Visualising Multi-objective Data: From League Tables to Optimisers, and back David Walker College of Engineering, Mathematics and Physical Sciences University of Exeter [email protected]8th March 2017 – University of Plymouth David Walker Visualising Multi-objective Data 8th March 2017 1 / 17
23
Embed
Visualising Multi-objective Data: From League Tables to Optimisers, and back
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Visualising Multi-objective Data:From League Tables to Optimisers, and back
David Walker
College of Engineering, Mathematics and Physical SciencesUniversity of Exeter
David Walker Visualising Multi-objective Data 8th March 2017 7 / 17
Water Quality Indicators
D. Walker, D. Jakovljevicc, D. Savic and M. Radovanovic,
Multi-criterion Water Quality Analysis of the Danube River
in Serbia: A Visualisation Approach. Water Research 79
(158–172), 2015.
David Walker Visualising Multi-objective Data 8th March 2017 8 / 17
Heatmaps
I A heatmap is a graphicalrepresentation of a dataset –rows indicate individuals andcolumns indicate KPIs
I “Warm” colours indicate largevalues
I “Cool” colours indicate smallvalues
1 2 3 4 5 6 7 8Criteria
0
20
40
60
80
100
Indi
vidu
als
15
30
45
60
75
90
105
David Walker Visualising Multi-objective Data 8th March 2017 9 / 17
Seriation of Heatmaps
I Reorder the rows of the heatmap so that similar individuals are placedtogether and patterns can be identified
I Seriation is a procedure for permuting items based on their similarity
Aij = 1− 1
M(N − 1)2
M∑m=1
(rim − rjm)2
g(π) =N∑i=1
N∑j=1
Aij(πi − πj)2
D. Walker, R. Everson and J. Fieldsend, Visualisation Mutually Non-dominating Solution Sets in Many-objective Optimisation.
In IEEE Transactions on Evolutionary Computation 17(2)165–184, 2013.
David Walker Visualising Multi-objective Data 8th March 2017 10 / 17
Seriation of Heatmaps
0 20 40 60 80 100
0
20
40
60
80
100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 20 40 60 80 100
0
20
40
60
80
100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
David Walker Visualising Multi-objective Data 8th March 2017 11 / 17
Seriation of Heatmaps
0 20 40 60 80 100
0
20
40
60
80
100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 20 40 60 80 100
0
20
40
60
80
100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
David Walker Visualising Multi-objective Data 8th March 2017 11 / 17
Seriation of Heatmaps: University League Tables
1 2 3 4 5 6 7 8Criteria
0
20
40
60
80
100
Indi
vidu
als
15
30
45
60
75
90
105
1 2 3 4 5 6 7 8Criteria
72
68
49
5
53
9
Indi
vidu
als
15
30
45
60
75
90
105
David Walker Visualising Multi-objective Data 8th March 2017 12 / 17
Seriation of Heatmaps: University League Tables
1 2 3 4 5 6 7 8Criteria
0
20
40
60
80
100
Indi
vidu
als
15
30
45
60
75
90
105
1 2 3 4 5 6 7 8Criteria
72
68
49
5
53
9
Indi
vidu
als
15
30
45
60
75
90
105
David Walker Visualising Multi-objective Data 8th March 2017 12 / 17
Seriation of Heatmaps: Radar Waveform Design
Seriate according to individuals then KPIs to reveal furtherinformation
1 2 3 4 5 6 7 8 9Criteria
0
20
40
60
80
100
120
140
160
180
Indi
vidu
als
20
40
60
80
100
120
140
160
180
200
1 2 3 4 5 6 7 8 9Criteria
77
28
142
185
104
114
147
65
76
32
Indi
vidu
als
20
40
60
80
100
120
140
160
180
200
4 9 2 8 6 5 7 1 3Criteria
77
28
142
185
104
114
147
65
76
32
Indi
vidu
als
20
40
60
80
100
120
140
160
180
200
David Walker Visualising Multi-objective Data 8th March 2017 13 / 17
Seriation of Heatmaps: Radar Waveform Design
Seriate according to individuals then KPIs to reveal furtherinformation
1 2 3 4 5 6 7 8 9Criteria
0
20
40
60
80
100
120
140
160
180
Indi
vidu
als
20
40
60
80
100
120
140
160
180
200
1 2 3 4 5 6 7 8 9Criteria
77
28
142
185
104
114
147
65
76
32
Indi
vidu
als
20
40
60
80
100
120
140
160
180
200
4 9 2 8 6 5 7 1 3Criteria
77
28
142
185
104
114
147
65
76
32
Indi
vidu
als
20
40
60
80
100
120
140
160
180
200
David Walker Visualising Multi-objective Data 8th March 2017 13 / 17
Treemaps
I Visualise data represented as a treeusing space to illustrate the importanceof a node
I Additional degrees of freedom (e.g.,colour)
I Many different algorithms for arranginga treemap
Classification of the top 100
websites visited in 2010
(UK, France, Germany,
Italy, Spain, Switzerland,
Brazil, US and Australia)
David Walker Visualising Multi-objective Data 8th March 2017 14 / 17
Dominance trees
Step 1: Pareto sortingConstruct a partial ordering of individuals using Pareto sorting – thisresults in a graph
Set 2: Prune edges using dominance distanceRemove edges such that each node has exactly one parent node (retainthe parent with the smallest dominance distance) and insert an artificial“root” using the global best
A
B
C
D
E
F
D. Walker, Visualising Multi-objective Populations with Treemaps. In Proc. Genetic and Evolutionary Computation Conference
(GECCO 2015) Companion Volume, 963–970, 2015.
David Walker Visualising Multi-objective Data 8th March 2017 15 / 17
Dominance trees
Step 1: Pareto sortingConstruct a partial ordering of individuals using Pareto sorting – thisresults in a graph
Set 2: Prune edges using dominance distanceRemove edges such that each node has exactly one parent node (retainthe parent with the smallest dominance distance) and insert an artificial“root” using the global best
A
B
C
D
E
F
nr
A
B
C
D
E
F
D. Walker, Visualising Multi-objective Populations with Treemaps. In Proc. Genetic and Evolutionary Computation Conference
(GECCO 2015) Companion Volume, 963–970, 2015.
David Walker Visualising Multi-objective Data 8th March 2017 15 / 17
Circular Treemaps
Good University Guide
Oxford
SOAS
Water Quality Analysis
David Walker Visualising Multi-objective Data 8th March 2017 16 / 17
Summary
Performance data
I Performance data is ubiquitous
I University league tables, hospital performance, quality of life, waterquality, optimisation. . .
I By visualising it we can better understand and make use of this data
Visualisation Methods
I Pareto shells
I Seriation
I Treemaps
David Walker Visualising Multi-objective Data 8th March 2017 17 / 17