Visualization of Multivariate Data with Tail Trees

Abstract

We introduce graphical tools to visualize the shape, the location, and the orientation of a multivariate data set. We define a tree structure among the observations, called a tail tree. A tail tree is a tree whose root node corresponds to a center point of the data, and whose branches correspond to the tails of the data. We visualize a tail tree with a tail tree plot. Visualizing the tree structure among the observations makes it feasible to detect features from the data. A tail tree may also be used to define and enhance other visualizations. We define a tail frequency plot which visualizes the empirical probabilities of the disconnected tails of the point cloud. A tail tree induces a segmentation of the data which may be used to enhance a grand tour, graphical matrices, and parallel coordinate plots. We apply tail tree plots in exploratory data analysis of financial data.