고차원 볼의 표면과 적도 체적 집중의 상대적 강도의 변화 양상 분석

Abstract

In this paper, an in-depth analysis is conducted on the relative strength of the volume concentration phenomena at the surface and equator of a high-dimensional ball defined in Euclidean space. For the volume of the high-dimensional ball, the surface and equator concentration measures are defined, and the relative strength measure is indicated as the ratio of the two measures. Through the 1st and 2nd partial derivations of the three measures with respect to the space dimension and the differential slice depth, the overall changing patterns of the three measures are examined analytically. Finally, the detailed changing patterns of the relative strength of the surface and the volume concentrations are verified using computer simulation results. The findings of this paper are expected to provide a theoretical basis for the strategic planning of the efficient search of high-dimensional data especially in the fields of big data and machine learning