Manifold valued data analysis of samples of networks, with applications in corpus linguistics

Severn, Katie E.; Dryden, Ian L.; Preston, Simon P.

Abstract

Networks arise in many applications, such as in the analysis of text documents, social interactions and brain activity. We develop a general framework for extrinsic statistical analysis of samples of networks, motivated by networks representing text documents in corpus linguistics. We identify networks with their graph Laplacian matrices, for which we define metrics, embeddings, tangent spaces, and a projection from Euclidean space to the space of graph Laplacians. This framework provides a way of computing means, performing principal component analysis and regression, and carrying out hypothesis tests, such as for testing for equality of means between two samples of networks. We apply the methodology to the set of novels by Jane Austen and Charles Dickens.

Citation

Severn, K. E., Dryden, I. L., & Preston, S. P. (2022). Manifold valued data analysis of samples of networks, with applications in corpus linguistics. Annals of Applied Statistics, 16(1), 368-390. https://doi.org/10.1214/21-aoas1480

• Journal Article Type: Article
• Acceptance Date: May 14, 2021
• Online Publication Date: Mar 28, 2022
• Publication Date: Mar 1, 2022
• Deposit Date: May 19, 2021
• Publicly Available Date: Mar 1, 2022
• Journal: Annals of Applied Statistics
• Print ISSN: 1932-6157
• Electronic ISSN: 1941-7330
• Publisher: Institute of Mathematical Statistics (IMS)
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Issue: 1
• Pages: 368-390
• DOI: https://doi.org/10.1214/21-aoas1480
• Keywords: Extrinsic mean, Graph Laplacian, Regression, Riemannian, Hypothesis test
• Public URL: https://nottingham-repository.worktribe.com/output/2458461
• Publisher URL: https://projecteuclid.org/journals/annals-of-applied-statistics/volume-16/issue-1/Manifold-valued-data-analysis-of-samples-of-networks-with-applications/10.1214/21-AOAS1480.short