Area Biplots
Area Biplots
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面积双图
DOI：
10.1198/jcgs.2010.07134
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
M. van de Velden
中科院分区：
文献类型：
--
作者：
J. Gower;P. Groenen;M. van de Velden
主成分分析和对应分析等经典的多元分析技术使用内积来近似数据值。这些技术的结果可以通过在双图中联合呈现行点和列点来可视化，其中将行点投影到列点向量上，然后乘以列点向量的长度给出近似于相应数据元素的内积。在本文中，我们提出了一种新的可视化：行点旋转 90° 后，旋转后的行点、列点和原点组成的三角形所跨越的区域近似于数据值。与投影双图相反，可以直接比较不同行和列点跨越的区域。此属性使面积双标图独一无二。因此，面积双图对于分析可以比较所有元素的数据矩阵特别有用。通过面积双图可以很容易地看出，与内积类似，高维面积解可以通过对后续维度对的面积求和来表示。这里，面积双图是为主成分分析、对应分析和交互双图而开发的，但它具有普遍的适用性。本文有在线补充材料。
Classical multivariate analysis techniques such as principal components analysis and correspondence analysis use inner products to approximate data values. Results of these techniques may be visualized by presenting row and column points jointly in a biplot, where the projection of a row point onto a column point vector followed by a multiplication by the length of the column point vector gives the inner product that approximates the corresponding data element. In this article, we propose a new visualization: after a 90○ rotation of the row points, the area spanned by a triangle of a rotated row point, a column point, and the origin approximates the data values. In contrast to the projection biplot, the areas spanned by different row and column points can be compared directly. This property makes the area biplot unique. Therefore, the area biplot is particularly useful for the analysis of a data matrix where all elements can be compared. The area biplot makes it easy to see that, similarly to inner products, higher dimensional area solutions can be represented by summing areas over subsequent pairs of dimensions. Here, the area biplot is developed for principal components analysis, correspondence analysis, and for interaction biplots, but it has general applicability. This article has supplementary material online.