Bidirectionally Densifying LSH Sketches with Empty Bins

Abstract

As an efficient tool for approximate similarity computation and search, Locality Sensitive Hashing (LSH) has been widely used in many research areas including databases, data mining, information retrieval, and machine learning. Classical LSH methods typically require to perform hundreds or even thousands of hashing operations when computing the LSH sketch for each input item (e.g., a set or a vector); however, this complexity is still too expensive and even impractical for applications requiring processing data in real-time. To address this issue, several fast methods such as OPH and BCWS have been proposed to efficiently compute the LSH sketches; however, these methods may generate many sketches with empty bins, which may introduce large errors for similarity estimation and also limit their usage for fast similarity search. To solve this issue, we propose a novel densification method, i.e., BiDens. Compared with existing densification methods, our BiDens is more efficient to fill a sketch's empty bins with values of its non-empty bins in either the forward or backward directions. Furthermore, it also densifies empty bins to satisfy the densification principle (i.e., the LSH property). Theoretical analysis and experimental results on similarity estimation, fast similarity search, and kernel linearization using real-world datasets demonstrate that our BiDens is up to 106 times faster than state-of-the-art methods while achieving the same or even better accuracy.