多维尺度投影的广义双标图
Generalized Biplots for Multidimensional Scaled Projections
摘要：
降维和可视化是数据分析的主要内容。诸如主成分分析（PCA）和多维标度（MDS）的方法提供高维（HD）数据的低维（LD）投影，同时保留观测之间的HD关系。传统的双标图通过显示属性的LD轴来为PCA投影的LD空间分配意义。然而，这些轴特定于PCA中使用的线性投影。MDS投影允许任意的应力和相异度函数，在标记LD空间时需要特别小心。我们提出了一个迭代方案，绘制LD轴为每个属性的基础上，用户指定的压力和相异性指标。我们讨论了我们的一般双标图方法的细节，它与PCA派生的双标图的关系，并提供使用真实数据的例子。
英文摘要：
Dimension reduction and visualization is a staple of data analytics. Methods such as Principal Component Analysis (PCA) and Multidimensional Scaling (MDS) provide low dimensional (LD) projections of high dimensional (HD) data while preserving an HD relationship between observations. Traditional biplots assign meaning to the LD space of a PCA projection by displaying LD axes for the attributes. These axes, however, are specific to the linear projection used in PCA. MDS projections, which allow for arbitrary stress and dissimilarity functions, require special care when labeling the LD space. We propose an iterative scheme to plot an LD axis for each attribute based on the user-specified stress and dissimilarity metrics. We discuss the details of our general biplot methodology, its relationship with PCA-derived biplots, and provide examples using real data.
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。
