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Multidimensional Detective

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:

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Multidimensional Detective

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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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