Multi-Frequency Joint Community Detection and Phase Synchronization

• URL: http://arxiv.org/abs/2206.12276v3
• Date: Fri, 8 Dec 2023 15:32:37 GMT
• Title: Multi-Frequency Joint Community Detection and Phase Synchronization
• Authors: Lingda Wang and Zhizhen Zhao
• Abstract summary: This paper studies the joint community detection and phase synchronization problem on the textitstochastic block model with relative phase We show this problem exhibits a textitmulti-frequency'' structure by closely examining its maximum likelihood estimation (MLE) formulation. Two simple yet efficient algorithms that leverage the MLE formulation and benefit from the information across multiple frequencies are proposed.
• Score: 22.683901672480353
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies the joint community detection and phase synchronization problem on the \textit{stochastic block model with relative phase}, where each node is associated with an unknown phase angle. This problem, with a variety of real-world applications, aims to recover the cluster structure and associated phase angles simultaneously. We show this problem exhibits a \textit{``multi-frequency''} structure by closely examining its maximum likelihood estimation (MLE) formulation, whereas existing methods are not originated from this perspective. To this end, two simple yet efficient algorithms that leverage the MLE formulation and benefit from the information across multiple frequencies are proposed. The former is a spectral method based on the novel multi-frequency column-pivoted QR factorization. The factorization applied to the top eigenvectors of the observation matrix provides key information about the cluster structure and associated phase angles. The second approach is an iterative multi-frequency generalized power method, where each iteration updates the estimation in a matrix-multiplication-then-projection manner. Numerical experiments show that our proposed algorithms significantly improve the ability of exactly recovering the cluster structure and the accuracy of the estimated phase angles, compared to state-of-the-art algorithms.

Related papers

• Multiple kernel concept factorization algorithm based on global fusion [9.931283387968856]
  In unsupervised environment, to design or select proper kernel function for specific dataset, a new algorithm called Globalized Multiple Kernel(GMKCF)was proposed. The proposed algorithm outperforms comparison algorithms in data clustering, such as Kernel K-Means(KKM), Spectral Clustering(SC), CF Kernel(KCF), Co-regularized multi-view spectral clustering(Coreg), and Robust Multiple KKM(RMKKM)
  arXiv  Detail & Related papers  (2024-10-27T09:13:57Z)
• An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
  Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
  arXiv  Detail & Related papers  (2023-09-30T15:57:14Z)
• Multi-View Clustering via Semi-non-negative Tensor Factorization [120.87318230985653]
  We develop a novel multi-view clustering based on semi-non-negative tensor factorization (Semi-NTF) Our model directly considers the between-view relationship and exploits the between-view complementary information. In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point.
  arXiv  Detail & Related papers  (2023-03-29T14:54:19Z)
• Optimal Algorithms for the Inhomogeneous Spiked Wigner Model [89.1371983413931]
  We derive an approximate message-passing algorithm (AMP) for the inhomogeneous problem. We identify in particular the existence of a statistical-to-computational gap where known algorithms require a signal-to-noise ratio bigger than the information-theoretic threshold to perform better than random.
  arXiv  Detail & Related papers  (2023-02-13T19:57:17Z)
• Fast conformational clustering of extensive molecular dynamics simulation data [19.444636864515726]
  We present an unsupervised data processing workflow that is specifically designed to obtain a fast conformational clustering of long trajectories. We combine two dimensionality reduction algorithms (cc_analysis and encodermap) with a density-based spatial clustering algorithm (HDBSCAN) With the help of four test systems we illustrate the capability and performance of this clustering workflow.
  arXiv  Detail & Related papers  (2023-01-11T14:36:43Z)
• Perfect Spectral Clustering with Discrete Covariates [68.8204255655161]
  We propose a spectral algorithm that achieves perfect clustering with high probability on a class of large, sparse networks. Our method is the first to offer a guarantee of consistent latent structure recovery using spectral clustering.
  arXiv  Detail & Related papers  (2022-05-17T01:41:06Z)
• A Spectral Method for Joint Community Detection and Orthogonal Group Synchronization [20.413250472034143]
  We propose a simple algorithm that consists of a spectral decomposition step followed by a blockwise column pivoted QR factorization (CPQR) The proposed algorithm is efficient and scales linearly with the number of data points. We also leverage the recently developed leave-one-out' technique to establish a near-optimal guarantee for exact recovery of the cluster memberships.
  arXiv  Detail & Related papers  (2021-12-25T07:38:14Z)
• Quantile-based fuzzy clustering of multivariate time series in the frequency domain [2.610470075814367]
  fuzzy C-means and fuzzy C-medoids algorithms are proposed. The performance of the proposed approach is evaluated in a broad simulation study. Two specific applications involving air quality and financial databases illustrate the usefulness of our approach.
  arXiv  Detail & Related papers  (2021-09-08T15:38:33Z)
• 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)
• Conjugate Mixture Models for Clustering Multimodal Data [24.640116037967985]
  The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. We show that multimodal clustering can be addressed within a novel framework, namely conjugate mixture models.
  arXiv  Detail & Related papers  (2020-12-09T10:13:22Z)
• Kullback-Leibler Divergence-Based Fuzzy $C$-Means Clustering Incorporating Morphological Reconstruction and Wavelet Frames for Image Segmentation [152.609322951917]
  We come up with a Kullback-Leibler (KL) divergence-based Fuzzy C-Means (FCM) algorithm by incorporating a tight wavelet frame transform and a morphological reconstruction operation. The proposed algorithm works well and comes with better segmentation performance than other comparative algorithms.
  arXiv  Detail & Related papers  (2020-02-21T05:19:10Z)

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.