Multi-Dimensional%20Data%20Visualization

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Multi-Dimensional Data Visualization

• cs5764 Information Visualization
• Chris North

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Review

• What is the Visualization Pipeline?
• What are the steps of Visual Mapping?
• What is the Info Vis Mantra?

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Information Types

• Multi-dimensional databases,
• 1D timelines,
• 2D maps,
• 3D volumes,
• Hierarchies/Trees directories,
• Networks/Graphs web, communications,
• Document collections digital libraries,

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The Simple Stuff

• Univariate
• Bivariate
• Trivariate

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Univariate

• Dot plot
• Bar chart (item vs. attribute)
• Tukey box plot
• Histogram

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Bivariate

• Scatterplot

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Trivariate

• 3D scatterplot, spin plot
• 2D plot size (or color)

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Multi-Dimensional Data

• Each attribute defines a dimension
• Small of dimensions easy
• Data mapping, Clevelands rules
• What about many dimensional data? n-D

What does 10-D space look like?
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Projection

• map n-D space onto 2-D screen

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Glyphs Chernoff Faces

• 10 Parameters
• Head Eccentricity
• Eye Eccentricity
• Pupil Size
• Eyebrow Slope
• Nose Size
• Mouth Vertical Offset
• Eye Spacing
• Eye Size
• Mouth Width
• Mouth Openness
• http//hesketh.com/schampeo/projects/Faces/chernof
  f.html

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Glyphs Stars
d1
d2
d7
d3
d6
d4
d5
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Multiple Views withBrushing-and-linking
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Scatterplot Matrix

• All pairs of attributes
• Brushing and linking
• http//noppa5.pc.helsinki.fi/koe/3d3.html

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on steroids
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Different Arrangements of Axes

• Axes are good
• Lays out all points in a single space
• position is 1st in Clevelands rules
• Uniform treatment of dimensions
• Space gt 3D ?
• Must trash orthogonality

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Parallel Coordinates

• Inselberg, Multidimensional detective
  (parallel coordinates)

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Parallel Coordinates

• Bag cartesian
• (0,1,-1,2)

x
y
z
w
0
0
0
0
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Star Plot
1
8
2
7
3
4
6
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Parallel Coordinates with axes arranged radially
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Star Coordinates

• Kandogan, Star Coordinates

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Star Coordinates

• Cartesian Star Coordinates

P(v1,v2,v3,v4,v5,v6,v7,v8)
P(v1, v2)
d1
d1
d8
d2
v3
v4
p
v2
v1
v5
v2
d7
d3
d2
p
v1
v8
v6
v7
d6
d4

• Mapping
• Items ? dots
• S attribute vectors ? (x,y)

d5
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Analysis
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Table Lens

• Rao, Table Lens

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FOCUS / InfoZoom

• Spenke, FOCUS

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VisDB

• Keim, VisDB

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Pixel Bar Charts

• Keim

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Comparison of Techniques
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Comparison of Techniques

• ParCood lt1000 items, lt20 attrs
• Relate between adjacent attr pairs
• StarCoord lt1,000,000 items, lt20 attrs
• Interaction intensive
• TableLens similar to par-coords
• more items with aggregation
• Relate 1m attrs (sorting), short learn time
• Visdb 100,000 items with 10 attrs
• Itemsattrs screenspace, long learn time,
  must query
• Spotfire lt1,000,000 items, lt10 attrs (DQ many)
• Filtering, short learn time

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Multi-DimensionalFunctions

• cs5764 Information Visualization
• Chris North

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Multi-Dimensional Functions

• y f(x1, x2, x3, , xn)
• Continuous
• E.g. y x13 2x22 - 9x3
• Discrete
• xi are uniformly sampled in a bounded region
• E.g. xi 0,1,2,,100
• E.g. measured density in a 3D material under
  range of pressures and room temperatures.

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Relations vs. Functions

• Relations
• R(A, B, C, D, E, F)
• All dependent variables (1 ind.var.?)
• Sparse points in multi-d dep.var. space
• Functions
• R(A, B, C, D, E, F, Y) Yf(A, B, C, D, E, F)
• Many independent variables
• Defined at every point in multi-d ind.var. space
  (onto)
• Huge scale 6D with 10 samples/D 1,000,000
  data points

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Multi-D Relation Visualizations

• Dont work well for multi-D functions
• Example
• Parallel coords
• 5D func sampled on 1-9 for all ind.vars.

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• Typically want to encode ind.vars. as spatial
  attrs

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1-D Easy

• b f(a)
• a ? x
• b ? y

b
a
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2-D Easy

• c f(a, b)
• Height field
• a ? x
• b ? y
• c ? z

c
b
a
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2-D Easy

• c f(a, b)
• Heat map
• a ? x
• b ? y
• c ? color

b
a
c
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3-D Hard

• d f(a, b, c)
• Color volume
• a ? x
• b ? y
• c ? z
• d ? color
• Whats inside?

c
b
a
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?4D Really Hard

• y f(x1, x2, x3, x4, , xn)
• What does a 5D space look like?
• Approaches
• Hierarchical axes (Mihalisin)
• Nested coordinate frames (Worlds within Worlds)
• Slicing (HyperSlice)
• Radial FocusContext (PolarEyez, Sanjini)

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Hierarchical Axes

• 1D view of 3D function
  (Mihalisin et al.)

f(x1, x2, x3)
x3
x2
x1
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as in TableLens
5D 9 samp/D
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(No Transcript)
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Hierarchical Axes

• 2D view of 4D function (using heat maps)
• y f(x1, x2, x3, x4)
• Discrete xi 0,1,2,3,4

x3
x1
x2
y f(x1,x2,0,0) as color
x4
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Hierarchical Axes

• Scale?
• 6d 3 levels in the 2d approach
• 10 samples/d 1,000,000 data points 1 screen
• For more dimensions
• zoom in on blocks
• reorder dimensions

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• 5D9 sample/D

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Nested Coordinate Frames

• Feiner, Worlds within Worlds

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Slicing

• Van Wijk, HyperSlice

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Radial FocusContext

• Jayaraman, PolarEyez
• infovis.cs.vt.edu

x3
x4
x2
x1
x5
-x5
-x1
-x2
-x4
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Comparison

• Hierarchical axes (Mihalisin)
• Nested coordinate frames (Worlds in Worlds)
• Slicing (HyperSlice)
• Radial FocusContext (PolarEyez)

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Comparison

• Hierarchical axes (Mihalisin)
• lt 6d by 10 samples, ALL slices, view 2d at a time
• Nested coordinate frames (Worlds in Worlds)
• lt 5-8d, continuous, no overview, 3d hardware
• Slicing (HyperSlice)
• lt 10d by 100 samples, 2d slices
• Radial FocusContext (PolarEyez)
• lt 10d by 1000 samples, overview, all D uniform,
  rays

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Dynamic Queries

• cs5764 Information Visualization
• Chris North

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HomeFinder
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Spotfire
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Limitations

• Scale
• Scatterplot screen space 10,000 1,000,000
• Data structures algorithms lt 50,000
• Poor screen drawing on Filter-out
• A Solution Query Previews!
• AND queries only
• Arbitrary boolean queries?
• A solution Filter Flow

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DQ Algorithm

• Idea incremental algorithm
• only deal with data items that changed state
• When slider moves
• Calculate slider delta
• Search in data structure for data items in the
  delta region
• If slider moved inward (filter out)
• Erase data items from visualization
• Else slider moved outward (filter in)
• Draw data items on visualization

Problem! Overlapped items, erases items
underneath too
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DQ Data Structures (1)

• Sorted array of the data for each slider
• Need counter for each data item sliders that
  filter it
• Attribute Explorer visualizes these counters too!
• O(delta)

Year
Delta
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DQ Data Structures (2)

• Multi-dimensional data structure
• E.g. K-d tree, quad-tree,
• Recursively split space, store in tree structure
• Enables fast range search, O()

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DQ Data Structures (2)

• Multi-dimensional data structure
• E.g. K-d tree, quad-tree,
• Recursively split space, store in tree structure
• Enables fast range search, O(logn)

Delta
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Erasure Problem

• Each pixel has counter number of items
• Can visualize this for density!
• Z-buffer?
• Redraw local area only

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Filter-Flow
Betty Catherine Edna Freda Grace Hilda Judy Marcus
Tom
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Influence/Attribute Explorer

• Tweedie, Spence, Externalizing Abstract
  Mathematical Models (Influence/Attribute
  Explorer)

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Query Previews

• Doan, Query Previews