摘要： 利用Hilbert曲线的数据聚类特性，将高维空间中的点映射到线性空间中，给出相应的降维方法，提出基于Hilbert曲线的高维k-最近对查询算法，并证实了其正确性。算法能够删减点集中大量的点以优化扫描过程，减少运行时间，实验结果表明该算法优于连续扫描算法。

关键词: 高维空间, 降维方法, Hilbert曲线, k-最近对查询算法

Abstract: Utilizing clustering quality of Hilbert curve, this paper presents definitions of reducing dimensionality, gives an algorithm to query k-closest pairs based on Hilbert curve, and proves the correctness of it. It can delete useless points in point set to optimize scanning procedure and reduce running time. According to the experiment, the algorithm is better than sequential-scan method.

Key words: high-dimensional space, dimensionality reduction, Hilbert curve, k-closest pairs query algorithm

中图分类号: 

• TP301.6