摘要
在高维空间下,研究了常用L_(k)范数的行为,并证明高维意义问题对k值是敏感的.引入并检验了L_(k)范数到分数距离度量的自然扩展.从理论的角度证明了分数距离度量提供了更有意义的结果.在高维空间下,随着样本点数量的增加,每个点的距离都趋于相等.
The behavior of the commonly used L_(k) norm is investigated in high-dimensional space and it is shown that the high-dimensional significance problem is sensitive to the value of k.A natural extension of the L_(k) norm to the fractional distance measurement is introduced and tested.It is shown that the fractional distance measurement provides more meaningful results from a theoretical point of view,the distance of each point tends to be equal as the number of sample points increases in a high-dimensional space.
作者
李亚辑
吴晟
LI Yaji;WU Sheng(School of Information Engineering,College of Arts and Sciences Kunming,Kunming 650222,China;School of Information Engineering and Automation,Kunming University of Science and Technology,Kunming 650500,China)
出处
《高师理科学刊》
2023年第2期20-24,共5页
Journal of Science of Teachers'College and University
基金
福建省自然科学基金面上项目(2020J01384)
福建省中青年教师教育科研项目(JAT190688
B201901)
三明学院引进高层次人才科研启动项目(19YG01)
黑龙江省自然科学基金项目(LH2019E085)。
关键词
向量范数
分数距离度量
均匀分布
中心极限定理
vector norm
fractional distance measurement
uniform distribution
central limit theorem