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: – All axes are parallel to one another – Equally spaced

An Example Representation of a 2-D line Parallel Cartesian

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

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

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

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

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

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.

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

Discovery Process Multivariate datasets Discover relevant relations among variables Discover sensitivities, understand the impact of constraints, optimization A dataset with P points has 2 P subsets, of which any of those can have interesting relationships.

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?

The Full Dataset The Full Dataset X1 is normal about its median X2 is bipolar

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

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

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

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

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

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

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

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

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

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

Demo _coordinates/stf/table1.stf