仿射归约的起源中心论视角
Affine Reduction of Dimensionality: An Origin-Centric Perspective
摘要：
我们认为统计方法减少的多元维数，具有不变性和/或交换性的仿射变换组（原点平移加上沿初始轴的坐标的线性组合）下的属性。这里讨论的方法不同于传统的主成分和坐标方法，因为它们是以原点为中心的。因为原点的所有笛卡尔坐标都为零，所以它是点散射的后续线性变换的唯一固定点。当可视化允许在笛卡尔坐标和极坐标表示之间移动和/或组合时，如在双标图中，该原点的位置是至关重要的。具体来说，以原点为中心的可视化通过产生可以被解释为戴森群的散射来增强图形感知的心理。关键因素通常是分析师通过初始“居中”平移对原点的选择;该选择确定恢复的散射是否将没有被描绘为靠近原点的点，或者一个（或多个）点与该原点完全重合。
英文摘要：
We consider statistical methods for reduction of multivariate dimensionality that have invariance and/or commutativity properties under the affine group of transformations (origin translations plus linear combinations of coordinates along initial axes). The methods discussed here differ from traditional principal component and coordinate approaches in that they are origin-centric. Because all Cartesian coordinates of the origin are zero, it is the unique fixed point for subsequent linear transformations of point scatters. Whenever visualizations allow shifting between and/or combining of Cartesian and polar coordinate representations, as in Biplots, the location of this origin is critical. Specifically, origin-centric visualizations enhance the psychology of graphical perception by yielding scatters that can be interpreted as Dyson swarms. The key factor is typically the analyst's choice of origin via an initial "centering" translation; this choice determines whether the recovered scatter will have either no points depicted as being near the origin or else one (or more) points exactly coincident with this origin.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
