Grand Tour and Projection Pursuit

Abstract

The grand tour and projection pursuit are two methods for exploring multivariate data. We show how to combine them into a dynamic graphical tool for exploratory data analysis, called a projection pursuit guided tour. This tool assists in clustering data when clusters are oddly shaped and in finding general low-dimensional structure in high-dimensional, and in particular, sparse data. An example shows that the method, which is projection-based, can be quite powerful in situations that may cause grief for methods based on kernel smoothing. The projection pursuit guided tour is also useful for comparing and developing projection pursuit indexes and illustrating some types of asymptotic results.

Projection inspector: Assessment and synthesis of multidimensional projections

“…Projection Pursuit [13] and its variants [14,1], for instance, generate a family of scatter plots ranked according to their concentration of points into clusters while preserving the separability of those clusters. Rank-byFeature [2] is an interactive framework that allows users to select interesting dimensions according to distinct rank criteria, producing a set of scatter plots from user selections.…”

“…However, the existing alternatives either rely on multiple views generated from a single MP method, such as Projection Pursuit [1] and ranked scatter plot matrices [2], or are not flexible enough to allow a free navigation throughout the possibilities, as is the case of Stress Maps [3] and CheckVis [4]. When faced with deciding what method to adopt for his or her data set and task, the analyst is often faced with various views, various numbers and in the end is not sure what alternative is offering a proper compromise in each case.…”

Visualization of Multidimensional Data in Purpose of Qualitative Classification of Various Types of Coal / Wizualizacja Wielowymiarowych Danych W Celu Klasyfikacji Jakościowej Różnych Typów Węgla

“…It was described by Asimov (Asimov, 1985), for the first time. Then, it was developed by many authors (Buja & Asimov, 1985;Cook et al, 1995;Hurley & Buja, 1990). The method of principal component analysis (Li et al, 2000) makes use of an orthogonal projection of the observation set into a plane represented by specially chosen vectors which are the eigenvectors corresponding with the two highest eigenvalues of the covariance matrix of the observation set.…”

Graphs as navigational infrastructure for high dimensional data spaces

“…Buja et al, 1988, Cook et al, 1995 and as implemented, for example, in XGobi (Swayne et al, 1998, now GGobi). The movement is no longer a rigid rotation and we lose this grounding of common visual experience.…”