When Is Network Lasso Accurate?

The “least absolute shrinkage and selection operator” (Lasso) method has been adapted recently for network-structured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regula...

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Bibliographic Details
Published inFrontiers in applied mathematics and statistics Vol. 3
Main Authors Jung, Alexander, Tran, Nguyen, Mara, Alexandru
Format Journal Article
LanguageEnglish
Published Frontiers Media S.A 19.01.2018
Subjects
big data
clustering
complex networks
compressed sensing
convex optimization
semi-supervised learning
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Summary:The “least absolute shrinkage and selection operator” (Lasso) method has been adapted recently for network-structured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While efficient and scalable implementations of the network Lasso are available, only little is known about the conditions on the underlying network structure which ensure network Lasso to be accurate. By leveraging concepts of compressed sensing, we address this gap and derive precise conditions on the underlying network topology and sampling set which guarantee the network Lasso for a particular loss function to deliver an accurate estimate of the entire underlying graph signal. We also quantify the error incurred by network Lasso in terms of two constants which reflect the connectivity of the sampled nodes.
ISSN:2297-4687
2297-4687
DOI:10.3389/fams.2017.00028