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https://doi.org/10.1007/978-94-011-4577-0_10

has been cited by the following article:

• TITLE: Mean Absolute Deviations about the Mean, the Cut Norm and Taxicab Correspondence Analysis

  AUTHORS: Vartan Choulakian, Ghassan Abou-Samra

  KEYWORDS: Mean Absolute Deviations about the Mean, Cut Norm, Balanced 2-Blocks Seriation, Taxicab Correspondence Analysis

  JOURNAL NAME: Open Journal of Statistics, Vol.10 No.1, February 25, 2020

  ABSTRACT: Optimization has two faces, minimization of a loss function or maximization of a gain function. We show that the mean absolute deviation about the mean, d, maximizes a gain function based on the power set of the individuals; and nd, where nis the sample size, equals twice the value of the cut-norm of the deviations about the mean. 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, dis the most robust based on the relative contribution criterion. More importantly, we show that the computation of each principal dimension of taxicab correspondence analysis (TCA) corresponds to balanced 2-blocks seriation. These ideas are applied on two data sets.