-12-03T14:39:10Z)
• Amortized Implicit Differentiation for Stochastic Bilevel Optimization [53.12363770169761]
  We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
  arXiv  Detail & Related papers  (2021-11-29T15:10:09Z)
• A proximal-proximal majorization-minimization algorithm for nonconvex tuning-free robust regression problems [4.261680642170457]
  We introduce proximal-proximal majorization-minimization (PPMM) algorithm for non regression problems. Our proposed algorithm outperforms the existing state-of-the-art algorithms.
  arXiv  Detail & Related papers  (2021-06-25T15:07:13Z)
• Converting ADMM to a Proximal Gradient for Convex Optimization Problems [4.56877715768796]
  In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. This paper proposes a general method for converting the ADMM solution to the proximal gradient method, assuming that the constraints and objectives are strongly convex. We show by numerical experiments that we can obtain a significant improvement in terms of efficiency.
  arXiv  Detail & Related papers  (2021-04-22T07:41:12Z)
• Accelerated Message Passing for Entropy-Regularized MAP Inference [89.15658822319928]
  Maximum a posteriori (MAP) inference in discrete-valued random fields is a fundamental problem in machine learning. Due to the difficulty of this problem, linear programming (LP) relaxations are commonly used to derive specialized message passing algorithms. We present randomized methods for accelerating these algorithms by leveraging techniques that underlie classical accelerated gradient.
  arXiv  Detail & Related papers  (2020-07-01T18:43:32Z)
• IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method [64.15649345392822]
  We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds.
  arXiv  Detail & Related papers  (2020-06-11T18:49:06Z)
• SONIA: A Symmetric Blockwise Truncated Optimization Algorithm [2.9923891863939938]
  This work presents a new algorithm for empirical risk. The algorithm bridges the gap between first- and second-order search methods by computing a second-order search-type update in one subspace, coupled with a scaled steepest descent step in the Theoretical complement.
  arXiv  Detail & Related papers  (2020-06-06T19:28:14Z)
• Optimal Randomized First-Order Methods for Least-Squares Problems [56.05635751529922]
  This class of algorithms encompasses several randomized methods among the fastest solvers for least-squares problems. We focus on two classical embeddings, namely, Gaussian projections and subsampled Hadamard transforms. Our resulting algorithm yields the best complexity known for solving least-squares problems with no condition number dependence.
  arXiv  Detail & Related papers  (2020-02-21T17:45:32Z)

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.