# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### eulerr: Area-Proportional Euler Diagrams with Ellipses

(2018) STAH11 20172
Department of Statistics
Abstract
Euler diagrams are common and intuitive visualizations for data involving
sets and relationships thereof. Compared to Venn diagrams, Euler diagrams do not
require all set relationships to be present and may therefore be area-proportional
also with subset or disjoint relationships in the input.
Most Euler diagrams use circles, but circles do not always
support accurate diagrams. A promising alternative for Euler diagrams is ellipses,
which enable accurate diagrams for a wider range
of set combinations. Ellipses, however, have not yet
been implemented for more than three sets or three-set diagrams where
there are disjoint or subset relationships. The aim of this thesis is
to present a method and software for elliptical Euler... (More)
Euler diagrams are common and intuitive visualizations for data involving
sets and relationships thereof. Compared to Venn diagrams, Euler diagrams do not
require all set relationships to be present and may therefore be area-proportional
also with subset or disjoint relationships in the input.
Most Euler diagrams use circles, but circles do not always
support accurate diagrams. A promising alternative for Euler diagrams is ellipses,
which enable accurate diagrams for a wider range
of set combinations. Ellipses, however, have not yet
been implemented for more than three sets or three-set diagrams where
there are disjoint or subset relationships. The aim of this thesis is
to present a method and software for elliptical Euler diagrams for any
number of sets.

In this thesis, we provide and outline an R-based implementation called eulerr.
It fits Euler diagrams using numerical optimization and exact-area
algorithms through two steps: first, an initial layout is formed using
the sets' pairwise relationships; second, this layout is finalized
taking all the sets' intersections into account.

Finally, we compare eulerr with other software implementations of Euler
diagrams and show that the package
is overall both more consistent and accurate as well as
faster for up to seven sets compared to the other R-packages. eulerr perfectly
reproduces samples of circular Euler diagrams as well
as three-set diagrams with ellipses, but performs suboptimally with elliptical
diagrams of more than three sets. eulerr also outperforms the other software tested in
this thesis in fitting Euler diagrams to set configurations that might
lack exact solutions provided that we use ellipses; eulerr's circular diagrams,
meanwhile, fit better
on all accounts save for the diagError metric in the case of three-set diagrams. (Less)
author
supervisor
organization
course
STAH11 20172
year
type
M2 - Bachelor Degree
subject
keywords
Euler diagrams, Venn diagrams, ellipses, R, computer graphics, area-proportional, software
language
English
id
8934042
2018-02-02 13:43:52
date last changed
2018-02-14 13:00:16
```@misc{8934042,
abstract     = {Euler diagrams are common and intuitive visualizations for data involving
sets and relationships thereof. Compared to Venn diagrams, Euler diagrams do not
require all set relationships to be present and may therefore be area-proportional
also with subset or disjoint relationships in the input.
Most Euler diagrams use circles, but circles do not always
support accurate diagrams. A promising alternative for Euler diagrams is ellipses,
which enable accurate diagrams for a wider range
of set combinations. Ellipses, however, have not yet
been implemented for more than three sets or three-set diagrams where
there are disjoint or subset relationships. The aim of this thesis is
to present a method and software for elliptical Euler diagrams for any
number of sets.

In this thesis, we provide and outline an R-based implementation called eulerr.
It fits Euler diagrams using numerical optimization and exact-area
algorithms through two steps: first, an initial layout is formed using
the sets' pairwise relationships; second, this layout is finalized
taking all the sets' intersections into account.

Finally, we compare eulerr with other software implementations of Euler
diagrams and show that the package
is overall both more consistent and accurate as well as
faster for up to seven sets compared to the other R-packages. eulerr perfectly
reproduces samples of circular Euler diagrams as well
as three-set diagrams with ellipses, but performs suboptimally with elliptical
diagrams of more than three sets. eulerr also outperforms the other software tested in
this thesis in fitting Euler diagrams to set configurations that might
lack exact solutions provided that we use ellipses; eulerr's circular diagrams,
meanwhile, fit better
on all accounts save for the diagError metric in the case of three-set diagrams.},