Clustering is Efficient for Approximate Maximum Inner Product Search

TL;DR

This paper introduces a simple spherical k-means clustering approach for approximate maximum inner product search, outperforming existing hashing and tree-based methods in speed and robustness on benchmark datasets.

Contribution

The paper demonstrates that a spherical k-means clustering method, combined with cosine similarity reduction, is a highly effective and robust solution for approximate MIPS, surpassing current state-of-the-art techniques.

Findings

Achieves higher speedups at the same precision compared to existing methods.

Provides more robust retrievals under noisy query conditions.

Effective on recommendation system benchmarks and large vocabulary embeddings.

Abstract

Efficient Maximum Inner Product Search (MIPS) is an important task that has a wide applicability in recommendation systems and classification with a large number of classes. Solutions based on locality-sensitive hashing (LSH) as well as tree-based solutions have been investigated in the recent literature, to perform approximate MIPS in sublinear time. In this paper, we compare these to another extremely simple approach for solving approximate MIPS, based on variants of the k-means clustering algorithm. Specifically, we propose to train a spherical k-means, after having reduced the MIPS problem to a Maximum Cosine Similarity Search (MCSS). Experiments on two standard recommendation system benchmarks as well as on large vocabulary word embeddings, show that this simple approach yields much higher speedups, for the same retrieval precision, than current state-of-the-art hashing-based and tree-based methods. This simple method also yields more robust retrievals when the query is corrupted by noise.