1. Exploring High-D Spaces with Multiform Matrices and Small Multiples Presented by Ray Chen and Sorelle Friedler Authors: MacEachren, A., Dai, X., Hardisty, F., Guo, D., and Lengerich, G.

2. Definitions {Multi/bi/uni}variate – involving {one or more/two/one} variable(s) Form – a generic label for a kind of representation Small multiples – a set of juxtaposed data representations that together support understanding of multivariate information

3. GeoVISTA Studio Open source visual programming environment (Java) Enables simple integration of visualization strategies Used to create suite of coordinated components with focus on multiform bivariate displays

4. Multiform Bivariate Small Multiple One common variable (assigned to rows) One form per row One additional variable per column

5. Multiform Bivariate Matrix Rows and columns have same variables Diagonal cells can show univariate forms Selection controls at right Components can be selected and highlighted in all views

6. Sorting and Conditioning Aspects of Small Multiple and Matrix Views Computational detection of related subsets by conditional entropy provides for meaningful default ordering Conditioning tool allows the user to specify variable ranges Columns can be manually sorted (for juxtaposition of variables) Rows in the small multiple view can be manually sorted (for juxtaposition of forms)

7. Conditional Entropy Calculation A weighted sum based on density of cells in partitioned dimensions Dimensions partitioned by nested-means (not by equal intervals) Clusters can be detected!

8. Dimension Ordering Low conditional entropy between two attributes  close together in ordering Build MST from graph with conditional entropy ratings as edge weights Derive an ordering from the MST

9. Grid-based space-filling display Ordering: column Color: row Allows easy visual understanding of population fractions Can be included in small multiple or matrix displays Linked with selection capabilities

10. Demo