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Multidimensional Detective: Discovering Relations Among Variables

Uncover relationships among variables using Cartesian and Parallel Coordinates. Represent multivariate datasets effectively. Critique strengths and weaknesses of the discovery process. Explore related works like InfoCrystal. Automate detection process for efficiency.

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Multidimensional Detective: Discovering Relations Among Variables

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  1. Multidimensional Detective Alfred Inselberg Presented By Rajiv Gandhi and Girish Kumar

  2. Motivation • Discovering relations among variables • Displaying these relations

  3. Cartesian vs. Parallel Coordinates • Cartesian Coordinates: • All axes are mutually perpendicular • Parallel Coordinates: • All axes are parallel to one another • Equally spaced

  4. An Example Parallel Cartesian Representation of a 2-D line

  5. Why Parallel Coordinates ? • Help represent lines and planes in > 3 D Representation of (-5, 3, 4, -2, 0, 1)

  6. Why Parallel Coordinates ? (contd..) • Easily extend to higher dimensions (1,1,0)

  7. Why Parallel Coordinates ? (contd..) Cartesian Parallel Representation of a 4-D HyperCube

  8. Why Parallel Coordinates ? (contd..) X9 Representation of a 9-D HyperCube

  9. Why Parallel Coordinates ? (contd..) Representation of a Circle and a sphere

  10. Multidimensional Detective

  11. 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”

  12. Discovery Process • Multivariate datasets • Discover relevant relations among variables

  13. 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?

  14. The Full Dataset X1 is normal about its medianX2 is bipolar

  15. Example (contd..) • Batches high in yield, X1 and quality, X2 • Batches with low X3 values not included in selected subset

  16. Example (contd..) • Batches with zero defect in 9 out of 10 defect types • All have poor yields and low quality

  17. Example (contd..) • Batches with zero defect in 8 out of 10 defect types • Process is more sensitive to variations in X6 than other defects

  18. 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

  19. 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

  20. 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

  21. Example

  22. Automated Multidimensional Detective • Automates discovery process • details not very clear

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