次线性时间中的近似Bregman近邻：超越三角不等式
Approximate Bregman near neighbors in sublinear time: Beyond the triangle inequality
摘要：
在本文中，我们提出了第一个可证明的近似最近邻（ANN）算法的Bregman分歧。我们的第一个算法使用O（n log^d n）空间在O（log^d n）时间内处理查询，并且仅使用底层距离函数的一般属性（其中包括Bregman分歧作为特殊情况）。第二个算法使用O（n）空间在O（log n）时间内处理查询，并利用与Bregman分歧具体相关的结构常数。我们的算法的一个有趣的特点是，它们扩展了环树+四叉树范式的ANN搜索超越欧几里德距离和度量的有界倍维的距离，甚至可能不对称或满足三角不等式。
英文摘要：
In this paper we present the first provable approximate nearest-neighbor (ANN) algorithms for Bregman divergences. Our first algorithm processes queries in O(log^d n) time using O(n log^d n) space and only uses general properties of the underlying distance function (which includes Bregman divergences as a special case). The second algorithm processes queries in O(log n) time using O(n) space and exploits structural constants associated specifically with Bregman divergences. An interesting feature of our algorithms is that they extend the ring-tree + quad-tree paradigm for ANN searching beyond Euclidean distances and metrics of bounded doubling dimension to distances that might not even be symmetric or satisfy a triangle inequality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
