均匀性度量中的密集性偏差与稀疏性偏差

该文根据王元，方开泰［２］的近似偏差（discrepancy）的均匀性准则，定义了理想布点情况下的标准半径，定义了ｍ 维单位子空间Ｃｍ＝［０，１］中两点间的ｆ距离和ｇ距离，由此定义了最大空穴半径和最小空穴半径，提出了均匀性度量的密集性偏差与稀疏性偏差．给出了二维情况 下的计算结果．我们的方法计算量不大，不仅能较好地度量布点的均匀性以及布点在低维投影的均匀性，而且能指导如何调整布点使之尽可能与理想布点接近．

New Measurements of Uniformity-Compression Discrepancy and Sparseness Discrepancy

Based on the discrepancy criteria of uniformity measurement proposed b y Wang Yuan and Fang K. T.\+\{2]\}, standard radius of ideal distribution i s defined. \$f\$ distance and \$g\$ distance between two points in \$m\$ dimensi onal cubic space \$C\+m=STHZ]0,1STBZ]]\$ are defined, and so, maximum cavity and minimum c avity are defined. New measurements of uniformity-compression discrepancy and sparseness discr epan cy are proposed. The result in two dimensions is calculated. With little calcu lat ion, our method can not only measure the uniformity of distributions well an d get a good unformity in low dimensional projection, but also can give advices on how to adjust the distribution and let it be as near to ideal distribution a s possible.