| 引用本文: | 吴国福,窦强,窦文华.基于查表的空间填充曲线映射算法.[J].国防科技大学学报,2010,32(5):75-79.[点击复制] |
| WU Guofu,DOU Qiang,DOU Wenhua.Table-based Space-filling Curve Generation[J].Journal of National University of Defense Technology,2010,32(5):75-79[点击复制] |
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| 基于查表的空间填充曲线映射算法 |
| 吴国福, 窦强, 窦文华 |
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(国防科技大学 计算机学院，湖南 长沙 410073)
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| 摘要: |
| 空间填充曲线是进行数据降维处理的典型方法。首先给出对角线空间填充曲线的映射规则，该规则使得在高维情况下存在唯一曲线，并且每一维度上的格点数目不受限制。然后提出等势面的概念，推导出不同等势面上格点数量的递推关系。在此基础上，给出基于查表的对角线空间填充曲线映射算法，该算法执行快、可扩展性好，其时间复杂度随维度的增加呈线性增长。 |
| 关键词: 空间填充曲线 对角线 等势面 降维 |
| DOI： |
| 投稿日期：2010-04-20 |
| 基金项目:国家自然科学基金资助项目(60633050) |
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| Table-based Space-filling Curve Generation |
| WU Guofu, DOU Qiang, DOU Wenhua |
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(College of Computer, National Univ. of Defense Technology, Changsha 410073, China)
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| Abstract: |
| Space-filling curves are classical ways to reduce the dimensions of data. This paper first presents the mapping rules of the diagonal space-filling curve. Unique curve which exists under the rules and the number of grids on each dimensionality is not constrained. Then a new conception about equipotential surface was given, and the relationship between the number of grids on different equipotential surface was dirived. Table-based space-filling curve generation algorithms on the basis of the realtionship were presented. It is found that the algorithms have low running time and high scalability. |
| Keywords: space-filling curve diagonal equipotential surface dimension reduction |
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