论文标题
用于多维缩放的局部双列，并应用于微生物组
Local biplots for multi-dimensional scaling, with application to the microbiome
论文作者
论文摘要
我们提出本地双单行器，这是经典的主要组件双皮子的扩展到多维缩放的。注意到主组件双头将其解释为从数据空间到主要子空间的地图的雅各布式，我们将局部双头定义为用于多维缩放的类似地图的雅各布。在此过程中，我们显示了本地双翼轴，广义欧几里得距离和广义主成分之间的密切关系。在模拟和实际数据中，我们显示了本地双头如何阐明哪些变量或变量组合对于多维缩放的低维嵌入至关重要。它们对微生物组数据分析中常用的一类系统发育信息的距离有特别的了解，表明这些距离的不同变体可以解释为沿系统发育树沿隐式平滑数据，并且这种平滑的程度是可变的。
We present local biplots, a an extension of the classic principal components biplot to multi-dimensional scaling. Noticing that principal components biplots have an interpretation as the Jacobian of a map from data space to the principal subspace, we define local biplots as the Jacobian of the analogous map for multi-dimensional scaling. In the process, we show a close relationship between our local biplot axes, generalized Euclidean distances, and generalized principal components. In simulations and real data we show how local biplots can shed light on what variables or combinations of variables are important for the low-dimensional embedding provided by multi-dimensional scaling. They give particular insight into a class of phylogenetically-informed distances commonly used in the analysis of microbiome data, showing that different variants of these distances can be interpreted as implicitly smoothing the data along the phylogenetic tree and that the extent of this smoothing is variable.
