Multidimensional Detective

1
Multidimensional Detective

• Alfred Inselberg
• Presented By
• Cassie Thomas

2
(No Transcript)
3
Motivation

• Discovering relations among variables
• Displaying these relations

4
(No Transcript)
5
Cartesian vs. Parallel Coordinates

• Cartesian Coordinates
• All axes are mutually perpendicular
• Parallel Coordinates
• All axes are parallel to one another
• Equally spaced

6
An Example
Parallel
Cartesian
Representation of a 2-D line
7
Why Parallel Coordinates ?

• Help represent lines and planes in gt 3 D

Representation of (-5, 3, 4, -2, 0, 1)
8
Why Parallel Coordinates ? (contd..)
Easily extend to higher dimensions
(1,1,0)
9
Why Parallel Coordinates ? (contd..)
Parallel
Cartesian
Representation of a 4-D HyperCube
10
Why Parallel Coordinates ? (contd..)
X9
Representation of a 9-D HyperCube
11
Why Parallel Coordinates ? (contd..)
Representation of a Circle and a sphere
12
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.

13
Favorite Sentence

• The paradigm is that of a detective, and since
  many parameters(equivalently dimensions) are
  involved we really mean a multidimensional
  detective

14
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.

15
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?

16
The Full Dataset
X1 is normal about its medianX2 is bipolar
17
Example (contd..)

• Batches high in yield, X1 and quality, X2
• Batches with low X3 values not included in
  selected subset

18
Example (contd..)

• Batches with zero defect in 9 out of 10 defect
  types
• All have poor yields and low quality

19
Example (contd..)

• Batches with zero defect in 8 out of 10 defect
  types
• Process is more sensitive to variations in X6
  than other defects

20
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

21
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

22
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

23
References

• Mathematics
• Graphics
• Data Mining
• Referenced in such work as parallel coordinates
  plots, hierarchical parallel coordinates

24
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

25
What has happened to this topic?

• Cornell University Parallel Coordinates using
  MATLAB

26
(No Transcript)
27
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

28
Demo

• http//csgrad.cs.vt.edu/agoel/parallel_coordinate
  s/stf/table1.stf