Barycentric subspace analysis of network-valued data

TL;DR

This paper introduces barycentric subspace analysis (BSA) for unlabeled network data, enabling interpretable dimensionality reduction by using point-generated subspaces, with a novel embedding for isomorphic and cospectral networks.

Contribution

It proposes BSA as a new method for network data analysis, overcoming interpretability limitations of PCA-based methods, and introduces a novel embedding for unlabeled networks.

Findings

BSA provides more interpretable subspaces than PCA-based methods.

The new embedding effectively handles isomorphic and cospectral networks.

BSA performs well on both simulated and real-world datasets.

Abstract

Certain data are naturally modeled by networks or weighted graphs, be they arterial networks or mobility networks. When there is no canonical labeling of the nodes across the dataset, we talk about unlabeled networks. In this paper, we focus on the question of dimensionality reduction for this type of data. More specifically, we address the issue of interpreting the feature subspace constructed by dimensionality reduction methods. Most existing methods for network-valued data are derived from principal component analysis (PCA) and therefore rely on subspaces generated by a set of vectors, which we identify as a major limitation in terms of interpretability. Instead, we propose to implement the method called barycentric subspace analysis (BSA), which relies on subspaces generated by a set of points. In order to provide a computationally feasible framework for BSA, we introduce a novel embedding for unlabeled networks where we replace their usual representation by equivalence classes of isomorphic networks with that by equivalence classes of cospectral networks. We then illustrate BSA on simulated and real-world datasets, and compare it to tangent PCA.