A multiscale method for data collected from network edges via the line graph
File(s)
Accepted version
Author(s)
Cao, Dingjia
Knight, Marina
Nason, Guy
Type
Journal Article
Abstract
Data collected over networks can be modelled as noisy observations of an unknown function over the nodes of a graph or network structure, fully described by its nodes and their connections, the edges. In this context, function estimation has been proposed in the literature and typically makes use of the network topology such as relative node arrangement, often using given or artificially constructed node Euclidean coordinates. However, networks that arise in fields such as hydrology (for example, river networks) present features that challenge these established modelling setups since the target function may naturally live on edges (e.g., river flow) and/or the node-oriented modelling uses noisy edge data as weights. This work tackles these challenges and develops a novel lifting scheme along with its associated (second) generation wavelets that permit data decomposition across the network edges. The transform, which we refer to under the acronym LG-LOCAAT, makes use of a line graph construction that first maps the data in the line graph domain. We thoroughly investigate the proposed algorithm’s properties and illustrate its performance versus existing methodologies. We conclude with an application pertaining to hydrology that involves the denoising of a water quality index over the England river network, backed up by a simulation study for a river flow dataset.
Date Issued
2025-12-01
Date Acceptance
2025-09-18
Citation
Statistics and computing, 2025, 35 (6)
ISSN
0960-3174
Publisher
Springer
Journal / Book Title
Statistics and computing
Volume
35
Issue
6
Copyright Statement
Copyright © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Article Number
200
Date Publish Online
2025-09-24