Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks

• URL: http://arxiv.org/abs/2206.08465v2
• Date: Wed, 5 Jun 2024 19:32:37 GMT
• Title: Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks
• Abstract summary: We introduce the degree-corrected latent block model (DC-LBM), which accounts for the varying degrees in row and column clusters. We develop an efficient variational expectation-maximization algorithm by creating closed-form solutions for parameter estimates in the M steps.
• Score: 1.0923877073891446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bipartite graphs are ubiquitous across various scientific and engineering fields. Simultaneously grouping the two types of nodes in a bipartite graph via biclustering represents a fundamental challenge in network analysis for such graphs. The latent block model (LBM) is a commonly used model-based tool for biclustering. However, the effectiveness of the LBM is often limited by the influence of row and column sums in the data matrix. To address this limitation, we introduce the degree-corrected latent block model (DC-LBM), which accounts for the varying degrees in row and column clusters, significantly enhancing performance on real-world data sets and simulated data. We develop an efficient variational expectation-maximization algorithm by creating closed-form solutions for parameter estimates in the M steps. Furthermore, we prove the label consistency and the rate of convergence of the variational estimator under the DC-LBM, allowing the expected graph density to approach zero as long as the average expected degrees of rows and columns approach infinity when the size of the graph increases.

Related papers

• Clusterpath Gaussian Graphical Modeling [0.0]
  We introduce the Clusterpath estimator of the Gaussian Graphical Model (CGGM) that encourages variable clustering in a data-driven way. We present a computationally efficient implementation of the CGGM estimator by using a cyclic block coordinate descent algorithm. In simulations, we show that CGGM not only matches, but oftentimes outperforms other state-of-the-art methods for variable clustering in graphical models.
  arXiv  Detail & Related papers  (2024-06-30T10:11:18Z)
• Maximum Likelihood Estimation on Stochastic Blockmodels for Directed Graph Clustering [22.421702511126373]
  We formulate clustering as estimating underlying communities in the directed block model. We introduce two efficient and interpretable directed clustering algorithms, a spectral clustering algorithm and a semidefinite programming based clustering algorithm.
  arXiv  Detail & Related papers  (2024-03-28T15:47:13Z)
• Sparse Training of Discrete Diffusion Models for Graph Generation [45.103518022696996]
  We introduce SparseDiff, a novel diffusion model based on the observation that almost all large graphs are sparse. By selecting a subset of edges, SparseDiff effectively leverages sparse graph representations both during the noising process and within the denoising network. Our model demonstrates state-of-the-art performance across multiple metrics on both small and large datasets.
  arXiv  Detail & Related papers  (2023-11-03T16:50:26Z)
• One-step Bipartite Graph Cut: A Normalized Formulation and Its Application to Scalable Subspace Clustering [56.81492360414741]
  We show how to enforce a one-step normalized cut for bipartite graphs, especially with linear-time complexity. In this paper, we first characterize a novel one-step bipartite graph cut criterion with normalized constraints, and theoretically prove its equivalence to a trace problem. We extend this cut criterion to a scalable subspace clustering approach, where adaptive anchor learning, bipartite graph learning, and one-step normalized bipartite graph partitioning are simultaneously modeled.
  arXiv  Detail & Related papers  (2023-05-12T11:27:20Z)
• 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)
• Interpolation-based Correlation Reduction Network for Semi-Supervised Graph Learning [49.94816548023729]
  We propose a novel graph contrastive learning method, termed Interpolation-based Correlation Reduction Network (ICRN) In our method, we improve the discriminative capability of the latent feature by enlarging the margin of decision boundaries. By combining the two settings, we extract rich supervision information from both the abundant unlabeled nodes and the rare yet valuable labeled nodes for discnative representation learning.
  arXiv  Detail & Related papers  (2022-06-06T14:26:34Z)
• An Interpretable Graph Generative Model with Heterophily [38.59200985962146]
  We propose the first edge-independent graph generative model that is expressive enough to capture heterophily. Our experiments demonstrate the effectiveness of our model for a variety of important application tasks.
  arXiv  Detail & Related papers  (2021-11-04T17:34:39Z)
• T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs [0.0]
  In graph-structured data, structured sparsity and smoothness tend to cluster together. We propose a new prior for high dimensional parameters with graphical relations. We use it to detect structured sparsity and smoothness simultaneously.
  arXiv  Detail & Related papers  (2021-07-06T10:10:03Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• Multilayer Clustered Graph Learning [66.94201299553336]
  We use contrastive loss as a data fidelity term, in order to properly aggregate the observed layers into a representative graph. Experiments show that our method leads to a clustered clusters w.r.t. We learn a clustering algorithm for solving clustering problems.
  arXiv  Detail & Related papers  (2020-10-29T09:58:02Z)
• Graph Gamma Process Generalized Linear Dynamical Systems [60.467040479276704]
  We introduce graph gamma process (GGP) linear dynamical systems to model real multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences. We use the generated random graph, whose number of nonzero-degree nodes is finite, to define both the sparsity pattern and dimension of the latent state transition matrix.
  arXiv  Detail & Related papers  (2020-07-25T04:16:34Z)
• Estimation of sparse Gaussian graphical models with hidden clustering structure [8.258451067861932]
  We propose a model to estimate the sparse Gaussian graphical models with hidden clustering structure. We develop a symmetric Gauss-Seidel based alternating direction method of the multipliers. Numerical experiments on both synthetic data and real data demonstrate the good performance of our model.
  arXiv  Detail & Related papers  (2020-04-17T08:43:31Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)

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.