Transcript AInselberg
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