Anonymisation of geographical distance matrices via Lipschitz embedding

Anonymisation of geographical distance matrices via Lipschitz embedding

BACKGROUND Anonymisation of spatially referenced data has received increasing attention in recent years. Whereas the research focus has been on the anonymisation of point locations, the disclosure risk arising from the publishing of inter-point distances and corresponding anonymisation methods have not been studied systematically. METHODS We propose a new anonymisation method for the release ...

Extending Lipschitz maps for graph embedding via PageRank

Embedding with a Lipschitz function

We investigate a new notion of embedding of subsets of {−1, 1}n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, ..., n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {−1, 1}n, the vast majority of such sets do not embed i...

Recovering Euclidean Distance Matrices via Landmark MDS

In network topology discovery, it is often necessary to collect measurements between network elements without injecting large amounts of traffic into the network. A possible solution to this problem is to actively query the network for some measurements and use these to infer the remaining ones. We frame this as a particular version of the Noisy Matrix Completion problem where the entries refle...

Bi-lipschitz Embedding of Projective Metrics

We give a sufficient condition for a projective metric on a subset of a Euclidean space to admit a bi-Lipschitz embedding into Euclidean space of the same dimension.