Sub-linear Memory Sketches for Near Neighbor Search on Streaming Data

TL;DR

This paper introduces a novel sublinear memory sketching method for near neighbor search in streaming data, combining LSH, kernel density estimation, and compressed sensing to achieve efficient, stable query results.

Contribution

The paper presents the first sublinear memory sketch for nearest neighbor search that works efficiently on streaming data and provides theoretical insights into the memory-accuracy tradeoff.

Findings

Achieves orders of magnitude better compression than random projections.

Retains the ability to report nearest neighbors for practical queries.

Demonstrates effectiveness on social media friend recommendation data.

Abstract

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by $b$. We achieve sublinear memory performance on stable queries by combining recent advances in locality sensitive hash (LSH)-based estimators, online kernel density estimation, and compressed sensing. Our theoretical results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google Plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries.