## Abstract

MinHash and SimHash are the two widely adopted Locality Sensitive Hashing (LSH) algorithms for large-scale data processing applications. Deciding which LSH to use for a particular problem at hand is an important question, which has no clear answer in the existing literature. In this study we provide a theoretical answer (validated by experiments) that MinHash virtually always outperforms SimHash when the data are binary as common in practice such as search. The collision probability of MinHash is a function of resemblance similarity (R), while the collision probability of SimHash is a function of cosine similarity (S). To provide a common basis for comparison, we evaluate retrieval results in terms of S for both MinHash and SimHash. This evaluation is valid as we can prove that MinHash is a valid LSH with respect to S, by using a general inequality S^{2} ≤ R ≤ S/2-S. Our worst case analysis can show that MinHash significantly outperforms SimHash in high similarity region. Interestingly, our intensive experiments reveal that MinHash is also substantially better than SimHash even in datasets where most of the data points are not too similar to each other. This is partly because, in practical data, often R ≥ S/z-S holds where z is only slightly larger than 2 (e.g., z ≤ 2.1). Our restricted worst case analysis by assuming S/z-S ≤ R ≤ S/2-S shows that MinHash indeed significantly outperforms SimHash even in low similarity region. We believe the results in this paper will provide valuable guidelines for search in practice, especially when the data are sparse.

Original language | English (US) |
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Pages (from-to) | 886-894 |

Number of pages | 9 |

Journal | Journal of Machine Learning Research |

Volume | 33 |

State | Published - 2014 |

Event | 17th International Conference on Artificial Intelligence and Statistics, AISTATS 2014 - Reykjavik, Iceland Duration: Apr 22 2014 → Apr 25 2014 |

## All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Statistics and Probability
- Artificial Intelligence