¹Department of Statistics, Economics Faculty, University of Mannheim, Mannheim, Germany

Correspondence: Jussi Klemelä, Department of Statistics, Economics Faculty, University of Mannheim, L7 3-5 Verfügungsgebäude, 68131 Mannheim, Germany. Fax: +49 621 1811931. E-mail: klemela@rumms.uni-mannheim.de

Received 13 July 2006; Revised 20 February 2007; Accepted 5 March 2007; Published online 17 May 2007.

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.