Visualising Multi-objective Data: From League Tables to Optimisers, and back

Visualising Multi-objective Data:From League Tables to Optimisers, and back

David Walker

College of Engineering, Mathematics and Physical SciencesUniversity of Exeter

[email protected]

8th March 2017 – University of Plymouth

David Walker Visualising Multi-objective Data 8th March 2017 1 / 17

[email protected]

League Tables

Times Good University Guide, 2009

I 8 KPIs – NSS, research quality, student-staff ratio, services andfacilities spend, entry standards, completion, good honours, graduateprospects

Uni NSS RAEStudent

staffratio

£/student

EntryReqs.

Compl-etion

1/2:1

Pros-pects

Ox. 0.840 6.200 11.600 2884.000 502.000 98.600 90.100 83.900

Camb. - 6.500 12.200 2299.000 518.000 97.900 85.400 88.400

Imp. 0.760 5.800 10.400 3218.000 473.000 96.000 69.100 89.300

LSE 0.740 6.300 12.600 1562.000 469.000 96.900 75.200 87.700

Warw. 0.760 5.600 13.600 1881.000 448.000 96.700 79.400 74.900

UCL 0.760 5.500 9.100 1702.000 434.000 94.300 75.100 81.500

Dur. 0.780 5.200 15.400 1375.000 447.000 96.400 78.800 75.900

York 0.770 5.500 13.100 1313.000 423.000 95.200 74.700 70.500

Bristol 0.750 5.200 14.700 1535.000 430.000 95.800 78.400 81.500

King’s 0.770 4.700 11.900 1696.000 406.000 93.200 72.100 80.400


Visualisation

Visualisation is a useful alternative to presenting data in a table – humanbeings are well suited to understanding information visually

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Visualisation

Visualisation is a useful alternative to presenting data in a table – humanbeings are well suited to understanding information visually

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High-dimensional Visualisation

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Evolutionary Many-objective Optimisation

I Evolutionary algorithms generate solutions to many-objectiveoptimisation problems – comprising M = 4 (or more) conflictingobjectives

I The quality of a solution p is evaluated using a set of objectivefunctions:

y = (f1(p), . . . , fM(p))

I Compare pairs of solutions using dominance:

f(p) ≺ f(q)⇔ ∀m(fm(p) ≤ fm(q)) ∧ ∃m(fm(p) < fm(q))

Visualise individuals according to their dominance relationships


Evolutionary Many-objective Optimisation

I Evolutionary algorithms generate solutions to many-objectiveoptimisation problems – comprising M = 4 (or more) conflictingobjectives

I The quality of a solution p is evaluated using a set of objectivefunctions:

y = (f1(p), . . . , fM(p))

I Compare pairs of solutions using dominance:

f(p) ≺ f(q)⇔ ∀m(fm(p) ≤ fm(q)) ∧ ∃m(fm(p) < fm(q))

Visualise individuals according to their dominance relationships


Pareto Shells

Non-dominated Sorting

1 Set k = 1

2 Identify all of thenon-dominated individualsand assign them to shell k

3 Increment k

4 If individuals remain, returnto step 2

Shell 1

Shell 2

Shell 3

Shell 4

Shell 5

Shell 6Oxford

St Andrews

Warwick

Durham

York

Bristol

King's

Loughborough

Exeter

Leicester

Nottingham

Southampton

Edinburgh

Lancaster

Glasgow

Aberdeen

Manchester

Strathclyde

Cambridge

Imperial

LSE

UCL

SOAS

Sheffield

East Anglia

Cardiff

Reading

Liverpool

Kent

Sussex

Essex

Hull

Royal Holloway

Bradford

Bedfordshire

Abertay

Bath

Newcastle

Surrey

Keele

Birmingham

Aston

Queen's Belfast

Queen Mary

Dundee

Heriot-Watt

City

Robert Gordon

N'ham Trent

Bournemouth

Brighton

Napier

UWIC Cardiff

Stirling

Brunel

Ulster

B'ham City

Glamorgan

Hertfordshire

Roehampton

Leeds

Oxford Brookes

Staffordshire

Coventry

Aberystwyth

Bangor

Swansea

Goldsmiths

Portsmouth

Plymouth

Central Lancs

West England

Winchester

Glasgow Cal

Lampeter

Bath Spa

Northumbria

U. Arts

S'field Hallam

De Montfort

Canterbury CC

Sunderland

Salford

Chester

Huddersfield

York St John

Manchester Met

Leeds Met

Anglia Ruskin

Bucks New

QM Edinburgh

Chichester

Gloucestershire

Derby

West Scotland

Edge Hill

Cumbria

Teesside

Middlesex

East London

Worcester

Northampton

Kingston

Soton Solent

Wolverhampton

London S Bank

Liverpool JM

Greenwich

Thames Valley

Westminster

Bolton

UWCN

Lincoln

Construct a graph

I Arrange individuals (nodes) into columns according to Pareto shell

I Place edges between individuals in adjacent shells where onedominates the other


University League Tables

Colour nodes according toaverage rank

I Rank the individuals mtimes (once for eachKPI) giving rim – therank of individual i onKPI m

I Average these ranks

ri =1

M

M∑m=1

rim

Shell 1

Shell 2

Shell 3

Shell 4

Shell 5

Shell 6Oxford (1)

St Andrews (7)

Warwick (4)

Durham (9)

York (11)

Bristol (10)

King's (8)

Loughborough (24)

Exeter (17)

Leicester (16)

Nottingham (12)

Southampton (13)

Edinburgh (15)

Lancaster (21)

Glasgow (17)

Aberdeen (29)

Manchester (22)

Strathclyde (36)

Cambridge (6)

Imperial (2)

LSE (5)

UCL (3)

SOAS (27)

Sheffield (20)

East Anglia (35)

Cardiff (26)

Reading (34)

Liverpool (31)

Kent (37)

Sussex (38)

Essex (43)

Hull (49)

Royal Holloway (33)

Bradford (42)

Bedfordshire (91)

Abertay (99)

Bath (14)

Newcastle (19)

Surrey (39)

Keele (40)

Birmingham (23)

Aston (30)

Queen's Belfast (25)

Queen Mary (28)

Dundee (41)

Heriot-Watt (44)

City (50)

Robert Gordon (55)

N'ham Trent (56)

Bournemouth (59)

Brighton (58)

Napier (71)

UWIC Cardiff (86)

Stirling (47)

Brunel (46)

Ulster (52)

B'ham City (60)

Glamorgan (69)

Hertfordshire (70)

Roehampton (80)

Leeds (32)

Oxford Brookes (53)

Staffordshire (72)

Coventry (68)

Aberystwyth (48)

Bangor (54)

Swansea (45)

Goldsmiths (51)

Portsmouth (60)

Plymouth (57)

Central Lancs (64)

West England (63)

Winchester (65)

Glasgow Cal (66)

Lampeter (81)

Bath Spa (75)

Northumbria (67)

U. Arts (72)

S'field Hallam (74)

De Montfort (78)

Canterbury CC (82)

Sunderland (84)

Salford (77)

Chester (87)

Huddersfield (89)

York St John (95)

Manchester Met (89)

Leeds Met (93)

Anglia Ruskin (103)

Bucks New (105)

QM Edinburgh (79)

Chichester (76)

Gloucestershire (62)

Derby (89)

West Scotland (100)

Edge Hill (106)

Cumbria (101)

Teesside (91)

Middlesex (98)

East London (104)

Worcester (85)

Northampton (83)

Kingston (94)

Soton Solent (110)

Wolverhampton (109)

London S Bank (112)

Liverpool JM (96)

Greenwich (108)

Thames Valley (113)

Westminster (97)

Bolton (111)

UWCN (107)

Lincoln (102)

D. Walker, R. Everson and J. Fieldsend, Visualisation and Ordering of Many-objective Populations. In Proc. IEEE Congress on

Evolutionary Computation (CEC 2010), pp3664–3671, 2010.


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.


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

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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.



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Seriation of Heatmaps: University League Tables

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Seriation of Heatmaps: University League Tables

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Seriation of Heatmaps: Radar Waveform Design

Seriate according to individuals then KPIs to reveal furtherinformation

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Seriation of Heatmaps: Radar Waveform Design

Seriate according to individuals then KPIs to reveal furtherinformation

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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)


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

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D. Walker, Visualising Multi-objective Populations with Treemaps. In Proc. Genetic and Evolutionary Computation Conference

(GECCO 2015) Companion Volume, 963–970, 2015.


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.


Circular Treemaps

Good University Guide

Oxford

SOAS

Water Quality Analysis


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


Data & Analytics

Visualising Multi-objective Data: From League Tables to Optimisers, and back