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

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.