平均值的绝对离差、截模与出租车对应分析
Mean absolute deviations about the mean, the cut norm and taxicab correspondence analysis
摘要：
优化有两个方面，损失函数的最小化或增益函数的最大化。我们表明，平均值的平均绝对偏差，d，最大化的增益函数的基础上的个人的权力集，它是等于两倍的值，其切割规范。这个属性被推广到双中心和三中心数据集。此外，我们表明，在三个众所周知的分散措施，标准差，最小绝对偏差和d，d是最强大的相对贡献标准的基础上。更重要的是，我们证明了出租车对应分析的每个主维的计算对应于平衡的2-块序列化。提供了实例。
英文摘要：
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.
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