2-D and 3-D Layouts to Aid Human Cognition of Local Structure in Multivariate Data

Abstract

This dissertation addresses the development of new 2-D and 3-D layout algorithms for statistical visualization purposes. These layouts serve tasks that include placing near neighbors close together, showing group or cluster membership, allocating space for glyphs and images used to characterize objects (cases), and approximating distances between objects. These tasks serve goals that include conveying structure, facilitating pattern discovery and hypothesis generation, and providing access to detailed information. The layouts are for human use, so they include considerations of human perception, cognition, and organizational regularity. This dissertation targets applications involving the study of cases, variables, clusters, and other multivariate objects. In these applications the notion of distances/dissimilarities between objects is important. However, accurate distances can not be maintained in low dimensional views. Researchers have developed a variety of layout methods to represent multivariate objects (including data summaries) in low dimensions. Common layout algorithms include multidimensional scaling, Kohonen self-organizing maps, Treemaps and spring models. This dissertation compares and contrasts the new layout algorithms with previous methods, develops new star glyphs, and demonstrates the new algorithms using multivariate data produced by AIRS (Atmospheric InfraRed Sounder) and other datasets.