Computing Similarity Queries for Correlated Gaussian Sources

Abstract

Among many current data processing systems, the objectives are often not the reproduction of data, but to compute some answers based on the data resulting from queries. The similarity identification task is to identify the items in a database that are similar to a given query item for a given metric. The problem of compression for similarity identification has been studied in [1]. Unlike classical compression problems, the focus is not on reconstructing the original data. Instead, the compression rate is determined by the desired reliability of the answers. Specifically, the information measure identification rate characterizes the minimum rate that can be achieved among all schemes which guarantee reliable answers with respect to a given similarity threshold. In this paper, we propose a componentbased model for computing correlated similarity queries. The correlated signals are first decorrelated by the Karhunen-Loève transform (KLT). Then, the decorrelated signal is processed by a distinct D-admissible system for each component. We show that the component-based model equipped with KLT can perfectly represent the multivariate Gaussian similarity queries when optimal rate-similarity allocation applies. Hence, we can derive the identification rate of the multivariate Gaussian signals based on the component-based model. We then extend the result to general Gaussian sources with memory. We also study the models equipped with practical component systems. We use TC-schemes that use type covering signatures and triangleinequality decision rules [1] as our component systems. We propose an iterative method to numerically approximate the minimum achievable rate of the TC-scheme. We show that our component-based model equipped with TC-schemes can achieve better performance than the TC-scheme unaided on handling the multivariate Gaussian sources.