Efficient Coding of Signal Distances Using Universal Quantized Embeddings

Traditional rate-distortion theory is focused on how to best encode a signal using as few bits as possible and incurring as low a distortion as possible. However, very often, the goal of transmission is to extract specific information from the signal at the receiving end, and the distortion should be measured on that extracted information. In this paper we examine the problem of encoding signals such that sufficient information is preserved about their pair wise distances. For that goal, we consider randomized embeddings as an encoding mechanism and provide a framework to analyze their performance. We also propose the recently developed universal quantized embeddings as a solution to that problem and experimentally demonstrate that, in image retrieval experiments, universal embedding can achieve up to 25% rate reduction over the state of the art.