Graph learning with Laplacian constraints: Modeling attractive Gaussian Markov random fields

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. This paper proposes a novel framework for learning graphs from data. The proposed framework (i) poses the graph learning problem as estimation of generalized graph Laplacian matrices and (...

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Bibliographic Details
Published in2016 50th Asilomar Conference on Signals, Systems and Computers pp. 1470 - 1474
Main Authors Egilmez, Hilmi E., Pavez, Eduardo, Ortega, Antonio
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.11.2016
Subjects
Covariance matrices
Estimation
Gaussian Markov random fields (GMRFs)
graph estimation
graph Laplacian matrices
Graph learning
Laplace equations
optimization
Probabilistic logic
Signal processing algorithms
sparse graph learning
Sparse matrices
Symmetric matrices
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Summary:Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. This paper proposes a novel framework for learning graphs from data. The proposed framework (i) poses the graph learning problem as estimation of generalized graph Laplacian matrices and (ii) develops an efficient algorithm. Under specific statistical assumptions, the proposed formulation leads to modeling attractive Gaussian Markov random fields. Our experimental results show that the proposed algorithm outperforms sparse inverse covariance estimation methods in terms of graph learning performance.
DOI:10.1109/ACSSC.2016.7869621