Multidimensional DetectiveMultidimensional Detective

Alfred Inselberg

Presented By

Cassie Thomas

MotivationMotivation

Discovering relations among variables Displaying these relations

Cartesian vs. Parallel Cartesian vs. Parallel CoordinatesCoordinates

Cartesian Coordinates: – All axes are mutually perpendicular

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

An ExampleAn Example

Representation of a 2-D line

ParallelCartesian

Why Parallel Coordinates ?Why Parallel Coordinates ?

Help represent lines and planes in > 3 D

Representation of (-5, 3, 4, -2, 0, 1)

Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)

Easily extend to higher dimensions

(1,1,0)

Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)

ParallelCartesian

Representation of a 4-D HyperCube

Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)

X9

Representation of a 9-D HyperCube

Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)

Representation of a Circle and a sphere

More on Parallel CoordinatesMore 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 SentenceFavorite Sentence

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

Discovery ProcessDiscovery Process

Multivariate datasetsDiscover relevant relations among variablesDiscover sensitivities, understand the

impact of constraints , optimizationA dataset with P points has 2P subsets, of

which any of those can have interesting relationships.

An ExampleAn Example

Production data of 473 batches of a VLSI chip

Measurements of 16 parameters - X1,..,X16Objective

– Raise the yield X1– Maintain high quality X2

Belief: Defects hindered yield and quality. Is it true?

The Full DatasetThe Full Dataset

X1 is normal about its medianX2 is bipolar

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

Example (contd..)Example (contd..)Batches with zero defect in 9 out of 10

defect typesAll have poor yields and low quality

Example (contd..)Example (contd..)Batches with zero defect in 8 out of 10

defect typesProcess is more sensitive to variations in X6

than other defects

Example (contd..)Example (contd..)Isolate batch with the highest yieldX3 and X6 are non-zeroDefects of types X3 and X6 are essential for

high yield and quality

CritiqueCritiqueStrengths

– 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 WorkRelated WorkInfoCrystal [Anslem Spoerri]

– Visualizes all possible relationships among N concepts

– Example: Get documents related to visual query languages for retrieving information concerning human factors

ReferencesReferences

MathematicsGraphicsData MiningReferenced in such work as parallel

coordinates plots, hierarchical parallel coordinates

ContributionsContributions

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 What has happened to this topic?topic?

Cornell University: Parallel Coordinates using MATLAB

What has happened to this What has happened to this topic? (cont)topic? (cont)

Fujitsu SymfoWARE visual minerSpotfire-parallel coordinates featureLifelines – UMD “constructing parallel coordinates plot for

problem solving” paper presented at Smart Graphics ’01

DemoDemo

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