空间点距离分析

Exploration of the distance between spatial points

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.