Visualising Multi-objective Data: From League Tables to Optimisers, and back
- 1. Visualising Multi-objective Data: From League Tables to Optimisers, and back David Walker College of Engineering, Mathematics and Physical Sciences University of Exeter D.J.Walker@exeter.ac.uk 8th March 2017 – University of Plymouth David Walker Visualising Multi-objective Data 8th March 2017 1 / 17
- 2. League Tables Times Good University Guide, 2009 8 KPIs – NSS, research quality, student-staff ratio, services and facilities spend, entry standards, completion, good honours, graduate prospects Uni NSS RAE Student staff ratio £/ student Entry Reqs. 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 David Walker Visualising Multi-objective Data 8th March 2017 2 / 17
- 3. Visualisation Visualisation is a useful alternative to presenting data in a table – human beings are well suited to understanding information visually 0.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.0 0.20.40.60.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 David Walker Visualising Multi-objective Data 8th March 2017 3 / 17
- 4. Visualisation Visualisation is a useful alternative to presenting data in a table – human beings are well suited to understanding information visually 0.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.0 0.20.40.60.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Unfortunately people can generally only think in three dimensions David Walker Visualising Multi-objective Data 8th March 2017 3 / 17
- 5. High-dimensional Visualisation −1.5 −1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 1.5 f1,f2 f1,f3 f1,f4 f1,f5 f2,f3 f2,f4 f2,f5 f3,f4 f3,f5 f4,f5 f1 f2 f3 f4 f5 0.0 0.5 1.0 1.5 2.0 David Walker Visualising Multi-objective Data 8th March 2017 4 / 17
- 6. Evolutionary Many-objective Optimisation Evolutionary algorithms generate solutions to many-objective optimisation problems – comprising M = 4 (or more) conflicting objectives The quality of a solution p is evaluated using a set of objective functions: y = (f1(p), . . . , fM(p)) Compare pairs of solutions using dominance: f(p) f(q) ⇔ ∀m(fm(p) ≤ fm(q)) ∧ ∃m(fm(p) < fm(q)) David Walker Visualising Multi-objective Data 8th March 2017 5 / 17
- 7. Evolutionary Many-objective Optimisation Evolutionary algorithms generate solutions to many-objective optimisation problems – comprising M = 4 (or more) conflicting objectives The quality of a solution p is evaluated using a set of objective functions: y = (f1(p), . . . , fM(p)) 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 David Walker Visualising Multi-objective Data 8th March 2017 5 / 17
- 8. Pareto Shells Non-dominated Sorting 1 Set k = 1 2 Identify all of the non-dominated individuals and assign them to shell k 3 Increment k 4 If individuals remain, return to step 2 Shell 1 Shell 4 Oxford St Andrews Warwick Durham York Bristol King's 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 Construct a graph Arrange individuals (nodes) into columns according to Pareto shell Place edges between individuals in adjacent shells where one dominates the other David Walker Visualising Multi-objective Data 8th March 2017 6 / 17
- 9. University League Tables Colour nodes according to average rank Rank the individuals m times (once for each KPI) giving rim – the rank of individual i on KPI m 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. David Walker Visualising Multi-objective Data 8th March 2017 7 / 17
- 10. Water Quality Indicators D. Walker, D. Jakovljevic´c, D. Savi´c and M. Radovanovi´c, 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
- 11. Heatmaps A heatmap is a graphical representation of a dataset – rows indicate individuals and columns indicate KPIs “Warm” colours indicate large values “Cool” colours indicate small values 1 2 3 4 5 6 7 8 Criteria 0 20 40 60 80 100 Individuals 15 30 45 60 75 90 105 David Walker Visualising Multi-objective Data 8th March 2017 9 / 17
- 12. Seriation of Heatmaps Reorder the rows of the heatmap so that similar individuals are placed together and patterns can be identified 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
- 13. 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 David Walker Visualising Multi-objective Data 8th March 2017 11 / 17
- 14. 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
- 15. Seriation of Heatmaps: University League Tables 1 2 3 4 5 6 7 8 Criteria 0 20 40 60 80 100 Individuals 15 30 45 60 75 90 105 David Walker Visualising Multi-objective Data 8th March 2017 12 / 17
- 16. Seriation of Heatmaps: University League Tables 1 2 3 4 5 6 7 8 Criteria 0 20 40 60 80 100 Individuals 15 30 45 60 75 90 105 1 2 3 4 5 6 7 8 Criteria 72 68 49 5 53 9 Individuals 15 30 45 60 75 90 105 David Walker Visualising Multi-objective Data 8th March 2017 12 / 17
- 17. Seriation of Heatmaps: Radar Waveform Design Seriate according to individuals then KPIs to reveal further information 1 2 3 4 5 6 7 8 9 Criteria 0 20 40 60 80 100 120 140 160 180 Individuals 20 40 60 80 100 120 140 160 180 200 1 2 3 4 5 6 7 8 9 Criteria 77 28 142 185 104 114 147 65 76 32 Individuals 20 40 60 80 100 120 140 160 180 200 David Walker Visualising Multi-objective Data 8th March 2017 13 / 17
- 18. Seriation of Heatmaps: Radar Waveform Design Seriate according to individuals then KPIs to reveal further information 1 2 3 4 5 6 7 8 9 Criteria 0 20 40 60 80 100 120 140 160 180 Individuals 20 40 60 80 100 120 140 160 180 200 1 2 3 4 5 6 7 8 9 Criteria 77 28 142 185 104 114 147 65 76 32 Individuals 20 40 60 80 100 120 140 160 180 200 4 9 2 8 6 5 7 1 3 Criteria 77 28 142 185 104 114 147 65 76 32 Individuals 20 40 60 80 100 120 140 160 180 200 David Walker Visualising Multi-objective Data 8th March 2017 13 / 17
- 19. Treemaps Visualise data represented as a tree using space to illustrate the importance of a node Additional degrees of freedom (e.g., colour) Many different algorithms for arranging a 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
- 20. Dominance trees Step 1: Pareto sorting Construct a partial ordering of individuals using Pareto sorting – this results in a graph Set 2: Prune edges using dominance distance Remove edges such that each node has exactly one parent node (retain the 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
- 21. Dominance trees Step 1: Pareto sorting Construct a partial ordering of individuals using Pareto sorting – this results in a graph Set 2: Prune edges using dominance distance Remove edges such that each node has exactly one parent node (retain the 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
- 22. Circular Treemaps Good University Guide Oxford SOAS Water Quality Analysis David Walker Visualising Multi-objective Data 8th March 2017 16 / 17
- 23. Summary Performance data Performance data is ubiquitous University league tables, hospital performance, quality of life, water quality, optimisation. . . By visualising it we can better understand and make use of this data Visualisation Methods Pareto shells Seriation Treemaps David Walker Visualising Multi-objective Data 8th March 2017 17 / 17