Mathematical Modeling
Lecture 1
Instructor: Liangfu Lu liangfulv@
Multi-Dimensional Data Visualization
---Parallel Coordinates
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Multi-Dimensional Data
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Cartesian vs. Parallel oordinates
Example 1:
Dataset in a Cartesian coordinate
Same dataset in parallel coordinates
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Example 2: Air traffic control
Cartesian Coordinates
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Bad Examples
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Parallel Coordinates: Disadvantages
• Axes are too close as dimensions increase. • Clutter can reduce perceived information. • Varying the order of axes scale, although indicating different patterns, may cause confusion.
Parallel Coordinates
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Good Example
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Parallel Coordinates: Advantages
• Multi-dimensional data can be visualized in two
dimensional space with low complexity. • Each variable is treated uniformly. • Relations within multi-dimensional data can be discovered (“data mining”).
Coordinates. Journal of the American Statistical Association, 1990.
85(411): p. 664-675. 3. Bertini, E., A. Tatu, and D. Keim, Quality Metrics in High-Dimensional
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Team Work: Improving Parallel Coordinates
References
1. Inselberg, A., The plane with parallel coordinates. The Visual Computer, 1985. 1(2): p. 69-91. 2. Wegman, E.J., Hyperdimensional Data Analysis Using Parallel
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Parallel Coordinates Visualization Summary
•Each data point is mapped to a line (Duality) •Similar points correspond to similar lines(Correlation) •Effective exploration and clustering(Pattern)
Parallel Coordinates. IEEE Transactions on Visualization and Computer Graphics, 2010. 16(6):stions? Thank you!
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parallel coordinates
glyphs
scatterplot matrices 4
Parallel
Coordinates
Glyphs
Scatterplot
Matrices
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Background
•Proposed in 1985 by Alfred Insellberg •Good for multi-dimensional data exploration •Widely used in information visualization of
•Problems: order of axes, limit to 1~20 dimensions
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Individual Assignment:Visualizing Iris Data
Iris setosa
Iris versicolor
Iris virginica
sepal sepal petal petal length width length width 5.1 3.5 1.4 0.2 4.9 ... 5.9 3 ... 3 1.4 ... 5.1 0.2 ... 1.8
Data Visualization: An Overview and Systematization. IEEE
Transactions on Visualization and Computer Graphics, 2011. 17(12): p. 2203-2212.
4. Dasgupta, A. and R. Kosara, Pargnostics: Screen-Space Metrics for
• Visualizing large information space through relatively small window screen. • Visualizing multi-dimensional data (n>3) in 2D space.
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•Axis reconfiguration techniques, such as parallel coordinates and glyphs; •Dimensional subsetting, such as scatterplot matrices
multi-dimensional data
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Rationale
To
represent N dimensional data
•Set N equidistant vertical axes in parallel •Each axis scaled to [min, max] range of attributes •Put data to intersects on corresponding axes •Connect intersects •Example: (0,1,-1,2)