A post by Annie Gray, PhD student on the Compass programme.
Initially, my Compass mini-project aimed to explore what we can discover about objects given a matrix of similarities between them. More specifically, how to appropriately measure the distance between objects if we represent each as a point in (the embedding), and what this can tell us about the objects themselves. This led to discovering that the geodesic distances in the embedding relate to the Euclidean distance between the original positions of the objects, meaning we can recover the original positions of the objects. This work has applications in fields that work with relational data for example: genetics, Natural Language Processing and cyber-security.
This work resulted in a paper  written with my supervisors (Nick Whiteley and Patrick Rubin-Delanchy), which has been accepted at NeurIPS this year. The following gives an overview of the paper and how the ideas can be used in practice.