[论文解读] A Comparative Study on Hierarchical Navigable Small World Graphs.

Peng-Cheng Lin, Wan‐Lei Zhao|arXiv (Cornell University)|Apr 3, 2019

Advanced Image and Video Retrieval Techniques参考文献 16被引用 9

一句话总结

本文研究了分层可导航小世界（HNSW）图在最近邻搜索中的应用，将其性能与经过多样化处理的平面k-NN图进行比较。研究发现，HNSW的分层结构在高维数据上并未实现预期的对数复杂度缩放，而通过多样化处理的平面k-NN图同样可以实现相似的搜索效率，但两者均受到维度灾难的限制。

ABSTRACT

Hierarchical navigable small world (HNSW) graphs get more and more popular on large-scale nearest neighbor search tasks since the source codes were released two years ago. The attractiveness of this approach lies in its superior performance over most of the nearest neighbor search approaches as well as its genericness to various distance measures. In this paper, several comparative studies have been conducted on this search approach. The role of hierarchical structure in HNSW and the function of HNSW graph itself are investigated. We find that the hierarchical structure in HNSW could not achieve a much better logarithmic complexity scaling as it was claimed in the paper, particularly on high dimensional data. Moreover, we find that similar high search speed efficiency as HNSW could be achieved with the support of flat k-NN graph after graph diversification. Finally, we point out the difficulty, faced by most of the graph based search approaches, is directly linked to curse of dimensionality. HNSW, like other graph based approaches, is unable to address such difficulty.

研究动机与目标

• 评估HNSW中分层结构在最近邻搜索中的有效性。
• 探究经过多样化处理的平面k-NN图是否能够达到与HNSW相当的搜索效率。
• 分析高维性对基于图的最近邻搜索方法的影响。
• 评估HNSW是否如先前研究声称的那样克服了维度灾难。

提出的方法

• 本研究在多种数据集和距离度量下，对HNSW与多样化处理的平面k-NN图进行了对比实验。
• 评估了搜索性能与复杂度缩放，尤其关注高维数据的表现。
• 对平面k-NN图应用了多样化处理，以提升连通性与搜索效率。
• 分析了HNSW的分层结构，以评估其对实现对数复杂度缩放的贡献。
• 从召回率、搜索速度和维度扩展性等方面衡量了两种方法的性能。

实验结果

研究问题

• RQ1 HNSW中的分层结构是否在高维空间中实现了所宣称的对数复杂度缩放？
• RQ2 经过多样化处理的平面k-NN图是否能够实现与HNSW相当的搜索效率？
• RQ3 HNSW的性能在多大程度上受到维度灾难的限制？
• RQ4 不同基于图的方法在数据维度增加时如何实现可扩展性？

主要发现

• HNSW中的分层结构并未在高维数据上实现预期的对数复杂度缩放。
• 通过多样化处理的平面k-NN图可以实现与HNSW相当的搜索速度效率，表明HNSW的分层结构可能并非性能的关键因素。
• HNSW与其他基于图的方法一样，从根本上受到维度灾难的限制。
• HNSW在高维空间中的性能退化与基于图的最近邻搜索方法普遍面临的问题一致。