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, 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.
Funding Statement
This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/T003928/1 and EP/M02315X/1].
Acknowledgments
The authors are grateful to Michaela Mahlberg, Viola Wiegand and Anthony Hennessey for their help and discussions about the data obtained from https://clic.bham.ac.uk and to the Editor, Associate Editor and two anonymous referees for their very helpful comments.
Citation
Katie E. Severn. Ian L. Dryden. Simon P. Preston. "Manifold valued data analysis of samples of networks, with applications in corpus linguistics." Ann. Appl. Stat. 16 (1) 368 - 390, March 2022. https://doi.org/10.1214/21-AOAS1480
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