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Urban Studies1–19! Urban Studies Journal Limited 2015Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0042098015601599usj.sagepub.com

Revealing centrality in the spatialstructure of cities from humanactivity patterns

Chen ZhongUniversity College London, UK

Markus SchlapferMIT, USA

Stefan Muller ArisonaUniversity of Applied Sciences and Arts Northwestern Switzerland FHNW, Switzerland

Michael BattyUniversity College London, UK

Carlo RattiMIT, USA

Gerhard SchmittETH Zurich, Switzerland

AbstractIdentifying changes in the spatial structure of cities is a prerequisite for the development and vali-dation of adequate planning strategies. Nevertheless, current methods of measurement arebecoming ever more challenged by the highly diverse and intertwined ways of how people actu-ally make use of urban space. Here, we propose a new quantitative measure for the centrality oflocations, taking into account not only the numbers of people attracted to different locations, butalso the diversity of the activities they are engaged in. This ‘centrality index’ allows for the identifi-cation of functional urban centres and for a systematic tracking of their relative importance overtime, thus contributing to our understanding of polycentricity. We demonstrate the proposedindex using travel survey data in Singapore for different years between 1997 and 2012. It is shown

Corresponding author:Chen Zhong, Centre for Advanced Spatial Analysis,University College London, 90 Tottenham Court Road,London, W1T 4TJ, UK.Email: [email protected]

at Massachusetts Institute of Technology on October 19, 2015usj.sagepub.comDownloaded from

http://usj.sagepub.com/

that, on the one hand, the city-state has been developing rapidly towards a polycentric urbanform that compares rather closely with the official urban development plan. On the other hand,however, the downtown core has strongly gained in its importance, and this can be partly attrib-uted to the recent extension of the public transit system.

Keywordspolycentricity, travel survey data, spatial convolution, urban centrality, urban functions, urban spa-tial structure

Received June 2014; accepted June 2015

Introduction

Over the last century and a half, new trans-port and information technologies haveenabled many cities to spread out from theirhistoric cores, sprawling at much lower popu-lation densities then anything possiblehitherto, and thus growing into vast metro-politan areas (Buliung, 2011). In tandem withthese developments, the socioeconomic func-tions of traditional central business districts(CBDs) have been increasingly evolved into amultitude of dispersed and interacting hubs ofemployment, business and leisure (Anas et al.,1998). Understanding these new ‘polycentric’forms of urban organisation is crucial for thedevelopment of adequate planning strategies,since spatial structure exerts such a stronginfluence on people’s daily life, economicgrowth, social equity and sustainable urbandevelopment (Anas et al., 1998; Horton andReynolds, 1971; Rodrigue et al., 2009). It istherefore hardly surprising that during recentyears the quantitative characterisation ofurban structure has gained much attention inmany scientific fields, ranging from urbangeography and regional science to urban eco-nomics, social physics and spatial planning(Burger and Meijers, 2012; Kloosterman andLambregts, 2001; Meijers, 2008).

Measuring urban spatial structure

Generally, it is agreed that the two mostimportant aspects of the (polycentric) urban

spatial structure are (1) its morphologicaldimension, which denotes the size and spa-tial distribution of intra-urban centres, and(2) its functional dimension, which addition-ally addresses the linkages between differentcentres such as the daily flows of commutingor the strength of business and social net-work connections (Burger and Meijers, 2012;Green, 2007; Vasanen, 2012). Though highcorrelation exists between these two aspects,in some cases, the functional changes are notnecessarily the result of morphologicalchanges (Burger and Meijers, 2012).

A wide range of analytical methods hasbeen proposed to measure morphological orfunctional aspects. Greene (1980), forinstance, identifies centres using a set of ref-erence thresholds that are derived from localknowledge. The method proposed byMcDonald (1987) examines the spatial dis-tribution of density functions and considerslocal peaks as possible sub-centres. A para-metric method has been proposed using aregression model based on density and dis-tance (McDonald and Prather, 1994), andnon-parametric methods have been intro-duced thereafter based on smoothed densityfunctions (McMillen, 2001; Redfearn, 2007).Weighted methods of combining retail den-sity and measures of diversity have beenused by Thurstain-Goodwin and Unwin(2000) to define town centres as hotspots ofretail, commercial and public services for allEngland and Wales. Drawbacks of these

2 Urban Studies



approaches are the arbitrariness of the cho-sen population or job density thresholds andthe sensitivity of the identified centres to thespatial scale of the analysis (Anas et al.,1998). There are other widely applied meth-ods based on accessibility measures. Onewith quite wide popularity is called spacesyntax, and is based on morphologicalaspects of urban spatial structure. Themethod extracts and quantifies the relativenearness of streets based on how they arerelated through their topology (Hillier,1996) but tends to ignore that centres arecomposed of activities other than thoseindirectly associated with the accessibilitiesof individual streets. Recent work has high-lighted the importance of considering theconnectivity between centres (Vasanen,2012). This functional aspect of urban spa-tial structure has been suggested as playing akey role in the overall performance of anurban system (Burger and Meijers, 2012).Exemplary approaches for measuring func-tional interdependencies include spatialinteraction models to predict the interactionsbetween spatial units based on their size anddistance (De Goei et al., 2010; van Oortet al., 2010), the use of network propertiesto measure connectivity based on peopleflows (Thiemann et al., 2010), or the conceptof connectivity fields to quantify the connec-tion of each centre to the rest of the urbansystem (Vasanen, 2012). A review of manyof these measures is given by Batty (2013).Together, polycentricity is usually associatedwith the number of co-existing centres inone urban region (Kloosterman andLambregts, 2001; Parr, 2004) and measuredwith the distributions of the relative impor-tance of those centres (Burger and Meijers,2012; Kloosterman and Lambregts, 2001;Meijers, 2008). Thus, a polycentric develop-ment can be studied as a spatial processwhere urban functions diffuse from majorcentres to sub-centres (Hall, 2009; Hall and

Pain, 2006; Kloosterman and Musterd,2001). Understanding this spatial process isparticularly important, providing the basisfor adequate urban planning policies(Champion, 2001; Lambregts, 2006; Riguelleet al., 2007).

Human activity data for measuring the useof urban space

As indicated above, most empirical studiesof urban structure have focused on singleattributes such as population or employmentdensity as proxies to measure morphologicalaspects (Hall and Pain, 2006; Riguelle et al.,2007), and commuting or shopping trips forthe functional aspect (Burger and Meijers,2012). In contrast, the multiplex nature ofspatial interactions that combine, for exam-ple, trips for commuting, shopping or lei-sure, has rarely been studied systematically(Burger et al., 2013). More importantly,these approaches are not able to measurethe increasingly intertwined use of urbanspace: people working at home instead of atthe office, students studying in coffee-shopsinstead of in university libraries, and so on(Harrison et al., 2003).

The recent availability of rich and oftenlarge-scale data on human activity now pro-vides unprecedented possibilities to fill thisgap and, more generally, to gain new insightsin the actual use of urban space. Examplesare the identification of urban functionsfrom smart card and related survey data(Ordonez Medina and Erath, 2013), asses-sing the function of different regions in a cityusing floating car and point of interest data(Yuan et al., 2012), or inferring land uses bycombining mobile phone records with zon-ing regulations (Toole et al., 2012). At alarger scale, smart card data of individualperson movements in the London subwayhas been analysed to identify the polycentricstructure and organisation of the city (Roth

Zhong et al. 3



et al., 2011). Together, these examplesdemonstrate a clear trend towards directlymeasuring the real usage and heterogeneousfunctions of urban space, resulting in a bet-ter understanding of the urban dynamics.

On these premises, this paper proposes anew approach to adequately measure thepolycentric spatial structure of cities. Themethod is able to capture the functionaldiversity of places as reflected in differenthuman activities for work, leisure, residenceand so on. The clustering of these activitiesand how they are linked in urban space givesrise to a more comprehensive definition offunctional urban centres that reflect theactual usage of places. More specifically, wepropose a simple centrality index that can beapplied to different kinds of human activitydata. It is demonstrated how this centralityindex can be deployed to identify urban cen-tres and to eventually track changes in theoverall spatial structure of cities over time.Note that the centrality index is not primar-ily designed to directly compare locationsfrom different cities in absolute terms; butrather to track changes in the spatial struc-ture and to compare cities in terms of thespeed of such changes. In this study, detailedtravel survey data is used which containsdirect information on human activities, butthe proposed method is equally applicableto other types of urban data from whichlocational activities can be derived.

Measuring the centrality oflocations

The theoretical basis: Applied central placetheory

Central place theory (CPT) emerged in the19th century in France as part of early loca-tion theory (Reynaud, 1841; Robic, 1982)but it was formally introduced by Christaller(1933) in empirical terms and theoretically

by Losch (1944, 1954). This constitutes thestarting point of our proposed method. CPTwas originally developed to explain the sizeand number of towns and cities, togetherwith their distribution in space as a result ofeconomic competition and optimisationprinciples. The theory is focused on theinter-urban scale, and is based on the formalidea of a hierarchy of centres that are per-fectly nested but overlapping within oneother (Berry and Garrison, 1958). Centres inthis hierarchy are differentiated by their sizein terms of population and their order interms of the range of functions that theyprovide. Accordingly, higher-order centresprovide more specialised functions (goodsand services) and thus are characterised by alarger trade area or hinterland from whichthey draw population. This nestednessimplies that higher-order centres embrace allthe functions of lower order centres plus anadditional set of functions that differentiatesthem from lower order centres, and in thissense, the diversity of centres increases withtheir increasing size.

All this implies that diversity is a keycomponent of centrality. Empirical studieshave shown that such a nested hierarchy isindeed present in real urban systems (Berryand Garrison, 1958) with such structuresbeing entirely consistent with spatial inter-action models. Translating these basic con-siderations into the context of urbanactivity and movement data, the two funda-mental aspects that determine the impor-tance, or centrality, of a location within agiven city are (1) the number of peopleattracted to different centres, reflectingtheir size, and (2) the diversity of theiractivities, reflecting their order. Functionalintra-urban centres can then be identified asspatial clusters of locations with a high cen-trality as for example shown by Roth et al.(2011) and Thurstain-Goodwin and Unwin(2000).

4 Urban Studies



Diversity and density as a basis forcentrality

Half a century ago, the notion that citiesbecome more diverse as they grow in sizeand in the populations served by their hin-terlands was hard to measure formallybecause of limits on data. Berry (personalcommunication, 2014) recalls that althoughit could be clearly observed that the func-tions of smaller cities were subsumed intolarger ones, there was little data on the fre-quency of visits to cities and thus it was notpossible to measure the extent to whichlower order goods were purchased more fre-quently than higher order. That large citieswere more diverse than smaller ones in termsof the opportunities they offered for workand social activities was argued much morequalititively, for example by Jacobs (1961)whose mantle has been taken up morerecently by Glaeser (2011). Since then therehas been a veritable explosion in the litera-ture characterising diversity (although muchless on its measurement) and there are nowexplicit attempts to measure size–diversityrelationships in works as diverse as that ofHidalgo and Hausmann (2009) on the eco-nomic performance of countries, of theSanta Fe group on the allometry of urbansize (Bettencourt et al., 2007; Schlapferet al., 2014), and of the service functions ofworld cities by the Globalization and WorldCities (GaWC) group (Taylor et al., 2002).

Density has been more widely used as ameasure of centrality largely because mostcities grow from their historic core which isthe functional centre for exchange of goods– in contemporary terms, the so-called cen-tral business district (CBD) – where residen-tial and employment densities are highest. Infact, residential densities tend to be lower inthe actual core as employment tends to dis-place residential land uses but in general,urban economic theory suggests that the costof space in terms of rent and consequently

densities for all land uses rises inexorably asone get closer to the CBD. Notwithstandingthe sorts of variations that distort such regu-lar monocentric patterns, the notion that thedemand for space is highest at the most cen-tral points of the cities is key to the way landuses are organised according to the trade-offbetween the ability to pay and the cost oftransport as encapsulated in the so-calledbid rent hypothesis (Alonso, 1964). What isclear now is that different kinds of densityassociated with different land uses character-ise different kinds of centrality and thus oneneeds to be careful about the choice of den-sity type.

Merging density and diversity into a com-posite measure of centrality has beenattempted before. Batty et al. (2004) mea-sure diversity as the amount of activity orland use of each type located in each place,but normalised so that it is expressed as adensity with respect to its distribution overthe whole space. They then measure this as adifference from the region-wide average.The measure is actually constructed to pickup the degree of multifunctionality of eachplace but it is also used as a measure of cen-trality. What this measure does not do iscompare the array of activity or land usetypes with other measures of concentrationsuch as the number of persons visiting eachplace which is related to how those activitiesare used – for work, residence, leisure and soon. What we need to develop is such a mea-sure and, in the next section, we will buildon these ideas to show how one such mea-sure can be constructed so that it identifiesthe degree of centrality of any place as aconvolution of density and diversity.

A centrality index

The method proposed here quantifies thecentrality of a given location by combiningthe number of people attracted to locationsand the range of their activities that they

Zhong et al. 5



engage in at these locations into a singlevalue called the Centrality Index (CI).Moreover, it provides a smoothed densityfunction that detects spatial clusters of loca-tions with high centrality (CI) values. Theseclusters can be understood as functional cen-tres that shape the overall spatial structureof a city. The calculation of the CI-valuesconsists of the following three steps:

Step 1: Density and diversity. We first definedensity and diversity before we combinethem. Density statistics measure how con-centrated human activities are in one spatialunit, while diversity measures how mixed thedifferent kinds of activities are (Cervero andKockelman, 1997; Mitchell Hess et al.,2001). For our purposes, we define densityhere as the number of distinct peopleattracted to a given unit area x, yð Þ, normal-ised by the total number of people visits inthe overall m # n unit space S during a timeunit which is implicit. Then:

D x, yð Þ= N x, yð ÞPmi= 1

Pnj= 1 N i, jð Þ

,

withXm

i= 1

Xn

j= 1

D i, jð Þ= 1

ð1Þ

where N (x, y) is the number of people visit-ing unit area (x, y) during a pre-determinedtime unit (e.g. one day). We will define thesenumbers below when we introduce theapplication.

Diversity is measured by an entropywhich here is a quantitative index thatdescribes the amount of disorder in activi-ties, as originating from information theory(Shannon, 1948). It has long been adoptedto measure the degree of complexity andorder in many different types of spatial dis-tribution, particularly in ecology but rele-vant here is their application to theorganisation of land use arrangement(Cervero and Kockelman, 1997; Kockelman,

1997). Diversity E x, yð Þ measures the mixingof activity types in a unit area x, yð Þ formu-lated as:

E x, yð Þ= $ KXJ

j= 1

Pj x, yð ÞLnPj x, yð Þ

withXJ

j= 1

Pj x, yð Þ= 1

ð2Þ

where Pj x, yð Þ is the proportion of those tra-velling to engage in activities in cell x, yð Þ forthe activity type j during a given period oftime. The constant K is defined from themaximum entropy Ln(J ) as K = 1=Ln(J )where J is the total number of activity types.From the definitions in equations (1) and(2), it is clear that the density and diversitymeasures are normalised over the rangefrom 0 to 1 such that 0%D x, yð Þ% 1, and0%E x, yð Þ% 1.

Step 2: Ranking density and diversity. Densityand diversity are two quantities with differ-ent dimensions and physical meanings. Tointegrate them into a single function, we firstconvert them from absolute values to anordering that we refer to as a ranking. Thesimplest way is to set the rank of the largestdensity (or entropy) to 1, and then the ranksof all other areas are scaled so that the com-parative scale between each of them and thehighest ranked area reflects an inverse order-ing. Another possibility is provided from theperspective of probability theory. Weassume that the area with highest density (orentropy) value implies a maximum probabil-ity of being a higher-order centre, and wethus set its probability to 1. The probabil-ities of the other locations are defined acrossthe related scales. A formal definition isgiven as follows. In a two-dimensional m # nspace S, we denote the density function asDxy =D(x, y), with x= 1, 2, :::::::::::::::,m,y= 1, 2, :::::::, n, and Dxy as being the den-sity of cell (x, y) in S. For each cell, there is a

6 Urban Studies



function RD x, yð Þ= f x, y,Dxy

! "that denotes

the probability of a cell to be a city centrei.e. the point of greatest centrality based onits density only. Thus, we define the densityranking function as:

RD x, yð Þ= f x, y,Dxy

! "=

Dxy

maxxy

Dxyð3Þ

Similarly, RE x, yð Þ= f x, y,Exy

! "is a prob-

ability density function related to the diver-sity Exy =E(x, y) at cell x, yð Þ. We define theprobability density function of diversity as:

RE x, yð Þ= f x, y,Exy

! "=

Exy

maxxy

Exyð4Þ

Step 3: Computing centrality by convolution-basedsmoothing. Density and diversity are twocomplementary indices referring to the spa-tial distribution of activities. None of themcan fully represent central areas individually,especially in the context of modern citieswhere mono-functional areas exist alongsidemulti-functional ones (Batty et al., 2004).For instance, a residential district might havevery high density but a limited number ofactivity types, which should be differentiated

for multi-functional centres. Moreover, asshown in Figure 1 (top), there could be twoareas having the same level of diversity butwith very different densities. Figure 1 (bot-tom) shows that there could be some non-central areas with a high diversity of activitytypes yet with only a small number of peoplewho interact (visit) the areas in question.The proposed centrality index considers bothlocational characteristics by integrating theminto a single value. To that end, we definethe centrality index C x, yð Þ as the probabilityof a grid cell x, yð Þ being a centre, derived bycombining the density of person interactionsand the diversity of their activities through aspatial convolution function.

C x, yð Þ=RD(x, y) # RE(x, y) ð5Þ

Convolution is a fundamental concept insignal processing and analysis (Young et al.,1998). Generally, given two time-dependentfunctions f1(t) and f2(t), their convolution is

calculated asÐ+‘

$‘f1(t)f2(t $ t)dt and often

being denoted as f tð Þ= f1 tð Þ # f2 tð Þ. A spatialconvolution follows directly and can bewritten as:

Figure 1. Possible differences between the density and diversity of activities in a given location. Circlesand triangles represent two different types of activities.

Zhong et al. 7



f x, yð Þ # g x, yð Þ=ð+‘

$‘

ð+‘

$‘

f (t1, t2)g(x$ t1, y$ t2)dt1t2

ð6Þ

where the function f (t1, t2) is convolutedwith a comparable filter g(t1, t2) that isapplied over the limits of the two-dimensional space. Equation (6) can betranslated into a discrete 2D spatial convolu-tion which ‘adds’ the variables RD(x, y) andRE(x, y) either of which can be considered asthe filter as the convolution operator issymmetric.

In Figure 2, we illustrate the mechanismas a moving window which introduces asmoothing (or sharpening) of the joint con-volution of the density and the diversitywhere the symmetry is visually obvious. Ateach cell x, yð Þ in the output function, weplace two 3*3 windows, each of which cov-ers 9 cells for RD(x, y) and RE(x, y) individu-ally, and the discrete form is thus defined as:

C x, yð Þ=Xt1 = + 1

t1 =$1

Xt2 = + 1

t2 =$1

RD(x, y) # RE(x$ t1, y$ t2)

ð7Þ

C x, yð Þ is therefore the sum of the ninemultiplications and the results of the

convolution operation are twofold: (1) twodimensions are reduced to a single index,which is then used to delineate urban centresby a customised ranking and (2) areas withopposed density and diversity values are ‘fil-tered out’. On a casual level, it is easy to seethat conjoint high values of density anddiversity are less likely than high values ofeither and in this sense, the centrality indexis sharpened while adjacent values tend tosmooth the overall function. There arestrong links here to kernel density estimationas used for the simpler index by Batty et al.(2004) and of course to many smoothingtechniques that are central to image process-ing and time-series analysis.

Measuring centrality in theevolving spatial structure ofSingapore

Urban planning in Singapore

Singapore is a city-state in Southeast Asiawith an area of 710 km2. Its populationincluding non-residents was approximately5.4 million in 2013, 4.6 million in 2007, 4.2million in 2004, and 3.7 million in 1997according to national statistics.1 Hence, thetotal population today has grown by about30% compared with its population a decadeago. During the last 50 years as an

Figure 2. Spatial convolution with contiguity edges and corners.

8 Urban Studies



independent city-state, Singapore has experi-enced rapid urban development and trans-formed itself from a declining trading postto a world city in the global economy (Huat,2011).

From the 19th to the mid-20th century,Singapore’s physical growth was rather hap-hazard and largely unregulated. It was onlyin the mid-1950s that the city-state began toimplement its first concept plan with far-reaching impacts on its urban spatial struc-ture. In particular, the revised concept plan2

of 1991 emphasised sustainable economicgrowth and proposed the idea of decentrali-sation. It has been one of the most influentialplans that shaped the structure of Singapore.The CBD was planned to be surrounded byseveral regional centres, sub-regional centresand fringe centres, as illustrated in Figure3(a), with the urban plan attempting to bringjobs closer to the homes and to relieve con-gestion in the old central areas. As such, theplan provided a focus of transforming thecity into a polycentric structure of higherand lower order centres.

The 1991 plan was implemented througha comprehensive set of planning instruments(Huat, 2011). For instance, new publictransportation infrastructures such as the‘Massive Rapid Transit’ (MRT) have beenbuilt to better link regional centres and togreatly shorten travel times. New residentialtowns along the MRT lines (e.g. Yishun orPunggol) were built, significantly increasingthe population density in those areas.Industrial zones became self-contained satel-lite towns and became better accessible bynew road systems. Moreover, several newcommercial and entertainment areas wereconstructed outside the traditional CBD, forinstance in Jurong East or Woodlands.

Data processing

Extensive travel survey data, the so-calledHousehold Interview Travel Survey (HITS),

is used to generate the measures for ourempirical demonstration. The survey is con-ducted by the Singapore Land TransportAuthority (LTA) every 4–5 years to providetransport planners and policy-makers withinsights into different forms of travel beha-viour. About 1% of all households inSingapore are surveyed, with householdmembers answering detailed questions abouttheir trip-making activities. The sampledlocations for the year 2008 are shown inFigure 3(b). The HITS data provide compre-hensive information about age, occupation,travel purpose, travel destination and travel-ling time for all those in the household whoengage in travel (see Cheong and Toh,2010).

To compare the urban spatial structure atdifferent years, we use the HITS data for1997, 2004, 2008 and 2012 and these contain48,881, 51,000, 76,923 and 75,646 recordsafter initial data processing. The data varyin terms of the way they are classified byactivity types for each year, as we show inTable 1, and thus to get a unified base classi-fication for the different years, an aggrega-tion was conducted resulting in a total ofnine aggregated activity categories. The totalnumber of trips for each aggregated activityis given in Table 2. With these available datasets, we first show the relationships betweendiversity, density and resulting centralityindices. Subsequently, we examine changesin the spatial structure over the differentyears and compare them with the officialurban plan.

Density, diversity and centrality

The values of density, diversity and central-ity for the year 2008 are shown in Figure 4.As indicated, there are some locations withhighly opposed density and diversity pat-terns. An example is the area around JurongWest, which is mostly occupied by residen-tial blocks and some schools. Consequently,

Zhong et al. 9



Jurong West is characterised by high densityvalues but low diversity values, resulting inrelatively low CI-values after the spatial con-volution. More examples are provided inFigure 5, showing the association betweendensity and diversity for each grid cell.Though the linear correlation between thetwo dimensions is very high (r & 0:5, seeTable 3), there are some clear exceptionsfrom this general trend. For instance, theselected grid cells in Figure 5 correspond toareas in the northeast of Singapore (theHougang area) which has comparativelyhigh density but a lower diversity of humanactivities. Similar to the case of JurongWest, residential buildings dominate the

land-use in that area, so that the spatial con-volution reduces the CI-values into lowerlevel bins as shown in the histograms inFigure 5. Note that the development path inthis area is also characterised by an increaseof the centrality values between 1997 and2004, followed by a decrease between 2004and 2008, as we will show below in Figure 6.Changes in these activity patterns can beattributed to a continuous development ofnew neighbourhoods in the area in the1990s, but the opening of a rapid transit linein the 2000s led to a reduction of externalvisitors, thus reducing the areas centrality. Itis worth noting that in order to assess theinfluence of the smoothing operation

Table 1. Aggregation of the different HITS activity categories for each year.

Aggregatedcategories

Original HITS categories for each year

1997 2004 2008 2012

1 Going home Go home Return home Household activities(household chores,personal care, rest)

2 Going to school Go to school Education Education3 Going to

workplaceGo to workplace Go to work Working for paid

employment4 Part of work Part of work

(travelling onbusiness)

Work-related business Work-related tripWork-related(meetings, sales etc.)

5 Shopping Shopping Shopping Shopping6 Eating Eating Meal/eating break Dining, refreshment7 Social Social Social visit/gathering/

religionReligious relatedmattersEntertainment – social

8 Recreation Recreation Recreation RecreationEntertainmentSports/exercise

9 Others For some otherreason

Others Others

Serve passenger Serve passenger(e.g.: pick up/dropoff passenger)

To drop off/pick-upsomeone

Pick up drop offprofessional driver

Personalbusiness

Personal business(e.g.: visit doctor,bank)

Personal errand/task(pay bill/banking)

Other personalbusiness

Medical/dental (self) Medical visit (self)To accompanysomeone

Accompanyingsomeone

10 Urban Studies



(equation (7)), we additionally calculatedcentrality values without applying this filter.We found that the resulting values revealqualitatively similar trends to those reportedabove.

Singapore’s polycentric urbantransformation

The statistical and spatial distributions ofcentres are compared for the different yearsfrom three perspectives: (1) in terms of theoverall value of centrality which reflects onhow Singapore has developed in general, (2)in terms of the balance of the spatial distribu-tion, that is, where and how are the locationsof high centrality located, and (3) in terms of‘anomalous’ developments, that is, any localdevelopments which fly against the generaltrends. A histogram indicating the number oflocations with a given CI-value is given inFigure 7 while the corresponding geographi-cal mapping is provided in Figure 6. A com-parison of further attributes of Singapore’sspatial structure is given in Table 3.

(1) The overall value of centrality. During theobservation period of this study the averagecentrality has increased substantially (seeTable 3), suggesting that people engage in

more diverse activities that require trips tomore diverse locations. A possible reasonbehind this trend could be the fast economicdevelopment that created many new com-mercial, entertainment and social activityplaces. This change can also be capturedfrom the geographical distributions shown inFigure 6, suggesting that areas with mediumcentrality values (0.1 \ CI \ 0.3) havebecome more dispersed.

At the same time, changes during differ-ent periods of the development can beobserved. The number of grid cells with highCI-values (CI . 0.3) has substantiallyincreased as Figure 7 and Table 3 reveal,indicating a significant increase in the num-ber of central hubs between 1997 and 2004.The histogram in Figure 7 also shows evi-dence of a high heterogeneity in the loca-tions with respect to their centrality. Simplyput, most locations are visited by just a fewpeople and for similar reasons, that is manyplaces have a lesser number of functions andfewer interactions while a few central ‘hubs’attract a huge part of Singapore’s popula-tion undertaking many different activitiesfor many different reasons.

(2) Balance of the distribution. To characterisethe spatial distribution of urban activity

Table 2. Number of trips broken down into the aggregated categories for each year.

Categories Year

1997 2004 2008 2012

1 21,100 23,543 34,314 35,4292 3177 7498 9757 86503 8407 10,425 18,310 18,2934 1166 736 1453 15465 3511 2372 2239 32266 2966 830 1634 19887 1768 1115 2108 5178 1212 267 767 4909 5574 4123 6341 5507Valid records in total 48,881 50,909 76,923 75,646Original records in total 52,801 60,917 88,601 85,880

Zhong et al. 11



Figure 3. The case study area. (a) The concept plan of 1991 redrawn from an image created by Field(1999). (b) The survey data: activity locations are arrival locations of trips in HITS 2008. Note: The areaswhich barely have any activity locations are mainly open space, port, reserve sites, special use areas, andwater bodies according to the 2008 Master Plan.

12 Urban Studies



centres we first delineate clusters of adjacentcells that have the same minimum centralityvalue. As indicated in Table 3, the numberof these clusters also increased during theperiod between 1997 and 2012. Inspectingthe geographic mapping in Figure 6, we cansee quite clearly how the location and clus-tering of high CI cells has changed between1997 and 2012. For instance, the threeregions Jurong (in the west), Tampines (inthe east), Woodlands (in the north) and TaoPayoh (in the middle) have gradually growninto intra-urban centres with similarly highcentrality values, which correspond well toSingapore’s official concept plan as shownin Figure 3. Comparing the centrality mapin 2004 with 2008 shows that the CI-valuesin the Hougang area have decreased, whilethose of the centres in the western part ofSingapore have slightly increased. The result

generated from Singapore’s latest travel sur-vey data shows an even more balanced dis-tribution where even the relative centralityvalue in downtown core area has decreased.This suggests a development trend towardsmore evenly distributed centres in the entirespace of the city-state. The standard devia-tions of both density and diversity increasedin 2004 and decreased in 2008 and 2012,which indicates that the distribution of activ-ity is volatile over the period influenced bythe fast development in Singapore. Forinstance, the western region of Singapore –the Jurong East area – was mainly occupiedby industry, and the blueprint to transformthe Jurong Lake district into unique lakesidedestinations for business and leisure hasbeen implemented only in recent years.

However, our study also reveals otheremerging sub-centres from the results of the

Figure 4. (a) Density of urban activities in 2008. (b) Diversity of urban activities in 2008. (c) Centralityvalues in 2008. (d) Differences between centrality and density to assess the functionality of convolution.The axes represent the geographical coordinate system of Singapore. The rectangles in (a) and (c) highlightthe area of Jurong West.

Zhong et al. 13



2008 analysis, such as the ones in Yishunand Bedok have higher relative CI-valuesthan one would anticipate from the officialplans. To some extent, this may show evi-dence of bottom-up and thus hard-to-predictchanges that are intrinsic to shaping urbanspatial structure going well beyond classictop-down planning.

(3) Anomalous developments. To further quan-tify the spatial clustering of locations withhigh CI-values, we have calculated the globalspatial autocorrelation using Moran’s Iindex (Moran, 1950). As reported in Table 3,this value increases throughout the analysisyears, suggesting first that there is a strongspatial clustering of high centrality areas andsecond, an increasing difference of centralitybetween distinct areas. This second point isin line with an increasing standard deviation

of the overall centrality values (see Table 3).Thereby the numbers of cells that form thehighest centrality indices in the southern partof Singapore (the traditional CBD area)have been increasing (see Figure 6). TheCBD has been growing (notwithstanding adecrease in the centrality values of somelocations between 2008 and 2012), since thedevelopment of this area has had high priori-ties in early 21st century urban plans thathave promoted its economic development.Retail and entertainment centres are agglom-erated and closely linked to form a big com-mercial belt, expanding the highly popularshopping area around Orchard Road. Inaddition, this growth is influenced by therecent development of the public transit sys-tem. The transit system was built to substan-tially shorten the travel time from almost allover the island to the CBD, which, in turn,may foster increased travel distances.

Table 3. Attributes describing the spatial structure of Singapore.

Attributes Year

1997 2004 2008 2102

Avg. centrality 0.025 0.040 0.047 0.049Max. centrality 0.5435 0.7083 0.8378 0.700Standard deviation centrality 0.057 0.091 0.096 0.097Moran I index 0.74 0.75 0.78 0.76Max. density 0.0185 0.0085 0.0091 0.0031Standard deviation density 0.0008 0.0007 0.0006 0.0004Moran I index 0.73 0.76 0.76 0.78Avg. diversity 0.29 0.21 0.28 0.09Max. diversity 2.03 2.13 1.97 1.91Standard deviation diversity 0.52 0.42 0.48 0.29Moran I index 0.86 0.84 0.86 0.89Density & diversity correlation coefficients 0.57 0.69 0.63 0.69Number of grid cells with centrality . 0.3 23 94 104 125Number of centres . 0.3 5 10 10 14Number of grid cells with centrality . 0.7 0 1 6 0Number of centres . 0.7 0 1 1 0Avg. travel distance (m)(point to point distance) 6679 6025. 7198 NAAvg. in vehicle time (walking excluded) NA 20.52 21.28 NAAvg. travel distance for working (m) NA 8233 9143 NAAvg. travel distance for shopping (m) NA 4790 6044 NAAvg. travel distance to school (m) NA 3697 4933 NAAvg. travel distance for eating (m) NA 3829 5135 NA

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The growing importance of the CBD isconsistent with a recent study of Zhonget al. (2014) and can be seen as a contra-development against the general trendtowards a more polycentric urban structurethrough the decentralisation of activities inSingapore. The increase in the average traveldistance and only small changes in the aver-age travel time further support this outcome(see Table 3).

Conclusions

Quantitative measures for the spatial struc-ture of cities have the potential to greatlycontribute to a better understanding andmanagement of the processes that determineurban evolution and transformation. Byrethinking recent debates about polycentri-city and motivated by the growing availabil-ity of human activity data, this paper hasproposed a new measure of locationalcentrality. In contrast to existing measuresthat focus on either the density or diversity

of human activities, this simple quantitativeindex integrates both aspects of centrality.Centres can thus be identified as spatial clus-ters of locations with high centrality,allowing us to assess how the spatial distri-bution of centres evolves over different yearsand tracing various processes of urban trans-formation. Taking Singapore as a case studyarea, we made use of extensive longitudinaltravel survey data to demonstrate the effec-tiveness of the proposed measurementmethod, revealing a clear urban transforma-tion towards polycentricity. Together ourquantitative approach can be used as a start-ing point for more explicitly interpreting andrepresenting urban change, being crucial fordata-informed urban planning applications.

Further research is needed to advance thecurrent method and to fully explore poten-tial applications. First, the proposed indicesare not limited to travel survey data, as theycan be derived from other human mobilitydata with a higher spatiotemporal resolu-tion, such as mobile phone records or smart

Figure 5. Density, diversity and centrality patterns. The density and diversity values are shown for theyear 2004 (top left). We selected a number of cells with high density but low diversity values, mostlycorresponding to areas in the northeast of Singapore (which we show in the map to the right). Thehistograms of density, diversity and centrality values of all areas are also given (bottom left). We highlightedthe bins to which the selected values belong.

Zhong et al. 15



Fig

ure

6.

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nera

ted

from

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avel

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eyfo

rth

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ars

1997

,200

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16 Urban Studies



card transit data. The growing availability ofsuch data may overcome possible limitationscaused by the scarcity or different nature ofthe data. Furthermore, the density anddiversity functions we proposed are rathersimple and can be replaced by more compre-hensive ones that include, for instance,multi-purpose trips. Beyond these two basicfunctions, other dimensions, for instance,economic factors could also be added to theconvolution. Finally, incorporating localexpert knowledge into our proposed frame-work may help to achieve a better monitor-ing and explanation of the spatial structureof urban phenomena.

Acknowledgements

The authors would like to acknowledge the valu-able comments of the anonymous reviewers. Thisresearch cooperation was established at theSingapore-ETH Centre (SEC) and the Singapore-MIT Alliance for Research and Technology(SMART), and is co-funded by the SingaporeNational Research Foundation (NRF), ETHZurich and the European Research Council under249393-ERC-2009-AdG. The authors thank theSingapore Land Transport Authority and UrbanRedevelopment Authority for supporting thisresearch and providing the required data.

Funding

This research was funded by the EuropeanResearch Council under grant number 249393-ERC-2009-AdG.

Notes

1. Singapore National Statistics http://www.singstat.gov.sg/ (accessed 26 May 2014).

2. Singapore Concept Plan https://www.ura.gov.sg/uol/concept-plan.aspx?p1=View-Concept-Plan&p2=Concept-Plan1991 (accessed 26May 2014).

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