Abstract
We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the graph distances and derive error bounds under various assumptions on the link function. In the simplest case where the link function is proportional to an indicator function, the bound matches an information lower bound that we derive.
Highlights
Suppose that we observe a undirected graph with adjacency matrix W = (Wij : i, j ∈ [n]) with Wij ∈ {0, 1} and Wii = 0
Our contribution here is of a different nature as we focus on the situation where the latent positions are well spread out in space, forming no obvious clusters
The method based on graph distances suffers from a number of serious limitations: Fig 5
Summary
We place ourselves in a setting where the adjacency matrix W is observed, but the underlying points are unknown. When the link function is unknown, all we can hope for is to rank these distances. Recovering the points based on such a ranking amounts to a problem of ordinal embedding (aka, non-metric multidimensional scaling), which has a long history [19, 36, 37, 45]. This is true in general, we focus our attention on the ‘local setting’ where the link function has very small support. We focus our attention on the estimation of the pairwise distances (2)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
