Seo, JinwookShneiderman, BenInteractive exploration of multidimensional data sets is challenging because: (1) it is difficult to comprehend patterns in more than three dimensions, and (2) current systems often are a patchwork of graphical and statistical methods leaving many researchers uncertain about how to explore their data in an orderly manner. We offer a set of principles and a novel rank-by-feature framework that could enable users to better understand distributions in one (1D) or two dimensions (2D), and then discover relationships, clusters, gaps, outliers, and other features. Users of our 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. We summarize our Graphics, Ranking, and Interaction for Discovery (GRID) principles as: (1) 1D, 2D, then features (2) graphics, ranking, summaries, then statistics. We implemented the rank-by-feature framework in the Hierarchical Clustering Explorer, but the same data exploration principles could enable users to organize their discovery process so as to produce more thorough analyses and extract deeper insights in any multidimensional data application, such as spreadsheets, statistical packages, or information visualization tools.en-USTechnical Report