network visualization techniques and evaluation...overview of tree visualizations mohammad ghoniem...

Definition and motivation of InfovisVisualization of structured data

Visualization of dense and dynamic networksConclusion

Network visualization techniques andevaluation

Mohammad GHONIEM

The Charlotte Visualization CenterUniversity of North Carolina, Charlotte

March 15th 2007

Mohammad GHONIEM Network visualization techniques and evaluation

Outline

1 Definition and motivation of Infovis

2 Visualization of structured dataVisualization of hierarchical dataVisualization of network data

3 Visualization of dense and dynamic networksThe matrix-based representation of graphsApplication to constraint-oriented programming graphs

4 Conclusion

Outline

4 Conclusion

Outline

4 Conclusion

Outline

4 Conclusion

Information Visualization

DefinitionA compact graphical representationA graphical user interfaceFor the visualization and interaction with large numbers ofitemsthat may be a subset of an even larger dataset.

Scope and usefulnessBears on data that are:

abstract, multi-dimensional, structured or unstructured.in order to:

Make discoveries, decisions, find explanations, orcommunicate about

visual patterns(trends, clusters, outliers, . . .)groups of items,individual items.

Historical background

Considerable leap in hardware technology and capabilitiesProduction and storage of large volumes of data;Increased processing capabilities;Improved display capabilities.

Birth of data miningMathematical and statistical data analysis;Visual information exploration.

Principles and roleMake the best use of human vision

detect patterns,sense correlations,confirm an intuition or formulate hypotheses.

Make the best use of user’s expertiseinteractive exploration,interactive construction of views.

Precedes but does not replace classical data mining.Provides robust solutions for the most frequent datastructures.

Visualization of hierarchical dataVisualization of network data

Organisation

4 Conclusion

Tree Visualization Techniques

2D representationsNode-link diagrams (cartesian / circular)Space-filling techniques (treemaps, icicle trees, circular)Non-euclidian space (hyperbolic trees)

3D representationsNode-link diagrams (cone trees)Non-euclidian space (hyperbolic trees)

Overview of Tree Visualizations

Organisation

4 Conclusion

Graph theory basics

DefinitionsG = (V, E),E ={(u, v)}, where (u, v) ∈ V × V,two vertices are adjacent if they are connected by an edge,an edge is directed if an order is defined on its extremities,a graph is directed if its edges are directed,a directed path is a sequence of vertices (v1, · · · , vk )where (vi , vi+1) ∈ E ∀i < k ,a directed path is a cycle if (vk , v1) ∈ E ,a directed graph is acyclic if it is cycle free,a graph is planar if it has an intersection free 2D drawing.

Graphs are ubiquitous

ExamplesInfrastructure networks (telecommunications, power,roads).Social networks (acquaintances, crime networks).Co-citation network, etc.

Graphs and representations

Definitiona graph is an abstract entity 6= its representations.

Layout

Graph visualization techniques

Visualization techniquesNode-link diagrams,Adjacency matrices.

Aesthetic rules and drawing conventionsDrawing conventions: polyline drawing, grid drawing,upward/downward etc.Aesthetic rules: min. intersections, min. edge length, min.area etc.Some rules are conflicting.Some user studies and experiments (H. Purchase, C.Ware).

Graph drawing approaches

Graph visualization overview

Graph visualization frameworks

Existing frameworksTulip (University of Bordeaux – France),Pajek (University of Ljubljani – Slovenia),GraphViz (AT&T),JUNG (University of California, Irvine).

Node-link diagramsWidespread and well studied wrt sparse graphs.Cluttered views when link density increases.Instable layout algorithmsUnusable for dynamic graphs.Begs for an alternate representation.

Monitoring co-activity graphs

Variables + Constraints

Variables

Contraintes

Variables

Contraintes

Variables

Contraintes

Variables

Contraintes

Variables

Contraintes

Variables

Contraintes

Variables

Contraintes

Variables

Contraintes

Co-activity graphs

The 8 queen problem

Co-activity graph

Co-activity graphs

The 8 queen problem Co-activity graph

The matrix-based representation of graphsApplication to constraint-oriented programming graphs

Organisation

4 Conclusion

Matrix-based representation of graphs

StrengthsRelies on a well-known mathematical representation.No clutter nor occlusion.Orderable, predictible for most common order relations.Displays existing and missing links.

ShortcomingsUnfamiliar visualization.Not effective for path related tasks.

The matrix of Bertin

Cluster revelation through permutations

Orderability magic

Cluster revelation through permutations

Orderability magic

Properties of matrices

Multi-scale self-contained visualization

But...How readable is the matrix-based representation ?

Evaluation of the readability of matrices

PrincipeCompare two alternative representations of graphs wrtA predefined list of common tasks,A set of graphs of variable sizes and link density.The readability is measured according to two indicators:

1 answer time;2 error rate.

Taxonomy of tasksTasks related to the overview.Tasks related to vertices.Tasks related to links.Tasks related to paths.Tasks related to subgraphs.

Seven tasks1 Estimate the number of vertices.2 Estimate the number of links.3 Find the most connected node.4 Find a node by its name.5 Say whether two links are connected.6 Say whether two nodes have a common neighbor.7 Find a path between two nodes.

A few observations about the tasksA minimal selection of tasks.Primitive tasks.

Experimental precautionsPreliminary demonstration and training stage.Guidelines : answer fast and right, may skip questions iftoo difficult.Two two-fold sessions.Three breaks (5 min, 10 min, 5 min).Equalize weariness effects.Equalize learning effects.Bounded answer time (45 sec. max.)

SetupNine random graphs with increasing size and link density.Use neato/graphviz package for node-link diagrams.Matrix-based representation in OpenGL/Java.Presets tothe best advantage of each representation.Minimal interaction (node and link highlights).

Highlight and selection of nodes and links

User population and result analysis36 Ph.D. students or assistant professors incomputer-science.Analysis: quantitative

and qualitative + 3D model.

User population and result analysis36 Ph.D. students or assistant professors incomputer-science.Analysis: quantitative

and qualitative + 3D model.

User population and result analysis36 Ph.D. students or assistant professors incomputer-science.Analysis: quantitative and qualitative

+ 3D model.

User population and result analysis36 Ph.D. students or assistant professors incomputer-science.Analysis: quantitative and qualitative + 3D model.

ResultsBetter results with the matrix-based representation for 6/7tasks wrt

dense graphs,large graphs.

Node-link diagrams are preferable for small sparse graphs.Path related tasks are difficult to carry out.

User reactionsNot so enthusiastic in the beginning, except a few.Very positive at the end of the evaluation, except a few.

Organisation

4 Conclusion

Visualization of constraint-oriented programminggraphs

Properties of such graphsVery densely connected.Large.Complex temporal relations between nodes.

Visualization solutionMatrix-based representation:

no clutter,space-filling technique,adapted for focus + context techniques (fisheye),multi-scale representation (clustering + agregation).

History animation through dynamic queries,Automatic segmentation of the solving process.Mohammad GHONIEM Network visualization techniques and evaluation

Monitoring of dynamic graphs: example 1

Pedagogical problem (sort 100 variables)

100 variables xi∈[1,100] in [1, 100].99 constraints : ∀i ∈ [1, 99], xi < xi+1.

Constraint graph of the sort problem

alldiff constraints problem

Automatic segmentation and animation of the solving process

Problem structure investigations

Aid for debugging andfine-tuning of programs

3 sets of variables withstrong internal links.Problem structure isvisible at the end ofpropagation phase.Link density has nonegative impact on theclarity of the overview.

Variables × Variables

Mindom heuristicexecuted during 2minutes and interrupted.Sets #1 and #2 have astrong impact on set #3.Weak links mislead thesolver into baddecisions.

Normalized view.Initial infrequentdecisions appear indark.Poor decisions involveset #2.

Discard gradually theeffects of old decisions.The solver is trappedinto a costlyenumeration on sets #1and #3 because of a baddecision taken wrt to set#2.

Adapt the mindomheuristic.Discard constraintscausing an abnormalvolume of activity.The problem is solvedimmediately.

Investigation of complex problem : graph coloring

Instance 4 of MycielskiVariables 11 to 21 arenot linked, obvious on amatrix.The problem can be splitinto two sub-problems.

Investigation of complex problem : graph coloring

Instance 5 of MycielskiThe structure of theproblem is recurrent.An incrementalresolution strategy canbe very effective.

Conclusion

Information visualizationThe purpose of information visualization is insight.The choice of a visualization metaphor depends on thenature of the data and the tasks at hand.Large and/or dense networks are best viewed asadjacency matrices.Dynamic graphs are best monitored as adjacencymatrices.

network visualization techniques and evaluation...overview of tree visualizations mohammad ghoniem...

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