Multidimensional Detective
Alfred Inselberg
Presented By
Cassie Thomas
Motivation

Discovering relations among variables
 Displaying these relations
Cartesian vs. Parallel
Coordinates

Cartesian Coordinates:
– All axes are mutually perpendicular

Parallel Coordinates:
– All axes are parallel to one another
– Equally spaced
An Example
Cartesian
Representation of a 2-D line
Parallel
Why Parallel Coordinates ?

Help represent lines and planes in > 3 D
Representation of (-5, 3, 4, -2, 0, 1)
Why Parallel Coordinates ?
(contd..)
Easily extend to higher dimensions
(1,1,0)
Why Parallel Coordinates ?
(contd..)
Cartesian
Parallel
Representation of a 4-D HyperCube
Why Parallel Coordinates ?
(contd..)
X9
Representation of a 9-D HyperCube
Why Parallel Coordinates ?
(contd..)
Representation of a Circle and a sphere
More on Parallel Coordinates

The design of the queries is important- one
must accurately cut complicated portions of
a N-dimensional “watermelon”
 If a query is not understood correctly then
the use of parallel coordinates is limited to
small datasets. As well as the geometry.
Favorite Sentence
“The paradigm is that of a detective, and since
many parameters(equivalently dimensions)
are involved we really mean a
multidimensional detective”
Discovery Process

Multivariate datasets
 Discover relevant relations among variables
 Discover sensitivities, understand the
impact of constraints , optimization
 A dataset with P points has 2P subsets, of
which any of those can have interesting
relationships.
An Example

Production data of 473 batches of a VLSI
chip
 Measurements of 16 parameters - X1,..,X16
 Objective
– Raise the yield X1
– Maintain high quality X2

Belief: Defects hindered yield and quality.
Is it true?
The Full Dataset
X1 is normal about its median
X2 is bipolar
Example (contd..)

Batches high in yield, X1 and quality, X2
 Batches with low X3 values not included in
selected subset
Example (contd..)

Batches with zero defect in 9 out of 10
defect types
 All have poor yields and low quality
Example (contd..)

Batches with zero defect in 8 out of 10
defect types
 Process is more sensitive to variations in X6
than other defects
Example (contd..)

Isolate batch with the highest yield
 X3 and X6 are non-zero
 Defects of types X3 and X6 are essential for
high yield and quality
Critique

Strengths
– Low representational complexity
– Discovery process well explained
– Use of parallel coordinates is very effective

Weaknesses
– Does not explain how axes permutation affects
the discovery process
– Requires considerable ingenuity
– Display of relations not well explained
– References not properly cited
Related Work

InfoCrystal [Anslem Spoerri]
– Visualizes all possible relationships among N
concepts
– Example: Get documents related to visual query
languages for retrieving information concerning
human factors
References

Mathematics
 Graphics
 Data Mining
 Referenced in such work as parallel
coordinates plots, hierarchical parallel
coordinates
Contributions

Inselberg pioneered a method for displaying
multivariate data
 Made displaying high dimensional data sets
useful and understandable.
 Spawned several new techniques for
displaying multidimensional data. Plots,
hierarchical.
 Software- Parallax
What has happened to this
topic?

Cornell University: Parallel Coordinates
using MATLAB
What has happened to this
topic? (cont)

Fujitsu SymfoWARE visual miner
 Spotfire-parallel coordinates feature
 Lifelines – UMD
 “constructing parallel coordinates plot for
problem solving” paper presented at Smart
Graphics ’01
Demo
http://csgrad.cs.vt.edu/~agoel/parallel
_coordinates/stf/table1.stf