Minwise-Independent Permutations with Insertion and Deletion of Features

TL;DR

This paper studies how to adapt minHash sketches efficiently when features are dynamically inserted or deleted, providing algorithms with theoretical guarantees and practical speed-ups for real-world datasets.

Contribution

It introduces algorithms for dynamic feature updates in minHash, a systematic study of their theoretical properties, and demonstrates practical efficiency and accuracy improvements.

Findings

Significant speed-up in updating minHash sketches with feature changes.

Algorithms maintain comparable accuracy to recomputing minHash from scratch.

The methods are efficient, accurate, and easy to implement.

Abstract

In their seminal work, Broder \textit{et. al.}~\citep{BroderCFM98} introduces the $\mathrm{minHash}$ algorithm that computes a low-dimensional sketch of high-dimensional binary data that closely approximates pairwise Jaccard similarity. Since its invention, $\mathrm{minHash}$ has been commonly used by practitioners in various big data applications. Further, the data is dynamic in many real-life scenarios, and their feature sets evolve over time. We consider the case when features are dynamically inserted and deleted in the dataset. We note that a naive solution to this problem is to repeatedly recompute $\mathrm{minHash}$ with respect to the updated dimension. However, this is an expensive task as it requires generating fresh random permutations. To the best of our knowledge, no systematic study of $\mathrm{minHash}$ is recorded in the context of dynamic insertion and deletion of features. In this work, we initiate this study and suggest algorithms that make the $\mathrm{minHash}$ sketches adaptable to the dynamic insertion and deletion of features. We show a rigorous theoretical analysis of our algorithms and complement it with extensive experiments on several real-world datasets. Empirically we observe a significant speed-up in the running time while simultaneously offering comparable performance with respect to running $\mathrm{minHash}$ from scratch. Our proposal is efficient, accurate, and easy to implement in practice.