Multidimensional Detective
Alfred Inselberg
Presented By
Rajiv Gandhi and Girish Kumar
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
Parallel
Representation of a 2-D line
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
Multidimensional Detective
Our Favorite Sentence
“The display of multivariate datasets in
parallel coordinates transforms the search
for relations among the variables into a 2D
pattern recognition problem”
Discovery Process
• Multivariate datasets
• Discover relevant relations among variables
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
Example
Automated Multidimensional
Detective
• Automates discovery process
• details not very clear