Spectral Graph Learning With Core Eigenvectors Prior via Iterative GLASSO and Projection

被引:0
|
作者
Bagheri, Saghar [1 ]
Do, Tam Thuc [1 ]
Cheung, Gene [1 ]
Ortega, Antonio [2 ]
机构
[1] York Univ, Dept Elect Engn & Comp Sci, Toronto, ON M3J 1P3, Canada
[2] Univ Southern Calif, Dept Elect Comp Engn, Los Angeles, CA 90089 USA
基金
加拿大自然科学与工程研究理事会;
关键词
Laplace equations; Symmetric matrices; Signal processing algorithms; Covariance matrices; Eigenvalues and eigenfunctions; Optimization; Reviews; Graph signal processing; graph learning; convex optimization;
D O I
10.1109/TSP.2024.3446453
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Before the execution of many standard graph signal processing (GSP) modules, such as compression and restoration, learning of a graph that encodes pairwise (dis)similarities in data is an important precursor. In data-starved scenarios, to reduce parameterization, previous graph learning algorithms make assumptions in the nodal domain on i) graph connectivity (e.g., edge sparsity), and/or ii) edge weights (e.g., positive edges only). In this paper, given an empirical covariance matrix (C) over bar estimated from sparse data, we consider instead a spectral-domain assumption on the graph Laplacian matrix L: the first K eigenvectors (called"core" eigenvectors){u(k)}of L are pre-selected-e.g., based on domain-specific knowledge-and only the remaining eigen vectors are learned and parameterized. We first prove that, inside a Hilbert space of real symmetric matrices, the subspace H+u of positive semi-definite (PSD) matrices sharing a common set of core K eigenvectors {u(k)} is a convex cone. Inspired by the Gram-Schmidt procedure, we then construct an efficient operator to project a given positive definite (PD) matrix on to H-u(+). Finally, we design a hybrid graphical lasso/projection algorithm to compute a locally optimal inverse Laplacian L-1 is an element of H-u(+) given (C) over bar. We apply our graph learning algorithm in two practical settings: parliamentary voting interpolation and predictive transform coding in image compression. Experiments show that our algorithm outperformed existing graph learning schemes in data-starved scenarios for both synthetic data and these two settings
引用
收藏
页码:3958 / 3972
页数:15
相关论文
共 33 条
  • [21] Multi-view Spectral Clustering via Integrating Label and Data Graph Learning
    El Hajjar, Sally
    Dornaika, Fadi
    Abdallah, Fahed
    Omrani, Hichem
    IMAGE ANALYSIS AND PROCESSING, ICIAP 2022, PT III, 2022, 13233 : 109 - 120
  • [22] FI-GRL: Fast Inductive Graph Representation Learning via Projection-Cost Preservation
    Jiang, Fei
    Zheng, Lei
    Xu, Jin
    Yu, Philip S.
    2018 IEEE INTERNATIONAL CONFERENCE ON DATA MINING (ICDM), 2018, : 1067 - 1072
  • [23] Multi-Task Learning for Lung Disease Classification and Report Generation via Prior Graph Structure and Contrastive Learning
    Guo, Kaifeng
    Zheng, Shihao
    Huang, Ri
    Gao, Rongjian
    IEEE ACCESS, 2023, 11 : 110888 - 110898
  • [24] LEARNING SPECTRAL-SPATIAL PRIOR VIA 3DDNCNN FOR HYPERSPECTRAL IMAGE DECONVOLUTION
    Wang, Xiuheng
    Chen, Jie
    Richard, Cedric
    Brie, David
    2020 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, 2020, : 2403 - 2407
  • [25] Spectral clustering via sparse graph structure learning with application to proteomic signaling networks in cancer
    Banerjee, Sayantan
    Akbani, Rehan
    Baladandayuthapani, Veerabhadran
    COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2019, 132 : 46 - 69
  • [26] Spectral CT Image-Domain Material Decomposition via Sparsity Residual Prior and Dictionary Learning
    Zhang, Tao
    Yu, Haijun
    Xi, Yarui
    Wang, Shaoyu
    Liu, Fenglin
    IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 2023, 72
  • [27] Spectral CT Image-Domain Material Decomposition via Sparsity Residual Prior and Dictionary Learning
    Zhang, Tao
    Yu, Haijun
    Xi, Yarui
    Wang, Shaoyu
    Liu, Fenglin
    IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 2023, 72
  • [28] Spectral CT Image-Domain Material Decomposition via Sparsity Residual Prior and Dictionary Learning
    Zhang, Tao
    Yu, Haijun
    Xi, Yarui
    Wang, Shaoyu
    Liu, Fenglin
    IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 2023, 72
  • [29] Deep-learning-based projection-domain breast thickness estimation for shape-prior iterative image reconstruction in digital breast tomosynthesis
    Lee, Seoyoung
    Kim, Hyeongseok
    Lee, Hoyeon
    Cho, Seungryong
    MEDICAL PHYSICS, 2022, 49 (06) : 3670 - 3682
  • [30] One step multi-view spectral clustering via joint adaptive graph learning and matrix factorization
    Yang, Wenqi
    Wang, Yansu
    Tang, Chang
    Tong, Hengjian
    Wei, Ao
    Wu, Xia
    NEUROCOMPUTING, 2023, 524 : 95 - 105