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DRAWING EULER DIAGRAMS AND GRAPHS IN COMBINATION

Mithileysh Sathiyanarayanan

University of Brighton, UK

M.Sathiyanarayanan@brighton.ac.uk

Supervised by

Gem Stapleton, John Howse and James Burton

Mithileysh Sathiyanrayanan © 2014

Diagrams Conferenc

e2014

Melbourne, Australia

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AN EULER DIAGRAM Euler diagrams represent relationships

between sets, including intersection, containment, and disjointness.

Euler diagrams are an attractive information visualization tool largely used in many application areas such as medicine and engineering.

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EULER DIAGRAM APPLICATION

Euler diagrams represent only relationship between the sets.

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GRAPH Graphs represent relationship between

the data items. Graphs are also visualization tool widely

used to visualize large amounts of interconnecting data in diverse application areas such as ontology modelling, bioinformatics and social network analysis.

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GRAPH APPLICATION

Graphs represent only relationship between the data items.

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EULER DIAGRAMS AND GRAPHS IN COMBINATION

Euler diagrams represent sets. Graphs represent networked data (i.e.

items and their relationships). Euler diagrams and graphs can be used

in combination which will have the potential to be a powerful technique for visualizing and analyzing large and complex data sets.

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COMBINATION OF EULER DIAGRAM AND GRAPH APPLICATION

Euler diagrams along with Graphs represent both relationship between the sets and the data items.

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AIM OF THE RESEARCH

The aim of the research is to significantlyimprove the analysis of grouped network datausing Euler diagrams with graphs by

automatedvisualization.

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OBJECTIVES To allow the automated visualization of

groups in networks by developing a novel layout method for drawing Euler diagrams and graphs in combination.

To develop proof-of-concept open source software that extends existing visualization tools and allows access to the tools and techniques developed in the project.

To evaluate the effectiveness of the layouts produced and to identify required improvements.

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AUTOMATIC DRAWING METHODS

We consider Euler drawing methods and graph drawing methods individually to drawEuler diagrams and graph in combination whichis expected to produce an effective layout.

There are existing methods which combine both Euler diagrams and graphs such as Bubble Sets and Euler View provide somewhat limited results with sub-optimal layout.

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EXAMPLE OF EULER VIEW METHOD

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EXAMPLE OF BUBBLE SET METHOD

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EULER DRAWING METHOD

These methods start with abstract description of the required diagram. These descriptions specify the set intersections to be visualized.

An important consideration are the well-formedness properties possessed by the diagrams.

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Z = {Ø, {A}, {B}, {AB}, {AC}}

Abstract Description

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Well-formedness Properties.

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Diagrams that are not well-formed are considered to reduce user comprehension.

An interesting aspect of Euler diagrams is that some of them cannot be drawn without breaking one or more well-formedness properties.

Why Well-formedness Properties?

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There are three classes of drawing methods which attempt to draw well-formed Euler diagrams where possible. These classes are Dual Graph, Inductive and, of particular interest to us, Circle-Based drawing methods.

Classes of Euler Drawing Methods

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The circle-based drawing method is our choice for extending because, it automatically draws Euler diagram using only circles to represent any data set.

This drawing process uses strategies to transform the abstract description so all abstract descriptions can be drawn with circles.

Nearly all of the well-formedness properties are possessed.

Effective layouts are produced and can always draw a diagram to represent the given data.

Why Circle Drawing Method?

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GRAPH DRAWING METHOD

These methods start with a set of vertices and a set of edges that connect the vertices, analogous to the abstract descriptions of Euler diagrams.

Again, it is important to consider the aesthetic properties possessed by graphs. One such property is that the edges do not cross.

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V = {1, 2, 3}E = {e1,2, e2,3, e3,1}

Description

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There are many algorithms that take into account aesthetic properties have been devised over the last 30 years.

These algorithms can be categorized as follows: force-directed, dimension reduction and multi-level layout methods

Classes of Graph Drawing Methods

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The force-directed method is a possible choice for extending because, for example, forces can be used to repulse vertices from Euler diagrams’ curves.

The other reasons are simple to implement and can be used effectively with other methods.

This method has good desirable aesthetic properties.

Why Force-directed Drawing Method?

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COMBINED DRAWING METHODS By contrast to the notations used

separately, there is not a well-developed theory for drawing Euler diagrams and graphs in combination.

An approach to solving our research problem is to draw the Euler diagram then the graph, or vice versa. However, this leads to suboptimal diagrams.

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The Euler diagram was drawn first, and this resulted in the graph having edge crossings, which is not a desirable aesthetic property.

Euler diagram and Graph in Combination

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Euler diagram and Graph in Combination

The graph was drawn first and this resulted in a triple point, yielding a non well-formed Euler diagram.

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Euler diagram and Graph in Combination

By contrast, this figure, represents the same data as the previous figure, the layouts of the Euler diagram and the graph are both well-formed and thus not compromised.

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WHAT NEEDS TO BE CONSIDERED?

We need methods that take account of both the Euler diagram and the graph, in combination, when constructing diagrams to produce effective layout.

Well-formedness properties of both Euler diagrams and graphs.

Strategies for transforming abstract descriptions into diagrams.

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FUTURE WORKS Ultimately we want to find an extension of the

circle-based and the force-directed methods for Euler diagrams along with graphs.

This will require diagram descriptions and the associated definitions to be extended to the combined context.

Secondly, we will develop software that extends existing visualization tools and allows access to the techniques developed in the research.

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FUTURE WORKS

Finally, we will evaluate the effectiveness of the layouts produced and identify required improvements.

In particular, we will conduct empirical studies and use the results to improve our novel layout techniques so that they produce better final diagrams.

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