Nearest Neighbor Search (NNS) over generalized weighted distance is fundamental to a wide range of applications. The problem of NNS over the generalized weighted Square Euclidean distance has been studied in previous work. However, numerous studies have shown that the Manhattan distance could be more practical than the Euclidean distance for high-dimensional NNS. To the best of our knowledge, no prior work presents a sublinear time solution to the problem of NNS over the generalized weighted Manhattan distance. In this paper, we propose two novel sublinear time hashing schemes ($d_w^{l_1},l_2$)-ALSH and ($d_w^{l_1},\theta$)-ALSH to solve the problem.

中文翻译：

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广义加权曼哈顿距离上的亚线性时间最近邻居搜索

广义加权距离上的最近邻居搜索（NNS）是广泛应用的基础。在先前的工作中已经研究了NNS在广义加权平方欧几里得距离上的问题。但是，大量研究表明，对于高维NNS，曼哈顿距离比欧几里得距离更实用。据我们所知，没有一项先前的工作提出关于广义加权曼哈顿距离上的NNS问题的亚线性时间解。在本文中，我们提出了两种新颖的亚线性时间散列方案（$ d_w ^ {l_1}，l_2 $）-ALSH和（$ d_w ^ {l_1}，\ theta $）-ALSH来解决该问题。