1 / 28

Multidimensional Detective

Multidimensional Detective. Alfred Inselberg Presented By Cassie Thomas. Motivation. Discovering relations among variables Displaying these relations. Cartesian vs. Parallel Coordinates. Cartesian Coordinates: All axes are mutually perpendicular Parallel Coordinates:

ethan-goff
Download Presentation

Multidimensional Detective

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multidimensional Detective Alfred Inselberg Presented By Cassie Thomas

  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. 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.

  11. Favorite Sentence “The paradigm is that of a detective, and since many parameters(equivalently dimensions) are involved we really mean a multidimensional detective”

  12. 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.

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

  22. 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

  23. What has happened to this topic? • Cornell University: Parallel Coordinates using MATLAB

  24. 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

  25. Demo http://csgrad.cs.vt.edu/~agoel/parallel_coordinates/stf/table1.stf

More Related