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Dimension reduction for covariates in network data
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Zhao, Junlong, Liu, Xiuming, Wang, Hansheng and Leng, Chenlei (2022) Dimension reduction for covariates in network data. Biometrika, 109 (1). pp. 85-102. asab006. doi:10.1093/biomet/asab006 ISSN 0006-3444.
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Official URL: https://doi.org/10.1093/biomet/asab006
Abstract
A problem of major interest in network data analysis is to explain the strength of connections using context information. To achieve this, we introduce a novel approach named network-supervised dimension reduction by projecting covariates onto low-dimensional spaces for revealing the linkage pattern, without assuming a model.We propose a new loss function for estimating the parameters in the resulting linear projection, based on the notion that closer proximity in the low-dimension projection renders stronger connections. Interestingly, the convergence rate of our estimator is shown to depend on a network effect factor which is the smallest number that can partition a graph in a way similar to the graph coloring problem. Our methodology has interesting connections to principal component analysis and linear discriminant analysis, which we exploit for clustering and community detection. The methodology developed is further illustrated by numerical experiments and the analysis of a pulsar candidates data in astronomy.
Item Type: | Journal Article | ||||||||
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Subjects: | H Social Sciences > HA Statistics H Social Sciences > HM Sociology Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Meta-analysis, System analysis -- Statistical methods, Data envelopment analysis , Social sciences -- Network analysis | ||||||||
Journal or Publication Title: | Biometrika | ||||||||
Publisher: | Biometrika Trust | ||||||||
ISSN: | 0006-3444 | ||||||||
Official Date: | March 2022 | ||||||||
Dates: |
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Volume: | 109 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 85-102 | ||||||||
Article Number: | asab006 | ||||||||
DOI: | 10.1093/biomet/asab006 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in Biometrika following peer review. The version of record Junlong Zhao, Xiumin Liu, Hansheng Wang, Chenlei Leng, Dimension Reduction for Covariates in Network Data, Biometrika, 2021;, asab006, is available online at:https://doi.org/10.1093/biomet/asab006 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Copyright Holders: | © 2021 Biometrika Trust | ||||||||
Date of first compliant deposit: | 3 February 2021 | ||||||||
Date of first compliant Open Access: | 9 February 2022 |
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