An Interpretable Data Embedding Under Uncertain Distance Information

A common assumption in embedding methodologies is the availability of exact pairwise distances. In this paper, we propose a 2D embedding that overcomes this limitation. It can operate on distances that are represented as a range of lower and upper bounds. Such bounds are typically available when objects are compressed, whence our approach is highly applicable in the case of big compressed datasets. We establish linear convergence (i.e., exponential decay of distance to optimality) for the proposed scheme, with a rate characterized by the topology of the data graph. We compare with prevalent embedding methodologies (ISOMAP, t-SNE, MDS) and illustrate that our approach can provide fidelitous preservation of distances, correlations, and object ranks, even in the presence of inexact distance information.