Transcript The Point Line Duality Taken from: Process Improvement

Opinion to ponder…
“Since we are a visual species (especially the
American culture), because of our educational
system. Many of the tools currently used to
educate children are graphic in nature. We teach
them words by showing them pictures of things.
We teach them to count by showing them the
order that numbers fall. Therefore, our visual
receptors are heightened at the expense of other
cognitive functions. I have also found that
business people respond better to graphs and
charts than they do to numbers.”
by Professor Hossein Arsham from University of Baltimore
“MultiDimensional Detective”
Alfred Inselberg, Multidimensional Graphs Ltd
A presentation by Margaret Ellis
“do not let the picture intimidate you”
Parallel Coordinates
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multi-dimensional information
equally spaced parallel axes
varying scales on axes
Point  Line duality
DEMO
http://csgrad.cs.vt.edu/~agoel/parallel_coordinates/
The Point Line Duality
Taken from: Process Improvement Laboratory’s Overview Of Parallel Coordinates
(University of Florida)
Inselberg’s Data
• VLSI chip production
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yield (% of useful chips)
quality
10 types of defects
4 physical parameters
• Objective: Raise the yield and maintain quality.
• Conclusion: Small amounts of certain defects
actually helped accomplish the objective!
Inselberg’s Data
Demonstrating Interior Point Algorithm
• Outputs of a country’s economic sectors
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output of 5 industries
output of the government
output of miscellaneous spending
resulting GNP
• A feasible economic policy can be visualized by
interactively varying the chosen first variable,
points interior to the region satisfy the constraints.
Advantages
• Multi-dimensional data can be visualized
in two dimensions with low complexity.
• Each variable is treated uniformly.
• Relations within multi-dimensional data
can be discovered (“data mining”).
• Because of its visual cues, can serve as a
preprocessor to other methods.
Disadvantages
• Close axes as dimensions increase.
• Clutter can reduce information perceived.
• Varying axes scale, although indicating
relationships, may cause confusion.
• Connecting the data points can be
misleading.
DISADVANTAGE: LEVEL OF CLUTTER
Taken from: “Hierarchical Parallel Coordinates”
Ying-Huey Fua, Elke A. Rundensteiner, Matthew O. Ward
16,384 records in
5 dimensions
causes
over-plotting.
DISADVANTAGE: Connecting Data Points
TAKEN FROM: “THE ANALYSIS OF T48 LOW PRESSURE TURBINE INLET
TEMPERATURES USING PARALLEL COORDINATES” By Frank S. Budny
X-longitude
Y-latitude Zheight
User Tasks and Metrics
• User performance for discovering relations among
multiple variables should be increased.
• User performance for discovering relations
between two variables may be decreased.
• Learnability can be low without proper
geometrical understanding.
• Error rate for the experienced user is probably
similar to other representations.
Do use parallel coordinates
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With multidimensional data!
When looking for relationships!
If occlusion would occur in 3-D.
For geometrical structures such as a Convex
Hypersurface in 20-D.
Do use parallel coordinates
With an interior point algorithm to
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analyze trade-off
discover sensitivities
understand the impact of constraints
optimize
Do not use parallel coordinates
when…
• the user doesn’t understand them.
• querying multidimensional data.
• other methods are better for user objective
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Glyphs?
Chernoff faces?
Star Coordinates?
Worlds within Worlds?
Table Lens?
Improvement: SUMMARIZATION
Taken from: “Hierarchical Parallel Coordinates”
Ying-Huey Fua, Elke A. Rundensteiner, Matthew O. Ward
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DEALING WITH
CLUTTER:
“ The deepest opacity is a
function of the density of a
cluster, defined as the
ratio .”
Which is better?
A.
B.
Improvement: MANIPULATION
Taken from: “Hierarchical Parallel Coordinates”
Ying-Huey Fua, Elke A. Rundensteiner, Matthew O. Ward
• Extent Scaling
–the thickness of the bands is varied
•Structure-Based Brushing
–localizing a subspace
•Drill-down and Roll-up
– increasing and decreasing detail
•Dimension zooming
– magnification or distortion
•Dynamic masking
–interactively fade out nodes
Goals of development
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Low representational complexity
Works for any N(number of dimensions)
Every variable is treated uniformly
Displayed object can be recognized under
projective transformations(i.e. rotation,
translation, scaling, perspective)
• Easily/intuitively conveys information
• Methodology is based on rigourous mathematical
and algorithmic results