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。
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.
出处
《国防科技大学学报》
EI
CAS
CSCD
北大核心
2010年第5期75-79,共5页
Journal of National University of Defense Technology
基金
国家自然科学基金资助项目(60633050)
关键词
空间填充曲线
对角线
等势面
降维
space-filling curve
diagonal
equipotential surface
dimension reduction
