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Cluster-and-Conquer: When Randomness Meets Graph Locality

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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 ×4.42 while incurring only a negligible loss in terms of KNN quality.
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Dates and versions

hal-02974077 , version 1 (21-10-2020)

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George Giakkoupis, Anne-Marie Kermarrec, Olivier Ruas, François Taïani. Cluster-and-Conquer: When Randomness Meets Graph Locality. 2020. ⟨hal-02974077⟩
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