Exploring high-D spaces with multiform matrices and small multiples

Abstract

We introduce an approach to visual analysis of multivariate data that integrates several methods from information visualization, exploratory data analysis (EDA), and geovisualization. The approach leverages the component-based architecture implemented in GeoVISTA Studio to construct a flexible, multiview, tightly (but generically) coordinated, EDA toolkit. This toolkit builds upon traditional ideas behind both small multiples and scatterplot matrices in three fundamental ways. First, we develop a general, MultiForm, Bivariate Matrix and a complementary MultiForm, Bivariate Small Multiple plot in which different bivariate representation forms can be used in combination. We demonstrate the flexibility of this approach with matrices and small multiples that depict multivariate data through combinations of: scatterplots, bivariate maps, and space-filling displays. Second, we apply a measure of conditional entropy to (a) identify variables from a high-dimensional data set that are likely to display interesting relationships and (b) generate a default order of these variables in the matrix or small multiple display. Third, we add conditioning, a kind of dynamic query/filtering in which supplementary (undisplayed) variables are used to constrain the view onto variables that are displayed. Conditioning allows the effects of one or more well understood variables to be removed from the analysis, making relationships among remaining variables easier to explore. We illustrate the individual and combined functionality enabled by this approach through application to analysis of cancer diagnosis and mortality data and their associated covariates and risk factors.

Novel Method to Measure Inference Affordance in Static Small-Multiple Map Displays Representing Dynamic Processes

“…Early on, cartographers achieved a high level of sophistication in representing complex, dynamic spatio-temporal reality through the power of abstraction, in the form of a series of static two-dimensional maps, which Bertin, (1967) calls the 'collection of maps with one map characteristic'. More recently, small multiples have resurfaced in highly interactive and dynamic visual analytics displays, allowing the user to reorder, brush, and otherwise manipulate the depicted spatio-temporal data on the fly (MacEachren et al, 2003). The informational effectiveness of a static small-multiple display compared with an animation depends on using the appropriate number of small multiples and choosing the key events; that is, it depends on how many and which of the key events (macro steps) are selected to discretely represent the continuous and dynamic process (of micro steps).…”

Graph-theoretic scagnostics

“…This approach follows those taken by the manifold learning community [32], [4], [6]. Second, we can use these methods to sort scatterplot matrices in order to make them more accessible to lensing and other focus methods [14], [26], [29], [34].…”

Multiple-view strategies for enhanced understanding of dynamic tourist activity through geovisualization at regional and national scales

“…These small views normally use the same form of representation and they are reorderable, which provides the potential for users to perceive trends and relationships in the data and to gain insights (MacEachren et al 2003).…”