ABSTRACT
In previous chapters we searched for lower-dimensional representations of our data that might show interesting structure. However, there are an infinite number of possibilities; so we might try touring through space, looking at many of these representations. This chapter includes a description of several tour methods that can be roughly categorized into the following groups:
Grand Tours : If the goal is to look at the data from all possible viewpoints to get an idea of the overall distribution of the p- dimensional data, then we might want to look at a random sequence of lower-dimensional projections. Typically, there is little user interaction with these methods other than to set the step size for the sequence and maybe to stop the tour when an interesting structure is found. This was the idea behind the original torus grand tour of Asimov (1985).
Interpolated Tours : In this type of tour, the user chooses a starting plane and an ending plane. The data are projected onto the first plane. The tour then proceeds from one plane to the other by interpolation. At each step of the sequence, the user is presented with a different view of the data, usually in the form of a scatterplot (Hurley and Buja, 1990).
Guided Tours : These tours can be either partly or completely guided by the data. An example of this type of tour is the EDA projection pursuit method. While this is not usually an interactive or visual tour in the sense of the others, it does look at many projections of the data searching for interesting structure such as holes, clusters, etc.
