Poster

Matrix factorisation and the interpretation of geodesic distance

Nick Whiteley · Annie Gray · Patrick Rubin-Delanchy

Keywords: [ Graph Learning ]

[ Abstract ]
[ OpenReview
Tue 7 Dec 8:30 a.m. PST — 10 a.m. PST

Abstract:

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 accomplished in two steps: matrix factorisation, followed by nonlinear dimension reduction. This combination is effective because the point cloud obtained in the first step lives close to a manifold in which latent distance is encoded as geodesic distance. Hence, a nonlinear dimension reduction tool, approximating geodesic distance, can recover the latent positions, up to a simple transformation. We give a detailed account of the case where spectral embedding is used, followed by Isomap, and provide encouraging experimental evidence for other combinations of techniques.

Chat is not available.