The K-nearest neighbor graph (K-NNG) is a data structure used by many machine-learning algorithms. Naive computation of the K-NNG has quadratic time complexity, which in many cases is not efficient enough, producing the need for fast and accurate approximation algorithms. NN-Descent is one such algorithm that is highly efficient, but has a major drawback in that K-NNG approximations are accurate only on data of low intrinsic dimensionality. This paper represents an experimental analysis of this behavior, and investigates possible solutions. Experimental results show that there is a link between the performance of NN-Descent and the phenomenon of hubness, defined as the tendency of intrinsically high-dimensional data to contain hubs – points with large in-degrees in the K-NNG. First, we explain how the presence of the hubness phenomenon causes bad NN-Descent performance. In light of that, we propose four NN-Descent variants to alleviate the observed negative inuence of hubs. By evaluating the proposed approaches on several real and synthetic data sets, we conclude that our approaches are more accurate, but often at the cost of higher scan rates.

中文翻译：

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Hubness 对 NN-Descent 的影响

K-最近邻图 (K-NNG) 是许多机器学习算法使用的数据结构。K-NNG 的简单计算具有二次时间复杂度，在许多情况下效率不够高，因此需要快速准确的近似算法。NN-Descent 是一种高效的算法，但有一个主要缺点是 K-NNG 近似仅在低固有维度的数据上是准确的。本文代表了对这种行为的实验分析，并研究了可能的解决方案。实验结果表明，NN-Descent 的性能与中心现象之间存在联系，中心现象定义为本质上高维数据包含中心的趋势——K-NNG 中具有大入度的点。第一的，我们解释了 hubness 现象的存在如何导致糟糕的 NN-Descent 性能。有鉴于此，我们提出了四种 NN-Descent 变体来减轻观察到的集线器的负面影响。通过在几个真实和合成数据集上评估所提出的方法，我们得出结论，我们的方法更准确，但通常以更高的扫描率为代价。