LSF-Join: Locality Sensitive Filtering for Distributed All-Pairs Set Similarity Under Skew

Cyrus Rashtchian, Aneesh Sharma, David P. Woodruff

Abstract: All-pairs set similarity is a widely used data mining task, even for large and high-dimensional datasets. Traditionally, similarity search has focused on discovering very similar pairs, for which a variety of efficient algorithms are known. However, recent work has highlighted the importance of discovering pairs of sets with relatively small intersection sizes. For example, in a recommender system, two users may be alike even though their interests only overlap on a small percentage of items. In such systems, it is also common that some dimensions are highly-skewed, because they are very popular. Together, these two properties render previous approaches infeasible for large input sizes. To address this problem, we present a new distributed algorithm, LSF-Join, for approximate all-pairs set similarity. The core of our algorithm is a randomized selection procedure based on Locality Sensitive Filtering. In particular, our method deviates from prior approximate algorithms, which are based on Locality Sensitive Hashing. Theoretically, we show that LSF-Join efficiently finds most close pairs, even for small similarity thresholds and for skewed input sets. We prove guarantees on the communication, work, and maximum load of LSF-Join, and we also experimentally demonstrate its accuracy on multiple graphs.