Visual Analytics
Multimedia Information Systems 2 VU
(SS 2014, 707.025)
Vedran Sabol
KTI, TU Graz
March 26th 2015
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
Structure of the Lecture
•
•
•
•
Visual Analytics (recapitulation)
Scalable Layout Algorithms
Clutter Reduction
Aggregation-based Methods
 Hierarchical Layout
 Level of Detail Rendering
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
2
Visual Analytics
(recapitulation)
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Visualization
• Definition
 Graphical representation of data, information and knowledge
 Use of human visual system, supported by computer graphics, to
analyze and interpret large amounts of data
• Approach
 Machines transform the data into a suitable graphical representation
 Employ the human visual system for pattern recognition
• Challenges
 How should the graphical representations look like (design)?
 How to compute the graphical representation (algorithms)?
 Which operations shall be supported on the graphical representation
(interactivity)?
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
4
Visualisation - Motivation
• Human visual apparatus is an highly efficient „processing machine“
• Enormous amounts of information are transferred by the visual
nerve into the brain cortex - extremely high bandwidth
• Visual cortex remains unbeatable in recognition of objects and
complex patterns - extreme parallel processing
• Pre-attentive processing: capability to process certain visual
information without focusing our attention
 Criterion 1: Processing time < 200 - 250ms (single glimpse)
 Criterion 2: Processing time does not correlate with the amount of
noise in the data
 Limited number of pre-attentive features
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Pre-attentive processing
Yes
Borderline
No
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Visualization
•
Fundamental categories of visual representation
 Formalisms: abstract schematic representations
• must be learnt
 Metaphors: representations based on a real-world equivalent
• Intuitive: user can understand the meaning through building analogies
 Models: based on mental representations of the physical world
• Data has a natural representation in the real world
• Visualisation subdivision



Data/Scientific Visualization
Information Visualization
Knowledge Visualization
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Visualization Examples
Pressure coefficients [NASA]
• Data visualisation
• Uses a model
Vedran Sabol (KTI, TU Graz)
Cultural Heritage - Roman Theatres
[Blaise]
• Knowledge visualisation
• Uses formalisms
Visual Analytics
March 26th, 2015
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Visualisation Examples
Information Visualisation
Themeriver [Havre]: trends in document clusters
• Uses a metaphor: river flow
Vedran Sabol (KTI, TU Graz)
Information Landscape [Sabol]: topical similarity
in document repositories
• Uses a metaphor: landscape
Visual Analytics
March 26th, 2015
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Visual Analytics
New Insights
New Knowledge
Repository
Algorithms
Visualization
• A new interdisciplinary research area at the crossroads of
• Data mining and knowledge discovery
• Data, information and knowledge visualisation
• Perceptual and cognitive sciences
• Human in the loop
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Visual Analytics
• Combines automatic methods with interactive visualisation to get the
best of both [Keim 2008]
• interaction between humans and machines through visual interfaces to
derive new knowledge
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Visual Analytics
1. Machines perform the initial analysis
2. Visualization presents the data and analysis results
3. Humans are integrated in the analytical process through means for
explorative analysis
• User spots patterns and makes a hypothesis about the data
• Further analysis steps - visual and/or automatic - to verify the hypothesis
• Confirmed or rejected hypothesis: new knowledge!
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Today’s Focus
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
13
Data
• Visual analysis of
 Weakly structured data: text repositories
• Most commonly used data type
• Text is highly unstructured
• Accompanied by structured metadata
 Structured Data: network data/graphs
• Rapidly gaining importance
• Social Networks
• Web graph
• Semantic Knowledge Bases (Ontologies, Linked Data)
• Approach
 Develop methods for unstructured data
 Extend them on structured data
• More complexity: consider relationships
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Methods
• Geometry computation
 Projection and layout algorithms: scalable, visually compelling 2D
layout of the data set
 Clarity improvement methods for graphs: edge bundling, edge routing
 Label overlap minimization
• Aggregation-based methods
 Provide a coarse overview of the whole data set
• To avoid the overload of the user (and of the Web client)
 Introduce more details when zooming
• Level of Detail based rendering
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Projection and Layout
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Layout
 How to visualize high-dimensional vector spaces?
• Project them into a „smaller“ (i.e. 2D or 3D) visualization space
– Relationships can be viewed, understood and explored by users
• Preserve original distances/similarities as far as possible
– Related data elements are spatially close – structures arise
• Dimensionality reduction techniques
 How to layout complex (semantic) graphs
• Connect nodes with edges
– Understand structures, explore relationships by following edges
• Maximize clarity of the potentially very complex representation
– Place strongly interconnected node groups (i.e. those sharing similar
neighborhood) spatially close together
– Minimize overlap and edge crossings
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Ordination Methods
 Distance-/similarity preserving methods
• Multidimensional scaling
• Input is a distance-/similarity matrix
–
Computed using similarity coefficients (e.g. cosine coefficient)
• Dimensions of the low-dimensional space have no meaning
–
and no relation to the original dimensions
 Transformations of the feature space
• Principal Component Analysis, Self Organizing Maps
• Input are high-dimensional feature vectors
• Dimensions of the low-dimensional space may be related to the highdimensional space
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Multidimensional Scaling
Motivation
 Example: distance (i.e. dissimilarity) matrix of car makers
• Which car makers are similar?
• Need visualisation: impossible to read from large matrices
Siehe http://www.wiwi.uni-wuppertal.de/kappelhoff/papers/mds.pdf
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Multidimensional Scaling
See: http://www.wiwi.uni-wuppertal.de/kappelhoff/papers/mds.pdf
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Multidimensional Scaling
Example: 2D to 1D space
 Information loss is inherent!
x
y
1
0.2
1
2
0.5
1
3
1.5
0.2
 Minimise differences between
HD and LD distances
Distance computation
a= dist(1,2)= 0.3
b= dist(2,3) = 0.6
c= dist(1,3) = 1.55
1
2
3
1
0
0.3
1.55
2
0.3
0
0.6
3
1.55
0.6
0
a
2
1
Dimensionality
Reduction
b
c
2
1
3
~a
~b
3
~c
High-Dim (2D)
Vedran Sabol (KTI, TU Graz)
Low-Dim (1D)
Visual Analytics
March 26th, 2015
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Multidimensional Scaling
Force-Directed Placement
 Heuristic multidimensional scaling method
 Spring model simulates a physical system
• Compute forces between objects
– Force between an object pair depends on similarity/distance in the highdimensional vector space
» Topical similarity for text documents
» Connectivity with the local neighborhood for graphs
– Similar/connected object attract, dissimilar/disconnected objects repulse
• Element position interactively computed depending on the forces
 Physical system converges towards a local minimum
 Stop condition
• Object movements have subsided (velocity)
• Difference between high- and low-dimensional distances stopped
sinking (stress)
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
22
Force-Directed Placement
Basic Force Model
dist high  distlow
force(d i , d j )  distlow (d i , d j )  dist high (d i , d j )
di
dj
disthigh  distlow
di
force(d i , d j )  0
attractive force
force(d i , d j )  0
dj
Repulsive force
 Attempts to reconstruct the original distances in the visualisation
space
 Disadvantages
• Scaling of high-dimensional distances often unsuitable for visualization
• Need to convey proportions, but not the exact distances
• No parameterization/tuning possibilities
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Force Directed Placement
Item Position Computation
N
1
d i .x  d i .x 
 force(di , d j )(d j .x  di .x)
N  1 j 1, j i
N
1
di . y  di . y 
 force(di , d j )(d j . y  di . y)
N  1 j 1, j i
force  1  d i .x  d i .x  1  (d j .x  d i .x)  d j .x
force  0  d i .x  d i .x  0  (d j .x  d i .x)  d i .x
Force
d3
d1
di
d2
Resulting Force
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
24
Force-Directed Placement
Improved Force Model
Similarity in original space
force(d i , d j )  sim(d i , d j ) d 
Constant
p
 grav
r
dist (d i , d j )
Repulsive force
Distance in projection space
 First term: attractive force proportional to similarity
• Attracts similar/connected objects
 Second term: rapidly rising, short-range repulsive force
• Prevents „gravitational collapse“ of very similar elements
 Third term: weak cohesive force
• prevent endless expansion of non-similar elements
 Vast parameterization and tuning possibilities
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
25
Force-Directed Placement
Graph Layout Specifics
 Adjacency Matrix used as input
 Specifies which nodes are directly connected by an edge
 Not all force interactions between non-connected nodes must be
computed
 Is suffices to consider the neighbourhood in the 2D layout: speeds up
computation enormously for sparse graphs
 Close non-connected nodes should repel each other
D
A
C
B
Vedran Sabol (KTI, TU Graz)
Visual Analytics
0

1
1

0

1
0
1
0
1
1
0
1
0

0
1

0 
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Force-Directed Placement
Advantages and Disadvantages
 Advantages:
• Good layout quality
• Visually pleasing results (with a little tuning)
• Incremental: changes in the data integrated smoothly in the layout
 Disadvantages:
• Tends to get stuck in local minima
– Especially for larger data sets
– Possible remedy: “shake out” techniques
• Scalability of the brute force algorithm:
– Text: O(n3) time-complexity due to full distance/similarity matrices
» May be improved by matrix pruning (not considering low similarity values)
– Graphs: much better for sparse graphs as adjacency matrix is sparser
» But still at least O(n2)
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Force Directed Placement
Addressing Scalability Issues
 More efficient approaches based on FDP
• Stochastic Sampling (neighbor + random sets) [Chalmers 1996]: O(n^2)
• Apply sampling and interpolation recursively [Jourdan & Melançon 04]:
O(n*log(n))
•  Aggregate data into hierarchy (clustering), apply FDP recursively
[Muhr, Sabol, Granitzer 2010]: O(n*log(n))
– Will be discussed into detail later
 Alternative Techniques:
• Least Square Projection, Random Projections, FASTMAP, IDMAP…
• Fast, but mostly inferior layout quality
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
28
Force-Directed Placement
Layout Quality
 Stress measure
• Difference between pairwise distances in high- and low-dimensional
spaces
stress (d i , d j ) 
1
(disthigh (d i , d j )  distlow (d i , d j ))2

N  1 i j
• Heat maps to visualise stress per object: find problem areas
[Seifert, Sabol, Kienreich 2010]
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Clutter Reduction
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Graph Visualization
Large Graphs
Cytoscape (http://cytoscape.org/)
•
•
Left: 50000 nodes, 250000 edges (http://cytoscape.org/manual/Cytoscape2_6Manual.html)
Right: 30000 nodes (http://www.mkbergman.com/419/so-what-might-the-webs-subject-backbone-look-like/)
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Graph Visualization
Force-Directed Edge Bundling


Idea: bundle Edges
which are
•
parallel rather than
perpendicular
•
of similar lengths
•
proximate in space
Reduces edge crossing
significantly
traffic between geographic locations
[Holten & van Wijk 2009]
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
32
Force-Directed Edge Bundling
 Input: straight line node-link diagram
• For example generated with FDP layout
 Straight edges are subdivided into segments
• The shape changes along subdivision points
 Forces applied on the subdivision points
• Spring forces between consecutive points of an edge:
Fs  K p  || pi  pi 1 ||
– Tend to straighten the edge, Kp controls the amount of bundling
• Electrostatic forces between corresponding point pairs from different
edges
Fe  1 / || pi  qi ||
– Attractive force bundling the edges together
Fe
P
Pi+1
Pi
Fs
Qi+1
Q
Vedran Sabol (KTI, TU Graz)
Visual Analytics
Qi
March 26th, 2015
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Force-Directed Edge Bundling
Fe
P
Pi+1
Pi
Fs
Qi+1
Q
Qi
 Need a finer control of Fe
• For some point pairs Fe too strong, for some too weak
• Introduce edge compatibility measure Ce(P,Q)
 Iteratively apply FDP
• Compute resulting force Fpi for each point
• Move point it in the resulting direction
Fpi  K p  (|| pi 1  pi ||  || pi  pi 1 ||)   Ce ( P, Q) / || pi  qi ||
QE
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
34
Force-Directed Edge Bundling
Edge Compatibility Measure
 Edge compatibility measure Ce (within the range [0,1]) composed of
•
•
•
•
Ca(P,Q) - angle compatibility: bundle almost parallel edges
Cs(P,Q) - scale compatibility: bundle edges of comparable length
Cp(P,Q) - position compatibility: bundle edges which are close
Cv(P,Q) – visibility compatibility: bundle edges which overlap
Ce ( P , Q )  C a ( P , Q )  C s ( P , Q )  C p ( P , Q )  Cv ( P , Q )
Taken from [Holten & van Wijk 2009]
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Force-Directed Edge Bundling
Example – Concept Co-occurrence over Time
 Concept and Links extracted from 10 years of i-Know conference papers
 Time encoding: Node importance for the time interval represented by the
inner (blue) circle
•
Timeline for choosing the time interval
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Edge Routing

Idea: Construct a grid and
route the edges along the grid
[Lambert et al. 2010]

Goals:
•
Vedran Sabol (KTI, TU Graz)
Visual Analytics
eliminate node-edge overlap
completely !
March 26th, 2015
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Edge Routing
Grid Generation



Discretise the 2D plane into regions (area subdivision)
Use region boundaries as “roads” for routing edges
Grid generation
•
•
Quad trees
–
Each area has exactly four children
–
Subdivide area until each data element (graph node) is
assigned one tree node
–
“Multi-resolution” grid: grid density higher where node
density is high
–
Disadvantage: rectangular edges
Voronoi diagrams
–
Subdivide areas so that each data element (graph node) is
assigned a convex polygon
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
39
Edge Routing
Voronoi Subdivision

Brute force approach
•
•
•
Compute Delaunay triangulation for the data points (black)
Compute perpendicular bisectors to triangulation edges (red)
Compute intersections of adjacent edges
–

These points define the Voronoi polygons
More efficient algorithm for the 2D plane: Fortune's algorithm
•

image:
Wikipedia
O(|V|*log(|V|)) time complexity
Weighted Voronoi Diagrams



Consider node weight
Slide bisectors towards lower weight nodes
Assign more area to nodes with higher weight
–
Useful: reserve area for icons of different sizes
[Andrews et al. 2003]
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
40
Edge Routing
Dijkstra's Shortest Path Algorithm

For a given node finds lowest weight path to any other node

For a current node: check unvisited neighbours and update distances
(if smaller)
•
Mark current node as visited, make the unvisited node with smallest
distance the new current node
•
Finished when target node marked visited
Efficient implementation complexity: O(|E|+|V|*log|V|)
•
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
41
Edge Routing
Road Metaphor



Route original graph edges along the Grid using Dijkstra
Problem: edges follow many different paths – low bundling of edges
Road metaphor: group edges along highly used paths
•
•
•
•

Reduce the weights of frequently used paths
Recompute the shortest path for each original edge
Frequently used paths attract more edges becoming “highways”
Iterate a fixed amount of times
Disadvantages of the edge routing method
•
•
Very high edge overlap
Edges can not be distinguished and followed easily
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Label Overlap Reduction


Overlapping labels can massively impair
readability
Possible solutions:



Size-sensitive layout algorithms
–
Assign enough space for each label (e.g.
using FDP)
–
Works only for limited number of labels
–
Attention when zooming: dynamic label
layout annoying for users [Granitzer et al.
2004]
Example: Abraham Lincoln's family Tree
[http://jay.askren.net/Genealogy/Projects/Tree/AbrahamLincolnRadialGraph.JPG]
Prioritisation
Aggregation
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Label Overlap Reduction

Label prioritisation
 Assign a priority to each label
 Begin label rendering with highest-priority labels
 If overlap (or too high label density) do not render the label
 Re-evaluate when zoom factor changes
[Kienreich et. al 2007]
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Aggregation and Hierarchical Layout
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Clustering
Application
 Browsing data collections
• Apply clustering recursively to compute a hierarchy
• Labeled hierarchy as “virtual table of contents”
Cluster hierarchy
Feature
Vectors
Similarities
46
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
Scalable Layout Algorithm
 Idea:
• Aggregate a large data set to a small number of clusters (hierarchically)
• Apply FDP separately on a small number of items (makes it fast)
– Clusters
– Clusters children
– …down to data element level
• Important: number of children is strictly limited (e.g. 20-50)
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
47
Scalable Layout Algorithm
 Input:
• Base area (rectangle, circle…)
• Data elements (nodes, documents)
– Incl. possibility to compute similarity between them
• Edges (in case of graphs)
 Output:
• Hierarchy of nested areas
• 2D data element positions
• Edge geometry (for graphs)
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
48
Scalable Layout Algorithm
 Recursive Algorithm:
• Aggregation:
– Clustering (e.g. k-means) and cluster labeling
– Alternative: use an existing hierarchy
» E.g. class hierarchy of an ontology, file system hierarchy…
• Layout:
– force-directed placement
– inscribing into parent area
• Area subdivision: Voronoi diagrams
• For each cluster: cluster size > threshold?
– Yes: apply algorithm recursively on the cluster
– No: layout data elements (bottom level) and terminate
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
49
Inscribing Into Voronoi Areas
 Given:
• Set of 2D points in the plane {p1, … pn}, normalised into [-1,1] space
• A Voronoi area A with m bounding edges aj
 Procedure
• Compute centre of gravity c for A, align it with plane origin (0,0)
ri
• For each pi
1
– Cast a ray ri from c to pi
– Find intersected aj and intersection point qi
pi
– Calculate pi’: translate pi along ri so that
d(c, pi’)/d(c, pi) = d(c, qi)
qi
pi‘
0
c
A
-1
Vedran Sabol (KTI, TU Graz)
Visual Analytics
0
March 26th, 2015
1
50
Scalable Layout Algorithm
Advantages
• Hierarchical labeled geometry
 Navigation and exploration along the hierarchy
 Labels and geometry adapted to the level of detail
• Scalable
 Time and space complexity: O(n*log(n))
 Parallelization fairly straightforward
 Tunable (FDP-based)
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Text - Information Landscape Visualisation
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
Scalable Graph Layouting
Edge Aggregation
• Input: edges, nodes aggregated to meta-nodes
• Aggregate inter-cluster edges to meta-edges connecting meta-nodes
 Bottom-up propagation of inter-cluster edges until they connect
siblings
 Meta-edge weight: aggregated weight of inner-cluster edges
• Inner-cluster edges remain unaffected
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
53
Graph Layout
Hierarchical Edge Bundling
• Edge bundling applied locally
 Within a meta-node’s area
 On relations between metanode’s children
 For all levels of hierarchy
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
54
Graph Visualization
Edge Bundling – Flat vs. Hierarchical Aggregation
• Reduces edge clutter massively
• Automatic meta-node/edge expansion on zoom in
• Disadvantage: some node-edge overlap remains
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
55
Graph Layout
Hierarchical Edge Routing
• Route edges along the hierarchical (Voronoi) Grid
• Inter-cluster edges are routed over several hierarchy levels
 Apply Dijkstra's shortest path algorithm in a top down manner
 Locally within an area’s Voronoi polygon
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
56
Graph Visualization
Edge Routing – Flat vs. Hierarchical Aggregation
• Reduces edge clutter and eliminates edge-node overlap
• Disadvantage: massive edge overlap on Voronoi boundaries
 Edge stroke indicator for number of overlapping edges
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Scalable Graph Visualization
Summary
Node Aggregation
Edge Aggregation
Hierarchical Node Layout
Hierarchical Edge Bundling
Grid Generation
Hierarchical Edge Routing
Graph Visualization
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Summary: Scalable Layout Pipeline
Similarities
Mathematical Model:
Vector Space Model
Feature Engineering
NLP, feature
frequencies + TF/IDF,
node connectivity …
Similarity/Connectivity
Euclidean distance,
Cosine coefficient…
Recursive k-means,
hierarchical
agglomerative
clustering…
HTML5 canvas,
SVG…
FDP, Voronoi
subdivision, edge
bundling/routing…
Rendering
Layout
Visualizations
Vedran Sabol (KTI, TU Graz)
Hierarchical geometry: spatial
proximity conveys relatedness
Visual Analytics
Aggregation
Data
(text, graphs)
Aggregation (Hierarchy)
“virtual table of contents”
March 26th, 2015
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Level of Detail Rendering
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
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Variable Level of Detail (LOD)
• Coarse-grained overview
 Decreased complexity of representation for far-away objects
• Provide more details when zooming-in
 Technique well-known from 3D environments
 and from GoogleMaps
• Make use of the hierarchical geometry
• Only a limited amount of geometrical detail shown at each moment
 Reduces clutter
 Reduces cognitive load on the user
 Useful for low computing power devices (Web, mobile)
– Client loads more detailed geometry on demand
– And discards it when not needed
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
61
Variable Level of Detail (LOD)
Mouse Anatomy Ontology
Zoom out
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
62
Variable Level of Detail (LOD)
Mouse Anatomy Ontology
Zoom level 1
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
63
Variable Level of Detail (LOD)
Mouse Anatomy Ontology
Zoom level 2
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
64
Variable Level of Detail (LOD)
Mouse Anatomy Ontology
Zoom level 3
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
65
Possible Applications for Graph Visualisation
• Analysis of Twitter data
 Nodes: users
 Edges: communication (weighted) between users
 Graph visualisation: show groups of communicating users,
communication between groups
 Label groups with conversation topics: frequent terms from the tweets
• Visualisation of aligned ontologies
 Alignment: connect nodes with equal or similar names (high weight)
 Graph visualisation: explore which ontology parts could be aligned and
which not
 Let users interactively connect and disconnect nodes
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
66
Thank you
Next lecture on 23.04.2015
“Visualisation of Semantic Data”
Vedran Sabol (KTI, TU Graz)
Visual Analytics
March 26th, 2015
67