Multidimensional Detective

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Multidimensional Detective

• Alfred Inselberg
• Presented By
• Rajiv Gandhi and Girish Kumar

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Motivation

• Discovering relations among variables
• Displaying these relations

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Cartesian vs. Parallel Coordinates

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

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

• Help represent lines and planes in gt 3 D

Representation of (-5, 3, 4, -2, 0, 1)
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Why Parallel Coordinates ? (contd..)

• Easily extend to higher dimensions

(1,1,0)
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Why Parallel Coordinates ? (contd..)
Parallel
Cartesian
Representation of a 4-D HyperCube
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Why Parallel Coordinates ? (contd..)
X9
Representation of a 9-D HyperCube
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Why Parallel Coordinates ? (contd..)
Representation of a Circle and a sphere
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Multidimensional Detective
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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

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Discovery Process

• Multivariate datasets
• Discover relevant relations among variables

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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?

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

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

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Example (contd..)

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

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Example (contd..)

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

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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

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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

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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

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Example
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Automated Multidimensional Detective

• Automates discovery process
• details not very clear