Interactive exploration of multidimensional data sets is challenging because: (1) it is difficult to comprehend patterns in more than three dimensions, and (2) current systems are often a patchwork of graphical and statistical methods leaving many researchers uncertain about how to explore their data in an orderly manner.

This dissertation offers a set of principles and a novel rank-by-feature framework that could enable users to better understand multidimensional and multivariate data by systematically studying distributions in one (1D) or two dimensions (2D), and then discovering relationships, clusters, gaps, outliers, and other features. Users of this rank-by-feature framework can view graphical presentations (histograms, boxplots, and scatterplots), and then choose a feature detection criterion to rank 1D or 2D axis-parallel projections. By combining information visualization techniques (overview, coordination, and dynamic query) with summaries and statistical methods, users can systematically examine the most important 1D and 2D axis-parallel projections. This research provides a number of valuable contributions:

Graphics, Ranking, and Interaction for Discovery (GRID) principles- a set of principles for exploratory analysis of multidimensional data, which are  summarized as: (1) study 1D, study 2D, then find features (2) ranking guides insight, statistics confirm.  GRID principles help users organize their discovery process in an orderly manner so as to produce more thorough analyses and extract deeper insights in any multidimensional data application.

Rank-by-feature framework - a user interface framework based on the GRID principles. Interactive information visualization techniques are combined with statistical methods and data mining algorithms to enable users to orderly examine multidimensional data sets using 1D and 2D projections.

The design and implementation of the Hierarchical Clustering Explorer (HCE), an information visualization tool available at www.cs.umd.edu/hcil/hce.  HCE implements the rank-by-feature framework and supports interactive exploration of hierarchical clustering results to reveal one of the important features - clusters.

Validation through case studies and user surveys: Case studies with motivated experts in three research fields and a user survey via emails to a wide range of HCE users demonstrated the efficacy of HCE and the rank-by-feature framework.  These studies also revealed potential improvement opportunities in terms of design and implementation.