论文标题
关于平均值，削减规范和出租车对应分析的平均绝对偏差
Mean absolute deviations about the mean, the cut norm and taxicab correspondence analysis
论文作者
论文摘要
优化有两个面，最小化损耗函数或增益函数的最大化。我们表明，基于个体的功率集，d，d的平均绝对偏差最大化增益函数，并且等于其剪切值的两倍。该属性被推广到以双重为中心的数据集。此外，我们表明，根据相对贡献标准，在三种众所周知的分散度量，标准偏差，最小偏差和D，D，D，D是最健壮的。更重要的是，我们表明，出租车对应分析的每个主维度的计算对应于平衡的2块序列。提供了示例。
Optimization has two faces, minimization of a loss function or maximization of a gain function. We show that the mean absolute deviations about the mean, d, maximizes a gain function based on the power set of the individuals, and it is equal to twice the value of its cut-norm. This property is generalized to double-centered and triple-centered data sets. Furthermore, we show that among the three well known dispersion measures, standard deviation, least absolute deviation and d, d is the most robust based on the relative contribution criterion. More importantly, we show that the computation of each principal dimension of taxicab correspondence analysis corresponds to balanced 2-blocks seriation. Examples are provided.
