165 citations · 244 across the 23 of their papers we have counts for
11 papers · 1 filter
How high is `high'? Rethinking the roles of dimensionality in topological data analysis and manifold learning
Hannah Sansford, Nick Whiteley, Patrick Rubin-Delanchy
We present a generalised Hanson-Wright inequality and use it to establish new statistical insights into the geometry of data point-clouds. In the setting of a general random functi…
Valid Conformal Prediction for Dynamic GNNs
Ed Davis, Ian Gallagher, Daniel John Lawson +1
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are p…
Hierarchical clustering with dot products recovers hidden tree structure
Annie Gray, Alexander Modell, Patrick Rubin-Delanchy +1
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant o…
Implications of sparsity and high triangle density for graph representation learning
Hannah Sansford, Alexander Modell, Nick Whiteley +1
Recent work has shown that sparse graphs containing many triangles cannot be reproduced using a finite-dimensional representation of the nodes, in which link probabilities are inne…
Spectral embedding for dynamic networks with stability guarantees
Ian Gallagher, Andrew Jones, Patrick Rubin-Delanchy
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of indi…
Matrix factorisation and the interpretation of geodesic distance
Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy
Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. We show that this can be accompl…
Spectral clustering on spherical coordinates under the degree-corrected stochastic blockmodel
Francesco Sanna Passino, Nicholas A. Heard, Patrick Rubin-Delanchy
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional…
The multilayer random dot product graph
Andrew Jones, Patrick Rubin-Delanchy
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- wh…
Manifold structure in graph embeddings
Patrick Rubin-Delanchy
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision i…
Spectral embedding of weighted graphs
Ian Gallagher, Andrew Jones, Anna Bertiger +2
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asympt…
A statistical interpretation of spectral embedding: the generalised random dot product graph
Patrick Rubin-Delanchy, Joshua Cape, Minh Tang +1
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network mo…