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.

翻译：功能数据分析(FDA)往往默认以一个层面的矢量为中心,因此一个层面的矢量为零。我们发现,在另一个层面的中心发现一种超越林业发展局熟悉的变量的新颖有用模式。我们探讨了矩阵方向和术语上的模糊之处。中心与潜在互动之间的差异很容易被误解。我们为中心作业提出了一个统一框架和新术语。我们用信息图形明确展示了每个选择的中心背后的直觉和后果。我们还提出一个新的方向能源假设测试,作为一系列诊断的一部分,以确定哪些中心选择最适合数据集。我们探索这些诊断在林业发展局若干环境中的应用。