Model selection-inspired coefficients optimization for polynomial-kernel graph learning

Cheng Yang, Fen Wang, Minxiang Ye, Guangtao Zhai, Xiao-Ping Zhang, Vladimir Stankovic, Lina Stankovic

Research output: Contribution to conferencePaperpeer-review

Abstract

Graph learning has been extensively investigated for over a decade, in which the graph structure can be learnt from multiple graph signals (e.g., graphical Lasso) or node features (e.g., graph metric learning). Given partial graph signals, existing node feature-based graph learning approaches learn a pair-wise distance metric with gradient descent, where the number of optimization variables dramatically scale with the node feature size. To address this issue, in this paper, we propose a low-complexity model selection-inspired graph learning (MSGL) method with very few optimization variables independent with feature size, via leveraging on recent advances in graph spectral signal processing (GSP). We achieve this by 1) interpreting a finite-degree polynomial function of the graph Laplacian as a positive-definite precision matrix, 2) formulating a convex optimization problem with variables being the polynomial coefficients, 3) replacing the positive-definite cone constraint for the precision
matrix with a set of linear constraints, and 4) solving efficiently the objective using the Frank-Wolfe algorithm. Using binary classification as an application example, our simulation results show that our proposed MSGL method achieves competitive performance with significant speed gains against existing node
feature-based graph learning methods.
Original languageEnglish
Number of pages7
Publication statusAccepted/In press - 31 Aug 2021
Event13th Asia Pacific Signal and Information Processing Association Annual Summit and Conference - Kokusai Fashion Centre Bldg., Yokoami 1-6-1, Sumida City, Tokyo, Japan
Duration: 14 Dec 202117 Dec 2021
Conference number: 13
https://www.apsipa2021.org

Conference

Conference13th Asia Pacific Signal and Information Processing Association Annual Summit and Conference
Abbreviated titleAPSIPA
Country/TerritoryJapan
CityTokyo
Period14/12/2117/12/21
Internet address

Keywords

  • graph signal processing
  • graph learning
  • convex optimization

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