Compression for similarity identification: Fundamental limits

We study the problem of compressing a source for the goal of answering similarity queries from the compressed data. Unlike classical compression, here there is no requirement that the source be reproduced from the compressed form. For discrete memoryless sources and an arbitrary similarity measure, we fully characterize the minimal compression rate that allows query answers, that are reliable in the sense of having a vanishing false-positive probability, when false negatives are not allowed. The result is partially based on a previous work by Ahlswede et al. [1], and the inherently typical subset lemma plays a key role in the converse proof. We then discuss the performance that is attainable by using schemes that use lossy source codes as a building block, and show that such schemes are, in general, suboptimal. Finally, we discuss the problem of computing the fundamental limit, and present numerical results.