Cluster-and-Conquer: When Randomness Meets Graph Locality

TL;DR

This paper introduces Cluster-and-Conquer, a novel method that enhances incremental KNN graph algorithms by pre-clustering similar nodes using FastRandomHash, resulting in significant speed-ups with minimal quality loss.

Contribution

The paper proposes FastRandomHash and Cluster-and-Conquer, innovative techniques that improve the efficiency of KNN graph algorithms by addressing initial dissimilar connections.

Findings

Achieves up to 4.42x speed-up over existing methods

Maintains comparable KNN quality with minimal loss

Demonstrates effectiveness on real datasets

Abstract

K-Nearest-Neighbors (KNN) graphs are central to many emblematic data mining and machine-learning applications. Some of the most efficient KNN graph algorithms are incremental and local: they start from a random graph, which they incrementally improve by traversing neighbors-of-neighbors links. Paradoxically, this random start is also one of the key weaknesses of these algorithms: nodes are initially connected to dissimilar neighbors, that lie far away according to the similarity metric. As a result, incremental algorithms must first laboriously explore spurious potential neighbors before they can identify similar nodes, and start converging. In this paper, we remove this drawback with Cluster-and-Conquer (C 2 for short). Cluster-and-Conquer boosts the starting configuration of greedy algorithms thanks to a novel lightweight clustering mechanism, dubbed FastRandomHash. FastRandomHash leverages random-ness and recursion to pre-cluster similar nodes at a very low cost. Our extensive evaluation on real datasets shows that Cluster-and-Conquer significantly outperforms existing approaches, including LSH, yielding speed-ups of up to x4.42 while incurring only a negligible loss in terms of KNN quality.