Exploring High-D Spaces with
Multiform Matrices
and Small Multiples
Authors: MacEachren, A., Dai, X., Hardisty, F.,
Guo, D., and Lengerich, G.
Presented by
Ray Chen and Sorelle Friedler
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
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
Multiform Bivariate Small Multiple
• One common variable
(assigned to rows)
• One form per row
• One additional
variable per column
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
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)
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!
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
Grid-based space-filling display
• Ordering: column
• Color: row
• Allows easy visual
understanding of
population fractions QuickTime™ an d a
TIFF (LZW) decompressor
• Can be included in are need ed to see this p icture.
small multiple or
matrix displays
• Linked with selection
capabilities
Demo