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Multidimensional Detective
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Multidimensional DetectiveMultidimensional Detective
Alfred Inselberg
Presented By
Cassie Thomas
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MotivationMotivation
Discovering relations among variables Displaying these relations
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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
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An ExampleAn Example
Representation of a 2-D line
ParallelCartesian
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Why Parallel Coordinates ?Why Parallel Coordinates ?
Help represent lines and planes in > 3 D
Representation of (-5, 3, 4, -2, 0, 1)
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Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)
Easily extend to higher dimensions
(1,1,0)
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Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)
ParallelCartesian
Representation of a 4-D HyperCube
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Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)
X9
Representation of a 9-D HyperCube
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Why Parallel Coordinates ? Why Parallel Coordinates ? (contd..)(contd..)
Representation of a Circle and a sphere
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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.
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Favorite SentenceFavorite Sentence
“The paradigm is that of a detective, and since many parameters(equivalently dimensions) are involved we really mean a multidimensional detective”
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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.
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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?
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The Full DatasetThe Full Dataset
X1 is normal about its medianX2 is bipolar
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Example (contd..)Example (contd..) Batches high in yield, X1 and quality, X2 Batches with low X3 values not included in selected subset
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Example (contd..)Example (contd..)Batches with zero defect in 9 out of 10
defect typesAll have poor yields and low quality
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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
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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
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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
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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
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ReferencesReferences
MathematicsGraphicsData MiningReferenced in such work as parallel
coordinates plots, hierarchical parallel coordinates
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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
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What has happened to this What has happened to this topic?topic?
Cornell University: Parallel Coordinates using MATLAB
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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
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DemoDemo
http://csgrad.cs.vt.edu/~agoel/parallel_coordinates/stf/table1.stf