Scalability和快速CoveringLSH的全面回忆
Scalability and Total Recall with Fast CoveringLSH
摘要：
局部敏感哈希（LSH）已经成为在高维空间中具有强性能保证的相似性搜索的主要算法技术。传统LSH方案的缺点是它们可能具有\emph{false negatives}，即，召回率小于100%.这限制了LSH在需要精确性能保证的环境中的适用性。基于最近理论上的“CoveringLSH”构造，消除了假阴性，我们提出了一个快速和实用的覆盖LSH方案的汉明空间称为\emph{Fast CoveringLSH (fcLSH)}。继承CoveringLSH的设计优势，我们的方法避免了假阴性，并始终报告所有近邻。与CoveringLSH相比，我们实现了从$\mathcal{O}(dL)$到$\mathcal{O}(d + L\log{L})$的哈希函数计算时间的渐进改进，其中$d$是数据的维数，$L$是哈希表的数量。我们对合成数据集和真实数据集的实验表明，\emph{fcLSH}在高维汉明空间中搜索半径高达20的情况下与传统的基于散列的方法相当（并且往往更优越）。
英文摘要：
Locality-sensitive hashing (LSH) has emerged as the dominant algorithmic technique for similarity search with strong performance guarantees in high-dimensional spaces. A drawback of traditional LSH schemes is that they may have \emph{false negatives}, i.e., the recall is less than 100\%. This limits the applicability of LSH in settings requiring precise performance guarantees. Building on the recent theoretical "CoveringLSH" construction that eliminates false negatives, we propose a fast and practical covering LSH scheme for Hamming space called \emph{Fast CoveringLSH (fcLSH)}. Inheriting the design benefits of CoveringLSH our method avoids false negatives and always reports all near neighbors. Compared to CoveringLSH we achieve an asymptotic improvement to the hash function computation time from $\mathcal{O}(dL)$ to $\mathcal{O}(d + L\log{L})$, where $d$ is the dimensionality of data and $L$ is the number of hash tables. Our experiments on synthetic and real-world data sets demonstrate that \emph{fcLSH} is comparable (and often superior) to traditional hashing-based approaches for search radius up to 20 in high-dimensional Hamming space.
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。
