L2AP: Fast cosine similarity search with prefix L-2 norm bounds

David C. Anastasiu, George Karypis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

36 Scopus citations


The All-Pairs similarity search, or self-similarity join problem, finds all pairs of vectors in a high dimensional sparse dataset with a similarity value higher than a given threshold. The problem has been classically solved using a dynamically built inverted index. The search time is reduced by early pruning of candidates using size and value-based bounds on the similarity. In the context of cosine similarity and weighted vectors, leveraging the Cauchy-Schwarz inequality, we propose new ℓ2-norm bounds for reducing the inverted index size, candidate pool size, and the number of full dot-product computations. We tighten previous candidate generation and verification bounds and introduce several new ones to further improve our algorithm's performance. Our new pruning strategies enable significant speedups over baseline approaches, most times outperforming even approximate solutions. We perform an extensive evaluation of our algorithm, L2AP, and compare against state-of-the-art exact and approximate methods, AllPairs, MMJoin, and BayesLSH, across a variety of real-world datasets and similarity thresholds.

Original languageEnglish (US)
Title of host publication2014 IEEE 30th International Conference on Data Engineering, ICDE 2014
PublisherIEEE Computer Society
Number of pages12
ISBN (Print)9781479925544
StatePublished - 2014
Event30th IEEE International Conference on Data Engineering, ICDE 2014 - Chicago, IL, United States
Duration: Mar 31 2014Apr 4 2014

Publication series

NameProceedings - International Conference on Data Engineering
ISSN (Print)1084-4627


Other30th IEEE International Conference on Data Engineering, ICDE 2014
Country/TerritoryUnited States
CityChicago, IL

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