Embedding-based representation of signal distances

Traditional signal representation and coding theory is focused on how to most efficiently represent and encode a signal with the goal of preserving it as best as possible. However, very often, the processing only concerns specific information in the signal and does not require conserving the signal itself. In this work we examine the problem of representing signals such that some function of their distance is preserved. For that goal, we consider randomized embeddings as a representation mechanism and provide a framework to design them and analyze their performance. This work generalizes previously developed universal embeddings, already proven quite successful in practice.