New Perspectives on Centering

Jack Prothero, Jan Hannig, J. Marron
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引用次数: 3

Abstract

Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering along the other dimension identifies a novel useful mode of variation beyond those familiar in FDA. We explore ambiguities in both matrix orientation and nomenclature. Differences between centerings and their potential interaction can be easily misunderstood. We propose a unified framework and new terminology for centering operations. We clearly demonstrate the intuition behind and consequences of each centering choice with informative graphics. We also propose a new direction energy hypothesis test as part of a series of diagnostics for determining which choice of centering is best for a data set. We explore the application of these diagnostics in several FDA settings.
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定心新视角
数据矩阵定心是数据分析中一个一直存在但尚未得到充分研究的方面。功能数据分析(FDA)通常使用默认的居中操作,使得一维向量的平均值为零。我们发现,沿着其他维度的中心确定了一种新的有用的变异模式,超出了FDA所熟悉的模式。我们探讨了矩阵取向和命名法的歧义。中心之间的差异及其潜在的相互作用很容易被误解。我们提出了一个统一的定心操作框架和新的术语。我们用信息图形清楚地展示了每个中心选择背后的直觉和后果。我们还提出了一个新的方向能量假设检验,作为一系列诊断的一部分,用于确定哪种定心选择最适合数据集。我们探讨这些诊断在几个FDA设置的应用。
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