Web: http://arxiv.org/abs/2106.01260

Sept. 23, 2022, 1:12 a.m. | Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy

cs.LG updates on arXiv.org arxiv.org

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 …

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