Visualization of
Multidimensional
Information from
Scientific Computations
Tomáš Gregar, Jan Pavlovič and Lukáš Kokrment
{xgregar,pavlovic,xkokrmen}@fi.muni.cz

Visualization of Multidimensional Information…
Visualization?
• Reveals factors governing the data
• Sketches data characteristics
• Improve understanding
– Utilizes rules of human reception & conception
• Source data
– D <= 3 – easy displayable
• How to show the message of the data?
– D>3
• How to display that?
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Scientific computations?
• Huge number of results
• Multidimensional
– Results for each studied aspect
• Decision support
– Results = selector for domain expert
– Insight required
• Visualization of possible results
– Interactive (zooming) – domain discovering
– Adaptable (re-computations)
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Motivation
• We need visualization:
• For multidimensional data
– From scientific calculations
• Interactive
– Optimalization of view
?
– Optimalization of calculations
• Easily understandable
• For different domains
– Use cases follows
[ 4 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Multidimensional data flattening
• Is needed for visualization in <3D
• Dimension count minimalization
– Problem simplification – visualization of (<3D)
subproblem
– Deep domain analysis
– Can use standard 2D, 3D visualizers
• histogram, scatter plot, parametric snake plot …
– Grand tour, 3D cluster-guided tour
• Walkable set of
lower-dimensional views
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Multidimensional data flattening (2)
• High-dimensional data mapping into 2D or 3D
– Readability?
– Numerical/categorical variables?
• N-dimensional parallel
coordinate plots
• Star plots
• Glyph using
• Circle Segments
[ 6 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Multidimensional data flattening (2)
• RadViz
– relational values between features
– Usually normalized (values 0-1)
– Keim, D. A. (2002): Information Visualization
and Visual Data Mining. IEEE Transactions
on Visualization and Computer Graphics, Vol. 7, No. 1.
• FreeViz
– RadViz modification
– Freed features
– Demšar, J., Leban, G., Zupan, B. (2005):
FreeViz – An Intelligent Visualization Approach
for Class-Labeled Multidimensional Data Sets
•…
[ 7 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
AxeViz
• Aimed for scientific computations.
– Retrieving results/objects are very time and resource
consuming
– Impossible at-once strategy
• Limits initial visualized area
– Later broading/limit
– Decreases computational demands of visualization.
– Increases readability
• Interactive evolutionary
computation (IEC) approach
[ 8 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
AxeViz - initialization
• Min – origin of axes
• Max – maximal values of quantities
(dimensions normalized)
– Result Area
• Initialization
– User limits computation, visualization
by limiting range of each quantity
– Target Area – computations will be
visualized there
• Latter interactivity
– Target area border is movable
– Understable, low resource-consuming
– discover further results not covered with
previous visualization step, but has
interesting neighbors in targeted area.
– Humans can reveal patterns and relations
in area of 2D or 3D representations.
[ 9 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
AxeViz - displaying
• Sum of vectors
– Vector space origin = min point.
• Vectors = value of quantity
– result of computation based on actual
target area adjustment
(vi – 0i),
– vi = described value (i-th anchor).
• Circle coordinates visualization
• RadViz
– Spring coordinates instead of weights
• Colors and glyphs
– Colors = different initial setting
– Glyphs = different iterations
[ 10 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
AxeViz – modifications
• More detailed insight with the same
visualization conditions
– Global zoom
– Zooming – change of rate – some axe(s)
– Ranges are intact = no need for new computations
• Changing conditions of visualization
– Range changing
– New computations – but only for newly added target area
• Adding or deleting of observed quantities
– addition or deleting of axes
– Complete recalculation
[ 11 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Use cases
• Microarrays
– Multidimensional data structure used in biology
• Enviromental calculator
– Energy management decision support tool
– Comparing remedial technologies outcome
• according to multidimensional input constraints
• Ontologies
– Network of shared concepts connected with nontrivial
relations
[ 12 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Microarrays - principles
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Microarrays - usage
• Identification of
– differentially expressed genes
– subtypes of diseases and disorders
• Diagnostics of diseases
• Predictive toxicology
• Gene regulatory networks
• …
[ 14 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Microarrays - data
• Data matrix (expression matrix)
⎛ x11 ... ... x1M ⎞
⎜ ⎟
E = (xij ) = ⎜
⎜ ... ... ⎟
...
⎟
... ... ...
⎜ ⎟
⎜x ⎟
⎝ N 1 ... ... x NM ⎠
• High dimensionality
– few samples
– huge number of genes
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Microarrays - problems
• Missing values
• Bias
• Biological interpretation
• …
• ⇒ Difficult processing, analyzing and
visualization
– Multidimensional
– Dimension reduction techniques necessary
[ 16 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Microarrays – AxeViz usage
• Axes:
– assigned to the genes
• Location of the anchor:
– determined by the differences in gene expression
• Data instances:
– displayed inside the target area, labeled with the class
assigned to the instance
• Position of the instance:
– determined by the position of the anchors on the axes
[ 17 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Environmental Calculator – goal
• Energy management decision support tool
• Decontamination Management
– Collaboration with
U.S. EPA
[ 18 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Calculator – questions
• How effectively are the technology and the
energy used in the remedial process?
• Are there any methods for the energy
minimization?
• Are there any possibilities of recycling
energy in the remedial process?
[ 19 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Calculator – SOA
• Visualization needs to be integrated
– Service with minimal dependencies
• Service-Oriented Architecture (SOA)
• Principles of SOA architecture
– Reuse, granularity, modularity, composability,
componentization, and interoperability
– Services identification and categorization
– Abstract Layer on Scientific Computation
– Easy to use, modify, deploy
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Calculator – SOA ESB
• ESB – Enterprise Servise Bus
– New approach in SOA
• Pros
– Faster and cheaper accommodation of existing systems.
– Increased flexibility; easier to change as requirements
change.
– Standards-based.
– Scales from point solutions to enterprise-wide
deployment (distributed bus).
– More configuration rather than integration coding.
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Calculator – ESB use case
Environmental Calculator
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InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Calculator – AxeViz usage
• This decision support tool can find the
optimal combination of remedial technologies
that should be used in cleaning process
– Since there exists vast number of technology
combinations, environmental specialist have to specify
several initial requirements than limits the result set.
• Results must be visualized
– Huge number of candidates to final solution.
• With axe-oriented visualization domain expert
is able to distinguish in a better way between
results according to the settings of initial
requirements.
[ 23 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Visual ontologies
• Ontologies of visual information
– E-learning project
– Exploring semantics of graphical data
– Visualization for describing, showing likeness between
objects and information stored about instances of visual
ontology concepts.
• Likeness
– Features computation = time-resource-consuming
• texture, structure, shape…
– Interactive evolutionary computation based visualization.
[ 24 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Visual ontologies – AxeViz usage
• Origin
– Most general concept of ontology
• Axes:
– Selected sub-concepts
– Two possibilities
• Each axe = one sub-concept (like microarrays visualization)
• Axe = concept hierarchy (loose ordered from ontology taxonomy)
• Location of the anchor:
– determined by computation of likeness with every studied
characteristic values of features for each concept
• Data instances:
– displayed inside the target area, labeled with the segment
identification
• Position of the instance:
– determined by the position of the anchors on the axes
[ 25 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Visual ontologies and AxeViz
• Visualization = new insight in data
• Visual images
– Each concept can have huge number of (dissimilar)
depictions.
• With AxeViz
– Clusterization
– Uncertain segments (low likeness to any concept)
– Concept assignment corectness
• Domain Ontology
– Ontology can alter visualization
– Display ontology-related quantity-axes visually related
[ 26 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
Implementation
• Actually
– Prototype development
– WS for usage in ESB
– Enviromental Calculator
[ 27 / 28 ]
InSciT 2006, Mérida
October 25.-28.

Visualization of Multidimensional Information…
• Thank you for your attention
[ 28 / 28 ]
InSciT 2006, Mérida
October 25.-28.