Regularized Projection Matrix Approximation with Applications to Community Detection

• URL: http://arxiv.org/abs/2405.16598v2
• Date: Thu, 07 Nov 2024 13:12:55 GMT
• Title: Regularized Projection Matrix Approximation with Applications to Community Detection
• Authors: Zheng Zhai, Jialu Xu, Mingxin Wu, Xiaohui Li,
• Abstract summary: 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.
• Score: 1.3761665705201904
• License:
• Abstract: This paper introduces a regularized projection matrix approximation framework designed to recover cluster information from the affinity matrix. The model is formulated as a projection approximation problem, incorporating an entry-wise penalty function. We investigate three distinct penalty functions, each specifically tailored to address bounded, positive, and sparse scenarios. To solve this problem, we propose direct optimization on the Stiefel manifold, utilizing the Cayley transformation along with the Alternating Direction Method of Multipliers (ADMM) algorithm. Additionally, we provide a theoretical analysis that establishes the convergence properties of ADMM, demonstrating that the convergence point satisfies the KKT conditions of the original problem. 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.

Related papers

• A unified consensus-based parallel ADMM algorithm for high-dimensional regression with combined regularizations [3.280169909938912]
  parallel alternating multipliers (ADMM) is widely recognized for its effectiveness in handling large-scale distributed datasets. The proposed algorithms serve to demonstrate the reliability, stability, and scalability of a financial example.
  arXiv  Detail & Related papers  (2023-11-21T03:30:38Z)
• Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model [13.082805815235975]
  We introduce a novel framework called Mode-wise Principal Subspace Pursuit (MOP-UP) to extract hidden variations in both the row and column dimensions for matrix data. The effectiveness and practical merits of the proposed framework are demonstrated through experiments on both simulated and real datasets.
  arXiv  Detail & Related papers  (2023-07-02T13:59:47Z)
• Bounded Projection Matrix Approximation with Applications to Community Detection [1.8876415010297891]
  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.
  arXiv  Detail & Related papers  (2023-05-21T06:55:10Z)
• Manifold Gaussian Variational Bayes on the Precision Matrix [70.44024861252554]
  We propose an optimization algorithm for Variational Inference (VI) in complex models. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models.
  arXiv  Detail & Related papers  (2022-10-26T10:12:31Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation [64.49871502193477]
  We propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. Comprehensive experimental results on six commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-05-21T01:47:17Z)
• Jointly Modeling and Clustering Tensors in High Dimensions [6.072664839782975]
  We consider the problem of jointly benchmarking and clustering of tensors. We propose an efficient high-maximization algorithm that converges geometrically to a neighborhood that is within statistical precision.
  arXiv  Detail & Related papers  (2021-04-15T21:06:16Z)
• Multi-View Spectral Clustering with High-Order Optimal Neighborhood Laplacian Matrix [57.11971786407279]
  Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data. This paper proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix. Our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base.
  arXiv  Detail & Related papers  (2020-08-31T12:28:40Z)
• Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes [3.564709604457361]
  "Projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. The benefits of our proposed framework, are illustrated on the computationally challenging three-dimensional aerodynamic optimization of a last-stage blade for an industrial gas turbine.
  arXiv  Detail & Related papers  (2020-08-05T22:28:53Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)

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.