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

arXiv: https://arxiv.org/abs/1902.08290 · HTML: https://mlsanity.com/paper/1902.08290/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2019.

## Built on by (most cited first, 8 of 8)

- [Interpreting Equivariant Representations](https://mlsanity.com/paper/2401.12588/) (2024)
- [End-to-End Deep Learning for Predicting Metric Space-Valued Outputs](https://mlsanity.com/paper/2509.23544/) (2025)
- [DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responses](https://mlsanity.com/paper/2510.17072/) (2025)
- [Barycentric subspace analysis of network-valued data](https://mlsanity.com/paper/2507.23559/) (2025)
- [Fr'echet Geodesic Boosting](https://mlsanity.com/paper/2509.18013/) (2025)
- [Metric space valued Fr'echet regression](https://mlsanity.com/paper/2602.05225/) (2026)
- [Fr'echet Regression on the Bures-Wasserstein Manifold](https://mlsanity.com/paper/2604.03566/) (2026)
- [Deep Single-Index Fr'echet Regression](https://mlsanity.com/paper/2606.06957/) (2026)

## Abstract (arXiv)

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.