Graph Learning from Data under Structural and Laplacian Constraints

Abstract

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretations and (iii) associated algorithms. Specifically, graph learning problems are posed as estimation of graph Laplacian matrices from some observed data under given structural constraints (e.g., graph connectivity and sparsity level). From a probabilistic perspective, the problems of interest correspond to maximum a posteriori (MAP) parameter estimation of Gaussian-Markov random field (GMRF) models, whose precision (inverse covariance) is a graph Laplacian matrix. For the proposed graph learning problems, specialized algorithms are developed by incorporating the graph Laplacian and structural constraints. The experimental results demonstrate that the proposed algorithms outperform the current state-of-the-art methods in terms of accuracy and computational efficiency.

To appear in IEEE Journal of Selected Topics in Signal Processing. The implementations of the algorithms proposed in this paper are available at: https://github.com/STAC-USC/Graph_Learning

References in corpus (1)

• Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies

Cited by in corpus (6)

• Learning graphs from data: A signal representation perspective
• Graph signal processing for machine learning: A review and new perspectives
• Feature Graph Learning for 3D Point Cloud Denoising
• Power Systems Topology and State Estimation by Graph Blind Source Separation
• Skeleton-based Hand-Gesture Recognition with Lightweight Graph Convolutional Networks
• Learning Chebyshev Basis in Graph Convolutional Networks for Skeleton-based Action Recognition