Eclipse Hashing：Alexandrov紧致化和使用Hypersphere进行快速相似性搜索的哈希
Eclipse Hashing: Alexandrov Compactification and Hashing with Hyperspheres for Fast Similarity Search
摘要：
使用由大量数据组成的高维特征向量进行相似性搜索有着广泛的应用。进行快速相似性搜索的一种方式是将特征向量转换成二进制向量，并通过使用汉明距离来执行相似性搜索。这种变换是一种哈希方法，哈希函数的选择很重要。提出了使用超平面或超球面的散列方法。这里报告的一项研究受到了Spherical LSH的启发，我们使用hypersperes来散列特征向量。我们的方法，称为哈希算法，通过使用逆赤平投影来执行R^n的紧化，这是一种Alexandrov紧化。通过使用哈希，可以获得超球哈希函数，而无需显式使用超球。因此，减少了非线性运算的数量，并且散列的处理时间变得更短。此外，我们还表明，作为提高近似精度的结果，超平面散列是更准确的。
英文摘要：
The similarity searches that use high-dimensional feature vectors consisting of a vast amount of data have a wide range of application. One way of conducting a fast similarity search is to transform the feature vectors into binary vectors and perform the similarity search by using the Hamming distance. Such a transformation is a hashing method, and the choice of hashing function is important. Hashing methods using hyperplanes or hyperspheres are proposed. One study reported here is inspired by Spherical LSH, and we use hypersperes to hash the feature vectors. Our method, called Eclipse-hashing, performs a compactification of R^n by using the inverse stereographic projection, which is a kind of Alexandrov compactification. By using Eclipse-hashing, one can obtain the hypersphere-hash function without explicitly using hyperspheres. Hence, the number of nonlinear operations is reduced and the processing time of hashing becomes shorter. Furthermore, we also show that as a result of improving the approximation accuracy, Eclipse-hashing is more accurate than hyperplane-hashing.
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。
