Visualization and the understanding of multidimensional data

This paper is concerned with the task of making sense out of a body of a large number of multivariate objects. The matter of 'making sense' or 'understanding' is described in terms of knowing three types of relationships and being able to keep such knowledge in mind. The paper argues that both matters, obtaining the knowledge, and keeping it in mind, available for use, would be facilitated by mapping the N-dimensional space to 2-dimensional space or 3-dimensional space, in a topologically meaningful manner. A 'ratio-conserving' mapping procedure is described and compared with some other previously proposed methods. A body of 5-dimensional semiconductor materials composition and properties data is used for illustration purposes. Three types of 'meaning' are discussed and it is shown that 'ratio-conserving' mapping does provide a way of obtaining and retaining a visualization of the meaning of large bodies of complex multivariate data. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.