We investigate an open question in the study of the curse of dimensionality: Is it possible to find the single nearest neighbor of a query in high dimensions? Using the notion of (in)distinguishability to examine whether the feature map of a kernel is able to distinguish two distinct points in high dimensions, we analyze this ability of a metric-based Lipschitz continuous kernel as well as that of the recently introduced Isolation Kernel. Between the two kernels, we show that only Isolation Kernel has distinguishability and it performs consistently well in four tasks: indexed search for exact nearest neighbor search, anomaly detection using kernel density estimation, t-SNE visualization and SVM classification in both low and high dimensions, compared with distance, Gaussian and three other existing kernels.

中文翻译：

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是否有可能在高维中找到查询的单个最近邻？


我们在维数灾难研究中研究了一个悬而未决的问题：是否有可能在高维中找到查询的单个最近邻？使用（不可）区分性的概念来检查内核的特征图是否能够区分高维中的两个不同点，我们分析了基于度量的 Lipschitz 连续内核以及最近引入的隔离内核的这种能力。在这两个内核之间，我们表明只有隔离内核具有可区分性，并且它在四个任务中始终表现良好：精确最近邻搜索的索引搜索、使用内核密度估计的异常检测、t-SNE 可视化以及低维和高维的 SVM 分类，与距离、高斯和其他三个现有内核相比。