We explore some ideas around quantifying and visualising classification uncertainty within a geodemographic classifier. We demonstrate spatially-constrained small-multiples to show geographical variation, their combination with a Gastner population cartogram projection to normalise with respect to population, explore a fuzziness parameter when producing fuzzy-sets, and look at implications of taking into account this uncertainty when profiling population, finding that this can have significant effects that are worth investigating further

Fisher, P.

Slingsby, A.

Tate, N.

City Research Online

Slingsby, A., Tate, N. & Fisher, P. (2014). Visualisation of Uncertainty in a Geodemographic Classifier. Paper presented at the GIScience 2014: Uncertainty Workshop, 23 September 2014, Vienna. City Research OnlineOriginal citation: Slingsby, A., Tate, N. & Fisher, P. (2014). Visualisation of Uncertainty in a Geodemographic Classifier. Paper presented at the GIScience 2014: Uncertainty Workshop, 23 September 2014, Vienna. Permanent City Research Online URL: http://openaccess.city.ac.uk/4119/ Copyright & reuseCity University London has developed City Research Online so that its users may access the research outputs of City University London's staff. Copyright © and Moral Rights for this paper are retained by the individual author(s) and/ or other copyright holders.  All material in City Research Online is checked for eligibility for copyright before being made available in the live archive. URLs from City Research Online may be freely distributed and linked to from other web pages. Versions of researchThe version in City Research Online may differ from the final published version. Users are advised to check the Permanent City Research Online URL above for the status of the paper.EnquiriesIf you have any enquiries about any aspect of City Research Online, or if you wish to make contact with the author(s) of this paper, please email the team at publications@city.ac.uk.Visualisation of Uncertainty in aGeodemographic ClassifierAidan Slingsby1, Nicholas J. Tate2, and Peter F. Fisher21 giCentre, Department of Computer Science, City University London, NorthamptonSquare, London, EC1V 0HB; a.slingsby@city.ac.uk2 Department of Geography, University of Leicester, Leicester LE1 7RH, UK;njt9@le.ac.ukAbstract. We explore some ideas around quantifying and visualisingclassification uncertainty within a geodemographic classifier. We demon-strate spatially-constrained small-multiples to show geographical varia-tion, their combination with a Gastner population cartogram projectionto normalise with respect to population, explore a fuzziness parameterwhen producing fuzzy-sets, and look at implications of taking into ac-count this uncertainty when profiling population, finding that this canhave significant effects that are worth investigating further.1 IntroductionGeodemographic classifiers characterise geographical areas based on character-istics of those who live there. A set of a geodemographic categories based on aset of census-derived population data is defined – often with short descriptivelabels such as ‘Multicultural’ and ‘Blue collar’ – and then one is assigned eachgeographical area. Thus, each small area is allocated a category that reflects thecharacteristics of the population living there (Figure 1, left). Geodemograph-ics are in widespread use, helping target campaigns and advertising, assessingthe viability of products and services, doing stratified sampling and enrichingexisting geographical data [7].2 Classification uncertaintyInevitably, characterising population into one of seven categories results in placeswhose population is characterised well and places where it is not.The 2001 “Output Area Classification (OAC)” is a geodemographic classi-fier [11] which classifies Output Areas (OAs; the smallest reporting spatial unitsfrom the 2001 UK census (average population of 297 [8] for England and Wales)into seven main geodemographic categories (‘super-groups’) indicated in Figure1 (left). We use it because unlike its commercial ‘black-box’ rivals, it is freelyavailable and full details of how it was built, population data variables used anduncertainty information are provided. Uncertainty information for each OA is2 Slingsby, Tate and FisherFig. 1. Left: Map of OAC’s geodemographic categories assigned to areas (Output Ar-eas; OAs) in Leicester (UK). The bottom right barchart indicates population in eachgeodemographic category. Right: As left, but lightness corresponds to classification un-certainty where dark is more certain. The top right barchart shows membership ofeach geodemographic category for the OA indicated by the mouse pointer. Data: 2001Census, Output Area Boundaries. Crown copyright c© 2003. Crown copyright materialis reproduced with the permission of the Controller of HMSO.provided as a set of seven ‘distances’ indicating similarity to the typical pop-ulation profiles of each geodemographic category. The larger the distance, theless well the category characterises the population. In normal use, the closestgeodemographic category is used, but this is not always a good characterisationof the population; hence the reason for this work.Slingsby et al [9] uses a measure of how well the allocated (closest) geode-mographic category characterises the population (see paper for details). This isshown as colour lightness in Figure 1 (right). Hue indicates category and light-ness indicates this ‘typicality’ measure. The figure shows that in the City centre(centre of the map), geodemographic categories poorly characterise population(pale) and characterise population better in more peripheral areas. The OA in-dicated with the mouse pointer is pale red which means ‘Prospering suburbs’but a poor characterisation of the OA’s population. The bar chart at the topright shows it is also close to ‘Countryside’ (green), ’Blue collar’ (orange) and‘Typical traits’ (yellow).This classification uncertainty and how it varies across space and by cate-gory may have implications for its application underpinning resource targeting,analytical work and decision-making. Slingsby et al [9] explored this with someexpert users who found this a thought-provoking exercise and were particularlysurprised at the degree of classification uncertainty in certain areas. It was un-clear how this would affect their use of geodemographics in future, but the workindicated that this issue is worth exploring.3 Spatially-varying graphsThus far, we have considered uncertainty information per OA and only mappedone uncertainty value per OA. If we aggregate space into grid cells and thenVisualisation of Uncertainty in a Geodemographic Classifier 3Fig. 2. Left: Graphs of membership of each geodemographic category of places withingrid squares. x-axis indicates proportional membership; y-axis indicates absolute degreeof membership. Right: As left, but first projecting the map as a population cartogramand then gridding that space. The overlain grid indicates geographical distortion. Basemap from OpenStreetMap.embed a chart that characterises the OAs within that grid cell, we can potentiallyprovide more uncertainty information, though arguably, the process of averagingvalues into grid cells introduces another kind of uncertainty.We will consider average distance to each geodemographic category for eachgrid cell (rather than OA). We will also consider two scalings of this: absolutemembership which uses the inverse distances directly and proportional member-ship which scales this between the minimum and maximum average distance.These two measure are depicted in Figure 2 (left) along the y-axis and x-axis,respectively. Around the periphery, ‘Countryside’ (green) and ‘Prospering sub-urbs’ (red) tend to dominate in both proportional and absolute terms: i.e. placesin these grid-cells are mainly characterised by these two categories. In centralareas, ‘Mulicultural’ dominates yet it is not such a good characterisation of thepopulation there.To take into account the denser population in central Leicester, in Figure 2(right) we have experimented with projecting the map as first projecting themap as a Gastner-type population cartogram [2] and then use the regular grid-based partitioning. Each grid square now contains a similar size of population.Although geographical space is distorted, more details of the dense central areaare visible; in particular, ‘City Living’ (indigo) in the SW portion.4 Possibilistic Fuzzy SetsThere are other ways to quantify geodemographic category membership. Pos-sibilistic c-Means (PCM) [4] does this using fuzzy sets and the m parameter4 Slingsby, Tate and FisherFig. 3. As the graphs in Figure 2 but using Possibilistic-Means (PCM) [6]. Top left:m = 1.1; Top right: m = 3.5. Bottom: Graphs of category membership (x axis) thatshows the effect of continuously varying m (y-axis) from m = 1.1 at the top to m = 3.5at the bottom. Base map from OpenStreetMap.Visualisation of Uncertainty in a Geodemographic Classifier 5that adjusts the fuzziness applied to the membership set. There has been debateabout what the best value to use for m [5] and Okeke and Karnieli’s [10] triedmultiple values of m. We investigate the effect of this parameter using the graphsfrom Figure 2. Figure 3 (top) shows the effect of low m and high m, with thelatter almost completely smoothing out category memberships. In Figure 3 (bot-tom) we continuously vary m from 1.1 to 3.5 along the y axis from top to bottomwith absolute membership on the x axis. Low m-values give lower membershipsin some areas (narrower at the top) and high memberships in other areas (widerat the top). As m approaches 2, memberships differences are smoothed out.5 ‘Monte Carlo’ type SimulationFig. 4. Top: Amount of population in each geodemographic category after 1000 ‘Monte-Carlo’ type runs. Bottom: Three alternative maps [3]. Notice how some of the largestOAs switch between ‘Countryside’, ’Prospering suburbs’ and ‘Typical Traits’. Data:2001 Census, Output Area Boundaries. Crown copyright c© 2003. Crown copyrightmaterial is reproduced with the permission of the Controller of HMSO.Finally, we turn our attention to possible implications of classification uncer-tainty. In Figure 4 we do a ‘Monte-Carlo’ type simulation where we randomlyassign a geodemographic category to each OA weighted by the category member-ship. This means that if a geodemographic category has double the membershipas another, it will be twice as likely to be allocated. The population barchartin Figure 4 shows the median population allocated to each category after 1000runs. Significantly, although Figure 1 shows that ‘Prospering suburbs’ has thelargest population share, here the greatest share of the population is ‘Typicaltraits’. This is because ‘Typical traits’ is close to most OAs but is rarely theclosest. Although a very simple experiment, it indicates that taking the degree6 Slingsby, Tate and Fisherof classification uncertainty into account may affect geodemographics-supportedanalysis and decision-making.6 ConclusionWe have explored some ideas around quantifying and graphically depicting ge-ographical classification uncertainty within the OAC geodemographic classifierand consider possible implications of this. We have suggested gridding space toproduce regular geographically-constrained small-multiples and have suggestedusing a Gastner Cartogram projection to give a population-weighted depictionof the results. We have quantified classification uncertainty as relative (propor-tion), absolute and fuzzy sets; in the latter case, we used graphics to depictthe effect of changing fuzziness (m) parameter. Finally, using a ‘Monte Carlo’style approach, we look at some of the implications of taking into account thisuncertainty when profiling population and we believe that finding ways to takeaccount of this uncertainty will help make more informed use geodemographics.AcknowledgementsOAC data were obtained from http://www.sasi.group.shef.ac.uk/area classificationand with help from Dan Vickers.References1. Bezdek, J.C. Pattern recognition with fuzzy objective function algorithms. PlenumPress, New York (1981).2. Dorling, D., Barford, A. and Newman, M. Worldmapper: The world as you’ve neverseen it before. IEEE Transactions on Visualization and Computer Graphics, 12 (5),757–764 (2006).3. Fisher, P. Visualizing Uncertainty in Soil Maps by Animation. Cartographica: TheInternational Journal for Geographic Information and Geovisualization, 30 (2), 20–27 (1993)4. Fisher, P.F. and Tate, N.J. Modelling Class Uncertainty in the GeodemographicOutput Area Classification. Environment and Planning B(in press).5. Fisher, P. Remote sensing of land cover classes as type 2 fuzzy sets. Remote Sensingof Environment 114 (2), 309–321 (2010).6. Fisher, P., Tate,N. and Slingsby, A. Type-2 Fuzzy Sets Applied to GeodemographicClassification. Proceedings of GIScience (extended abstracts), Vienna, (2014).7. Harris, R., Sleight, P. and Webber, R. Geodemographics, GIS and neighbourhoodtargeting. John Wiley and Sons. (2005).8. ONS. Changes to Output Areas and Super Output Ar-eas in England and Wales, 2001 to 2011 http://www.ons.gov.uk/ons/guide-method/geography/products/census/report--changes-to-output-areas-and-super-output-areas-in-england-and-wales--2001-to-2011.pdf (2012)Visualisation of Uncertainty in a Geodemographic Classifier 79. Slingsby, A., Dykes, J. and Wood, J. Exploring Uncertainty in Geodemograph-ics with Interactive Graphics. IEEE Transactions on Visualization and ComputerGraphics 17 (12), 2545–2554 (2011).10. Okeke, F., and Karnieli, A. Linear mixture model approach for selecting fuzzy ex-ponent value in fuzzy c-means algorithm. Ecological Informatics 1, 117–124 (2006).11. Vickers, D. and Rees, P. Introducing the national classification of census outputareas. Population Trends, 125:380403, (2007).

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