Data Mapping

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Data Mapping
Day 1
Raphael Grasset
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Topics

• Data Mapping Concept
• Dataset Components
• Topology, Geometry, Attributes
• Data Transformations

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Visualization Pipeline

• From Raw Data to Data to Visualize

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Your Data

• Conceptual Model vs Data Model
• Conceptual model (include type and reasoning)
• Example temperature
• Data model (include type and operation)
• Example 1D float for the temperature
• Data Model understandable by computer

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Your Data

• Continuous vs Discrete Data
• Example New Zealand Surface
• Real World continuous
• Computer World discretized mesh representation
• Discrete vs Discretized
• Sampling of Data Discretized
• Temperature Measurement discrete

Slides From Munzner
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Your Data in the Vizualization Pipeline

• Visualization Data Discrete Dataset Format
• Filtering Transformation Algorithm

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Dataset

• Dataset
• Structure structure of the data (spatial order)
• Topology
• Geometry
• Attributes value(s) associated to the structure

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Dataset

• Dataset
• Structure
• Topology
• Relationship of data samples invariant to
  geometric transformation (rotation, translation,
  etc).
• Geometry
• Attributes

c2
C1-C2C2-C3C3-C4C4-C5C5-C1
c3
c1
c4
topology
c5
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Dataset

• Dataset
• Structure
• Topology
• Relationship of data samples (e.g. neighbourhood,
  connectivity) invariant to geometric
  transformation (rotation, translation, etc).
• Geometry
• Attributes

c3
c2
C1-C2C2-C3C3-C4C4-C5C5-C1
c1
c4
c5
topology
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Dataset

• Dataset
• Structure
• Topology
• Geometry
• Specification of topology in Space (usually 3D)
• Attributes

p2
p3
p1
p4
y
p5
x
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Dataset

• Dataset
• Structure
• Topology
• Geometry
• Attributes data associated with topology and
  geometry of the dataset (e.g. temperature,
  pressure, wind direction, etc)

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Dataset
Data View (used in the visualization pipeline)

• Structure
• Topology
• Geometry
• Attributes

Conceptual View

• Cells
• Points
• Scalar, vectors, etc

Consists of
p2
p1-p2p2-p3p3-p4p4-p5p5-p1
p3
p1
p4
y
p5
x
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Topology and Geometry

• Dimensionality
• Topological dimension number of independent
  continuous variables specifying a position within
  the topology of the data
• Geometric dimension (position general space)

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Topology Examples

• Primary and Composites

vertex polyvertex line polyline
triangle triangle strip
quadrilateral pixel polygon
Tetrahedron hexahedron
voxel
VTK Model
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Topology Examples

• Primary 2D Cell type
• Counter-clockwise ordering of 3 points

triangle
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Topology Examples (3D)
Pyramid wedge
quadratic quadrilateral
Two tetrahedras Three tetrahedras Four
quadrilaterals
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Topology Examples (3D)
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Structured vs Unstructured Data

• Generally dependent of measurement vs simulation
• Explicit vs Implicit information about structure
• Structured (Regular) clearly defined
  neighbourhood (implicit to the type of
  structure).
• Unstructured (Irregular) unknown. Need to
  explicitly defined.

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Common Type of Structure

• In SciViz
• Unstructured
• Scattered Data
• (No cells, only points)
• 2D/3D grids
• Structured
• Curvilinear grid
• Rectilinear grid
• Uniform grid
• (medical field)

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Common Type of Structure

• In InfoViz
• Unstructured
• Data tables
• Text
• Structured
• Trees, hierarchies
• Graph networks

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Structure of Your Data
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Attributes

• Associated with the structure (points or cells)
• Category
• Scalar single value per sample
• Vector n-vector values per sample
• Tensor matrix
• Others
• Normal, Texture, Color (Computer Graphics)
• User Defined

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Attribute Scalar

• Single Value for each point
• Simplest case

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Attribute Vector

• N-values at each point
• -gt3D give you magnitude and direction

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Attribute Tensor

• N dimensional array at each point
• Matrices
• Rank order 0 (scalar), 1 (vector), 2 (matrix),
  3..
• Challenging depiction of high dimensional data?

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Attributes

• Dimensionality
• Univariate single scalar
• Multivariate
• Bivariate 2 scalars
• Trivariate 3 scalars (separated attribute) or a
  vector
• multidimensional

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Type

• Physical Types
• Points and attributes need to be stored in memory
• Format dependant of machines, OS, application
• Bool, short, int32, float, double, string
• Abstract Types
• Nominal (labels)
• Ordinal
• Interval (location of a zero arbitray)
• Ratio (zero fixed)
• Physical measurement temperature

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Types

• N - Nominal (labels)
• Operations , ?
• O - Ordered
• Operations , ?, lt, gt, ,
• Q - Interval (Location of zero arbitrary)
• Operations , ?, lt, gt, , , -
• Can measure distances or spans
• Q - Ratio (zero fixed)
• Operations , ?, lt, gt, , , -,
• Can measure ratios or proportions

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Physical Format

• Dataset is stored with an internal format in the
  memory of your PC (depending on the visualization
  software)
• Dataset can be also stored on disk
• Standardized format (DEM, DXF, RAW, etc.)
• Proprietary format (AVS, VTK, etc.)
• Compressed formats (ZIP, RAR, etc)

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Chemistry Logical Data Format
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Transformation

• Now we have data, lets transform it
• Categorized by action on the dataset
• Geometric Transformation
• Topological Transformation
• Attribute Transformation
• Combined Transformation

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Transformation

• Categorized by type of data
• Scalar Field Algorithms
• Vector Field Algorithms
• Tensor Field Algorithms
• Modelling Algorithms

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Data Transformation

• Dimensionality Reduction
• Principal Components Analysis (PCA)
• Multidimensional scaling
• Dimension similarity
• Aggregation, Clustering
• Segmentation
• Interpolation

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Data Interpolation

• What is between my Points?
• Interpolation for visual continuity
• Different interpolation functions
  (linear/polynomial/spline)

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Data Interpolation

• 2D nearest neighbor, bilinear, bicubic (slow)
• 3D trilinear, tricubic

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Data Design Guidelines

• What does your data represent?
• What is the structure of your data? How to
  structure them?
• How to combine them?
• What do you want to identify, prove, factor to
  explore, in your data?

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Data Design Guidelines

• Compact
• Efficient
• Mappable
• Minimal Coverage
• Simple

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Summary

• From the Real World to a Dataset
• Structure of your data, different factors
• Filtering of your data to get a visualization
  data format (dataset)
• You need to know your data to understand
  visualization

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