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