Discovering and Characterizing Mobility Patterns in Urban Spaces: A Study of Manhattan Taxi Data

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by  Lisette Espín-Noboa

Discovering and Characterizing Mobility Patterns in
Urban Spaces: A Study of Manhattan Taxi Data∗
Lisette Espín-Noboa Florian Lemmerich
GESIS-LeibnizInstitutefortheSocialSciences GESIS-LeibnizInstitutefortheSocialSciences
[email protected] [email protected]
Philipp Singer Markus Strohmaier
GESIS-LeibnizInstitutefortheSocialSciences GESIS-LeibnizInstitutefortheSocialSciences
[email protected] &UniversityofKoblenz-Landau
[email protected]
6
1
0
2 ABSTRACT tend to ignore several aspects of human mobility such as time,
weather,raceofpeopleormeansoftransportation. Towardsthat
b Nowadays, humanmovementinurbanspacescanbetraceddig-
e itallyinmanycases. Itcanbeobservedthatmovementpatterns end,weproposetodiscoverandcharacterizemobilitypatternsin
F are not constant, but vary across time and space. In this work, humanbehaviorinurbanspace.
9 wecharacterizesuchspatio-temporalpatternswithaninnovative Material and approach. In this work, we expand existing re-
combinationoftwoseparateapproachesthathavebeenutilizedfor search[3,23]onstudyinghumanmobilitywithacasestudyusing
] studyinghumanmobilityinthepast.First,byusingnon-negative taxidataofManhattan. Foridentifyingbehavioraldifferencesin
I tensorfactorization(NTF),weareabletoclusterhumanbehavior termsoftimeandspace,previousresearch[29,36]hassuggested
S
basedonspatio-temporaldimensions. Second,forunderstanding toutilizetensordecomposition[5,14]. However,interpretingre-
.
s theseclusters,weproposetouseHypTrails,aBayesianapproach sultsfromtensordecompositioncanbedifficultandhasbeenbased
c forexpressingandcomparinghypothesesabouthumantrails. To onpersonalintuitionsinpreviousapproaches. Ontheotherhand,
[
formalizehypothesesweutilizedatathatispubliclyavailableon recentresearch[1,33]proposedmethodsthatallowtounderstand
2 theWeb,namelyFoursquaredataandcensusdataprovidedbyan humansequencesbycomparinghypothesesabouttheproduction
v opendataplatform.Byapplyingthiscombinationofapproachesto ofmobilitytrailsatinterest. Yet, thisapproachislimitedinthe
4 taxidatainManhattan,wecandiscoverandcharacterizedifferent sensethatitcanonlyexplainglobalbehaviorwithoutbeingableto
7 patternsinhumanmobilitythatcannotbeidentifiedinacollective providemoredetailedinsights.Tocircumventtheselimitations,we
2 analysis. Asoneexample,wecanfindagroupoftaxiridesthat proposeauniqueandoriginalcombinationoftensordecomposition
5 endatlocationswithahighnumberofpartyvenues(accordingto andHypTrailstounderstandhumanbehavioronaspatio-temporal
0 Foursquare)onweekendnights. Overall,ourworkdemonstrates level. Inparticular,wefirstutilizenon-negativetensorfactoriza-
. thathumanmobilityisnotone-dimensionalbutrathercontainsdif- tion(NTF)[5,14]forautomaticallyidentifyingclustersofmobility
1
ferentfacetsbothintimeandspacewhichweexplainbyutilizing behavior.Second,forcharacterizingtheseclusters,weutilizeHyp-
0
6 onlinedata.Thefindingsofthispaperargueforamorefine-grained Trails [33]—a Bayesian approach for expressing and comparing
1 analysisofhumanmobilityinordertomakemoreinformeddeci- hypotheses,i.e.,transitionalassumptions,abouthumantrails.
: sionsfore.g.,enhancingurbanstructures,tailoredtrafficcontrol Findingsandcontributions.Insummary,ourmaincontributions
v
andlocation-basedrecommendersystems. arethree-fold:First,wepresentaninnovativecombinationoftwo
i
X Keywords:HumanMobility;TensorFactorization;HypTrails methodologies,i.e.,non-negativetensorfactorizationandHypTrails,
inordertocharacterizeheterogeneoushumanmobilitybehavior.
r
a 1. INTRODUCTION Second, we incorporate existing human mobility patterns into a
Humanmobilitycanbestudiedfromseveralperspectivesutilizing hypothesis-based schema built upon human beliefs. Third, we
differentkindsofdatafromtheonline(e.g.,TwitterorFoursquare) demonstratethebenefitsofonlinedatainourattempttoexplain
andtheoffline(e.g.,taxiridesorbiketrips)world. Alargebody humanbehavioronaspatio-temporallevel. Asoneexample,we
ofworkhasfocusedonidentifyinggeneralmechanismsthatguide candiscoveragroupoftaxiridesthathavedrop-offlocationswith
and explain human mobility behavior on an individual [13, 34] ahighnumberofpartyvenues(accordingtoFoursquare)onweek-
or collective level [1, 25]. For example, previous research has endnights. Resultsofthisstudycouldimprovee.g.,planningof
shownthathumanmobilityishighlypredictable[34]andshows futureeventsorreconstructions,trafficcontrol,location-basedrec-
temporal and spatial regularity [13]. At the same time, spatio- ommendersystemstoenablepublictransportationcompaniesto
temporalheterogeneityexists,as,forexample,discussedinprevious adapttheircapacitiesbasedonthedemandatcertainhoursorareas.
studies[3,23].Forinstance,dailyroutinessuchasgoingfromhome
towork(space)inthemorning(time)andfromworktohomein 2. DATASETS
theeveningcanbeobserved. Thisarguesforamorefine-grained
WefocusonManhattan,oneofthemostdenselypopulatedareas
analysis,thatgoesbeyondtheuniversal(mobility)patternswhich
intheworld,sinceithasahugeamountofgovernmentalandprivate
datapubliclyavailableontheWeb.Indetail,westudytaxiridedata
∗
PleasecitetheWWW’16versionofthispaper. inthiswork.Whilethisdatarepresentsaprominentrepresentative
ofhumanmobility,ourmethodologypresentedinthispapercanbe Table 1: Centroids of places of interest: This table lists geo-
appliedtootherkindsofmobilitydata.Werepresenthumanmobility coordinatesandcorrespondingtractsofthegeographicalcen-
asusertrailswhichcanbeseenassingletransitionsbetweenpick- terofManhattan,theFlatironbuildingandTimesSquare.
upanddrop-offlocationsoftaxirides.Inordertoconstructarichset Place lat,lon TractID
ofhypothesesforexplainingthemovementofusers,weadditionally Manhattan(geo-center) 40.79090,-73.96640 018100
retrievedinformationonlocalvenues(e.g.,parks,schools,churches) FlatironBuilding 40.74111,-73.98972 005600
fromFoursquareandpubliccensusdata(i.e.,demographics,land- TimesSquare 40.75773,-73.98570 011900
useandsocio-economics). Next, weshortlyexplainthevarious
datasetsingreaterdetail.
Taxirides. Weusepubliclyavailabledata1of173,179,759NYC wesuggesttousenon-negativetensorfactorization(NTF)[5]for
Taxiridesin2013. Itconsistsofanonymizedrecordsregistering automaticallyclusteringhumanmobilitybehavior. Researchhas
whenandwhereataxiridestartedandendedandvariousfeatures shown thatNTFcandetect latentfeaturesofhuman mobility in
suchasthenumberofpassengersorthetotalfareofthetrip.Fromall differentdimensionssuchasspaceandtime,cf.forexample[36].
records,weremovedtaxiridesoutsidethearea(polygon)ofManhat- Second,forintuitivelycharacterizetheseclusters,weutilizeHyp-
tanandsomeinconsistenciessuchasrecordswithtrip_distance≤0, Trails [33]—a Bayesian approach for expressing and comparing
trip_time_in_secs≤0andpassenger_count≤0;ourfinaldataset hypothesesabouthumantrails. Weoutlineinthefollowingboth
consistsof143,064,684rides. Adescriptionofallattributesand methodologicalcomponentsofthiswork,butrefertotheoriginal
datatypescanbefoundintheTLCTaxiData-APIDocumentation2. publicationsfordetails.
Censusdata. Insteadofworkingdirectlywithlongitudeandlati- Clusteringmobilitypatterns. Forclusteringthedata,weutilize
tudedata,ourmethodologicalapproach(seeSection3)operateson NTFwhichdecomposesagivenn-waytensorXintoncomponents
adiscretetractstatespace.Tractsaresmallsubdivisionsofacounty (matrices) that approximate the original tensor when multiplied
thatprovideastablesetofgeographicunitsforthepresentationof with each other. Each matrix contains information on r factors
statisticaldata3. Weextractedthespecificationsofall288tracts (clusters).Inthispaper,wedefineathree-waytensoroftaxirides
inManhattanfromtheNYCPlanningportal4asashapefilefrom whose dimensions capture human transitions from one place to
the 2010 census. Having this information, we mapped the GPS anotheratacertaintime: pick-uptract,drop-offtractandpickup
coordinatesofalltaxiridestooneofthe288tracts. Besidesthe time(hourofweek)respectively;thus,clusteringintermsofboth
areaandlocationoftracts,wequeriedtheNYCOpenData5andthe spaceandtime.Eachelementofeverycomponentdeterminesthe
AmericanFactFinder6databasesforaccessingrelevantonlinedata scaleofmobilityflow(weight)withrespecttothecorresponding
suchascensusandland-use.Moreover,wecalculatedtheoverlap factor. Inotherwords,thehighertheweight,themoredominant
betweenlanduse-typessuchasresidentialandcommercialzones thatinstanceisinthatcluster.Similartootherclusteringmethods,
andeachtracttoobtaininformationonatractlevel. definingthenumberofclustersisarbitrary. However,thereexist
Foursquarevenues. Accordingtopreviousworks,humanmobil- some guidelines to determine a good value of r, see e.g., [12].
itycanbeexplainedbythetransitionofvisitedplaces[29]orby Inthiswork,wearenotfocusedonfindingthemostappropriate
interveningopportunities[25,35]. Forstudyingtheseandsimilar numberofbehavioralcomponents,butbeingabletocharacterize
theories, we gathered information about physical places such as differentbehaviors,whichwillbedetailedinthefollowingsection.
churches,housesandparkssituatedinManhattanbyqueryingthe
Characterizingclusteredmobilitypatterns. Forcharacterizing
FoursquareSearchAPI7 toextractplacesineachtractfor10dif-
theclusteredhumanmobilitybehavior,weutilizeHypTrails[33],a
ferentcategories8(e.g.,Residence,WorkPlaceorNightlifeSpot).
Bayesianapproachforexpressingandcomparinghypothesesabout
Overall, we collected 153,694 unique places within Manhattan.
human trails. Technically, HypTrails models the data with first-
Sinceeveryvenueisdescribed(besidesothersattributes)byaGPS
orderMarkovchainmodelswherethestatespacecontainsall288
location,theyallweremappedtotheirrespectivetract.
tractsofManhattan. Fundamentally, hypothesesarerepresented
Centroids.Typically,popularplacesaremostlikelytobevisitedat asmatricesQexpressingbeliefsinMarkovtransitions;Section4
anytime.Forthisreason,weconsideredthreecandidateplacesas describesthehypothesesabouthumanmobilityusedinthiswork.
centroidstostudywhetherpeoplevisitthemornot.Table1,shows Elements qi,j indicate the belief in the corresponding transition
thegeographicalcoordinatesandrespectivetractsofthecenterof probability between states i and j; higher values refer to higher
Manhattan(approximatedasthegeographicalcenterofManhattan), belief.ThemainideaofHypTrailsistoincorporatethesehypotheses
theiconicFlatironbuildingandwell-knownTimesSquare. asDirichletpriorsintotheBayesianinferenceprocess.HypTrails
automatically elicits these priors from expressed hypotheses; an
3. METHODOLOGY additionalparameterk(weightingfactor)needstobeprovidedto
steer the overall belief in a hypothesis. For then comparing the
Thegoalofthisworkistodiscoverandcharacterizemobility
relativeplausibilityofhypotheses,HypTrailsutilizesthemarginal
patternsintaxidata,inordertobetterunderstandpeople’stravel
likelihood(evidence)oftheBayesianframeworkwhichdescribesthe
behaviorfromoneplacetoanotherwithinthecity.Tothatend,we
probabilityofahypothesisgiventhedata.Wecaninferthepartial
proposeaninnovativecombinationoftwomethodologies. First,
orderingbasedontheplausibilityofagivensetofhypothesesby
1 rankingtheirevidencesfromthelargesttothesmallestforaspecific
http://www.andresmh.com/nyctaxitrips/
2 valueofk.
https://dev.socrata.com/foundry/data.cityofnewyork.us/gkne-dk5s
3
https://www.census.gov/geo/reference/gtc/gtc_ct.html
4
http://www.nyc.gov/dcp
4. HYPOTHESES
5
https://nycopendata.socrata.com/
6http://factfinder.census.gov/faces/nav/jsf/pages/index.xhtml Inthissection,wedescribeourdifferenthypothesesatinterestthat
7https://developer.foursquare.com/docs/venues/search areusedtoexplaintheindividualclusterswithHypTrails.Theseare
8https://developer.foursquare.com/categorytree expressedashypothesismatricesQwheretheelementsqi,jcapturea
Table2:UniversalTheories:Listof10universaltheoriesonhumanmobility.FollowingtheMarkovchainassumption,indexesiand
jrefertostartandendstatesrespectively.Functionsdist(.,.),venues(.),andcheckins(.)denotethegeographicaldistancebetweentwo
states,allFoursquarevenuesinagivenstate,andthenumberofcheck-insinFoursquarefromagivenvenue,respectively.VectorsA
andBrepresentcategoricalinformationofthestartandendstate,respectively(e.g.,race,poverty,land-use).
# MobilityTheory Formulaforqi,j Description
Thenextlocationischosenrandomly,independentlyofthecurrent
1 Uniform 1
location.
2 InverseGeographicDistance 1 Thecloserthetargetlocation,themorelikelyitistobevisited,see[15].
dist(i,j)
Theprobabilityofvisitingaplace j isgivenbyatwo-dimensional
3 GaussianDistribution σ√12π e−dis2t(σi,2j)2 Garaouusnsdiatnhedipstlraicbeutii,otnhewcitlhossetrantodatrhdedleovciaattiioonniσ. ;itchaensmeitahlleerrbtehethσe
currentlocationorafixedlandmarkinthecity,see[1].
4 Density |(venues(j)| Peoplegetattractedbytheamountofvenuesatdestinationplace.
5 Popularity ∑V∈venues(j)checkins(V) Venueswithmorenumberofcheck-insattractmorepeople,see[26].
6 GravitationalMass venues(i).venues(j) Peoplegetattractedbytheproductofforcesfromthecurrentandclose
dist(i,j) targetlocations,see[42].
7 GravitationalTarget venues(j) Peoplegetattractedonlybyaforceinatargetlocationwhichisclose
dist(i,j) tothecurrentplace.Thisisavariantof(6)
8 RankDistance 1 Theprobabilityofmovingtoaplaceincreasesiftherearefewvenues
|{w:dist(i,w)<dist(i,j)}| waroundthecurrentlocation,see[25].
Thenumberofpersonsgoingagivendistanceisdirectlyproportionalto
9 InterveningOpportunities |{w1:dist(i,w1)=dist(i,j)}| thenumberofopportunitiesatthatdistanceandinverselyproportional
|{w2:dist(i,w2)<dist(i,j)}| tothenumberofinterveningopportunities,see[35].
10 CosineSimilarity A.B Measureshowsimilarthecurrentandnextlocationare,see[37].
||A||||B||
beliefinpeopletransitioningtostate(tract) jwhencurrentlylocated rides—which(inthiswork)donotcontributeonmobility(i.e.,taxi
atstate(tract)i(seeSection3). ridesthatstartandendinthesametract).
Ourhypothesesaremostlybasedonexistingtheories.Inthisre-
Distance-basedhypotheses.Basedonthegeographicdistance[15],
gard,themostprevailinghumanmobilitymodelisthegravitational
wecanconstructverysimpleandintuitivehypotheses:theproximity
law[42],whichexplainsmobilitybyanattractionforcebetween
hypothesisandthecentroidhypothesis.Theproximityhypothesis
twoplacesthatisdeterminedbysomeweightforeachplace(e.g.,
assumesthatplacesnearbythecurrentlocationaremorelikelyto
densityofvenues/pointsofinterest)andtheinvertedshortestdis-
bevisitednext,thecentroidhypothesissuggeststhatlocationsnear
tancebetweenthem.However,duetosomelimitationsfoundinthis
tothecitycenter(specifiedbyfixedgeographiccoordinates,see
model[32],manyothersolutionshaveemergedtocircumventsuch
Section2)aremorelikelyforthenextstop. Accordingtothese
problems.Forexample,therankmodel[25]hasbeenproposedas
hypotheses, the location of the next visited place follows a two-
avariationoftheradiationmodel,whichindicatesthatthenumber
dimensionalGaussiandistributionthatiscenteredatthecurrent
ofpeopletravelingtoagivenlocationisinverselyproportionalto
locationorthecitycenterrespectively,see[1]foramoredetailed
thenumberofplacessurroundingthesourcelocation.Similarly,the
description.Fortheparametrizationofthedistribution,weincluded
socalledinterveningopportunities[35],additionallyincludesthe
severalvariationsofthehypotheseswithdifferentvaluesforthe
numberofopportunitiesatagivendistance.Cosinesimilaritycan
standarddeviationσ,i.e.,σ∈{0.01,0.5,1.0,2.0,3.0,4.0,5.0}km.
alsobeusedundertheassumptionthatpeopleprefertovisitplaces
Foursquarehypotheses.Tobuildmoreinformedhypotheses,we
whicharesimilar(accordingtosomemetric)tothedepartureplace.
leverageFoursquarevenuesbymeasuringthedensityofaplace,
Table2summarizes10universaltheoriesconsideredinthiswork.
which consists of counting the number of all venues (regardless
Forpracticalapplicationsthesetheoriesrequireadditionaldata,
oftheircategories)inagivenlocation. Similarly,thenumberof
e.g.,todeterminetheweightofplacesforthegravitationallaw.In
check-inscanbeusedtomeasurethepopularityofagivenplace.
our attempt to explain mobility we also utilize online data from
Thesecanbecombinedwiththegeographicaldistanceinvarious
Foursquarevenuesandcensusdata.Wecategorizeourhypotheses
intothreetypes:Distance-based,FoursquareandCensushypothe- waysaccordingtomobilitytheories,seetheoriesNo.6,7,8and9in
Table2.Additionally,wegroupplacesaccordingtotheircategory
ses,seeTable3.Additionally,weusetheuniformhypothesisasa
(e.g.,residence,shoporchurch)basedonvenuesofasingletype.
baselinetoexpressthebeliefthatalltractsareequallylikelyforthe
nextstopofataxi.Forallhypotheses,wesetthediagonalofQto0 Inotherwords,weusecategoriesasfiltersoftheavailablevenues.
toavoidself-looptransitions—accountingforonly1.5%ofalltaxi Thus,everyFoursquarecategoryinducesasubsetofallvenuesper
state(i.e.,tract). Table3showsall10categoriesincludedinthis
Table3: Tractproperties. Thesethreecategoriescontainalltractindicators,i.e.,statisticsabouttracts,usedincombinationwith
universaltheoriestoconstructhypotheses. Forinstance, thehypothesischurchexpressesthattheprobabilityofvisitingacertain
locationisproportionaltoitsnumberofchurches(usingforexamplethedensitytheory).
Category Propertiespertract
Distance-based Fixedpointsofinterest:GeographicalCenter,FlatironBuilding,TimesSquare.
Numberofvenues:Arts&Entertainment,Education(i.e.,colleges,universities,elementaryschoolsandhighschools),
Food, Nightlife Spot, Outdoors & Recreation, Work (i.e., auditoriums, buildings, convention centers, event space,
Foursquare
factories,governmentbuildings,libraries,medicalcenters,militarybase,non-profit,office,postoffice,prison,radio
station,recruitingagency,TVstation,andwarehouse),Residence,Shop&Service,Travel&Transport,andChurch.
Populationsize,andTractarea.Percentageof:Whitepeople,Blackpeople,Peopleinlaborforce,Unemployedpeople,
Peoplebelowpovertylevel,Peopleabovepovertylevel.Numberofplaces:Libraries,ArtGalleries,Theaters,Museums,
Census
WiFi Hotspots, and Places of Interest. Moreover, the occupied area of: Residential Zoning, Commercial Zoning,
ManufacturingZoning,Parkproperties,HistoricDistrictsandEmpowerzones.
study. Toavoidanabundantamountofhypotheses,weonlyuse 5.2 NTF:Mobilitypatterns
the gravitational target theory in combination with the category- Sinceourdatatensorhasthreedimensions,thedecomposition
basedhypotheses. Furthermore, weconstructasimilarity-based returnedthreedifferentcomponentswhichdeterminethescaleof
hypothesisthatsuggeststhattransitionsaremorelikelybetween mobilityflowineachdimensionforeverycluster: time(hourof
twostatesthathaveasimilarcategorydistributionofvenuesbased week) and space (departure and arrival tracts). Thus, individual
onCosinesimilarity,seeTable2. clustersrepresentgroupsoftaxiridesindifferentplacesatdifferent
Census hypotheses. Similar to the Foursquare hypotheses, the periodsoftimeinaweekday-hourscale.
Census hypotheses add relevant information to every state (i.e., The time component is shown in Figure 1a, whereas location
tract).Thisinformationondemographics(e.g.,%ofwhitepeople), componentsforpickups(departures)anddrop-offs(arrivals)are
land-use(e.g., residentialzoning)orsocio-economics(e.g., #of shownontheright-handsideofFigure1.Duetospacelimitations
peopleabovepovertylevel)canbeusedinsteadofthenumberof we show only the first three clusters. From Figure 1a, it can be
venues(i.e.,density)ofagivenstate.Table3showsall20indicators observedthatallclustersshowstrongdailyregularities,whichcan
usedtoformulatethiskindofhypotheses.Similaritymeasures(i.e., beassumedasdailyroutinesinhumanmobilitybehavior.Clusters
cosinesimilarity)wereobtainedunderthreedifferentcategories: C1,C2,C4,C5andC7captureallbehaviorsonworkdays(almostall
RaceGroup(i.e., white, black, americanindian, asian, hawaiian peaksarewithinthefirstfivedaysoftheweek),whereasclusterC3is
andotherpacificislander,otherrace,tworaces),PovertyLevel(i.e., stronglydominatedbyweekends,speciallybyFridayandSaturday
below,above)andEmploymentstatus(i.e.,employed,unemployed, nights. ClusterC6 on the other hand, shows a more periodical
inlaborforce). behavioracrosstheentireweek,howeveritspeaksarearound6pm
Overallwedefined70hypotheses:(a)1uniform,(b)29distance- fromMondaytoSaturdayand2pmonSaturdaysandSundays.
based(i.e.,geographicaldistance,proximityand3centroidstimes ThelocationcomponentsshownfromFigure1btoFigure1g,
7; for each value of σ), (c) 17 from Foursquare (i.e., all venues togetherwiththeirrespectivetimeperiods,provideusinitialcontext
integratedinformulas4to9fromTable2,gravitationaltargetfor aboutwhenandwherepeoplemovewithinthecity. Forinstance,
eachFoursquarecategoryand1similarity),and(d)23fromCensus clusterC1representsmorningtaxiridesaround9am(seeFig.1a)
data(i.e.,20fromthegravitationaltargetwitheachcensusindicator whichgotothesouth-eastofManhattan(seeFig.1e).ClusterC2
and3fromsimilarities.). ontheotherhand,concentratesitstaxisridesintheeveningaround
6pmnearCentralPark(seeFig.1f).Finally,clusterC3includesall
5. EXPERIMENTS taxiridesonFridayandSaturdayaround1aminthelowerpartof
Manhattan(seeFig.1g).
Thissectionreportsonexperimentalresultsobtainedbyapplying
Thefollowingsectionpresentscharacterizationsforsuchbehav-
thepresentedmethodstotheManhattantaxiridesdataset.
iorsbycomparingalistof70hypothesesusingHypTrails.
5.1 Configuration
5.3 HypTrails: Rankingofhypotheses
AsdescribedinSection3,westartedbyusingNTFinorderto
identifydifferentclustersinthetaxidata.Weworkedwithathree- SinceNTFonlyassignsaweighttoeveryinstanceofeachfactor
waytensorwhosedimensionsrepresentthepickuphourofweek, (i.e.,doesnotexplicitlypartitionthetransitioninput),wefirstneed
thetractofthepickupofthetaxirideandthetractofthedrop-off toidentifyalltransitionsforeachclusterinordertorunHypTrails.
ofthetaxiride.Forthehourofweek,thefirststatecorrespondsto Generally[29,36],interpretingclustersreturnedbyNTFrequires
thetimefrom12:00a.m.to12:59a.m.onMonday,thelastofthe toextractthetop-Nmostrepresentativestatesfromeachfactorto
168statestothetimefrom11:00p.m.to11:59p.m.onSunday.We determinetheinstancesthatarepartofeverycluster.Inoursetting,
didnotincludetimeofthedrop-offasanextradimensionbecause weextractedthetop-10pickupweekday-hoursanddrop-offtracts,
mostoftherideslastlessthananhour.Sincethereare288different andqueryalltaxiridesfulfillingtheseconditions.Notethatwedid
tracts,thetensorforthedecompositionhassize168×288×288. notincludethetoppickuptracts,becauseweareinterestedonplaces
Afterexperimentingwithdifferentparameters,wesetthenumber wherepeoplegoto,ratherthanplaceswheretheycomefrom.We
ofclusterstor=7toclusterthedataintosevendifferentgroups,as thenappliedHypTrailsandcomputedtherankingsfortheweighting
thisnumbersubjectivelybestcapturedallbehavioralcomponents. factork=10—seeSection6foradiscussion.
(b)DeparturesC1 (c)DeparturesC2 (d)DeparturesC3
(a)Temporaldistributionofclusters (e)ArrivalsC1 (f)ArrivalsC2 (g)ArrivalsC3
Figure1:Spatio-Temporalbehaviorobtainedbytensorfactorization.ThisfigureillustratestheresultsobtainedwhenapplyingNTF
on a three-way tensor. (a) Each row represents a behavioral component respect to pickup time (hour of week). Maps shown at
therightofthisfigureshowlowandmidtownManhattan,thecolorofeachtractdetermineshowrepresentativethatlocationisin
thatcluster;thedarker,themoredominant. (b,e)clusterC1standsfortaxisridesat9amaroundthesouth-eastofManhattan;(c,f)
ClusterC2containsalleveningshorttaxiridesat6pmaroundthecenterofManhattan;and(d,g)ClusterC3representsallweekend
nighttaxiridesaroundthelowerandmiddlepartofManhattan.
Exemplaryresultsofthecharacterizationstepforahandselected Peopleinthisclusterusuallygotonearbytractscontainingvery
subsetofhypothesesaredisplayedinTable4. Itshowsforeach popularplacessuchasnightlifespotsandrestaurants. Below,we
hypothesistherespectiverankinthecluster;lowernumbersimply discussthecharacteristicpropertiesofallclusterssummarizedby
a higher rank and therefore a better explanation. We show the thetypesofhypotheses.
resultsoftheFoursquareandCensushypothesesonlyappliedtothe
Distance-based. AsmentionedinSection2,thesehypothesesre-
gravitationaltargetformula(seeSection4).Gravitationallaws(i.e.,
quire the standard deviation (σ) of a two-dimensional Gaussian
gravitationaltargetandgravitationalmass)inallcasesperformthe
distribution. InTable4,weshowthebestresultforparametrized
sameduetothenormalizationsappliedintheHypTrailsapproach.
hypothesesandtheirrespectivevalueofσ inparenthesis. Inthe
Thus,fromnowonwardstheywillbereferredtoasgravitational.
overalldataaswellasclustersC2andC3,taxiridesaremorelikely
Thus,forinstance,thehypothesisGravitational(%Whitepeople)
tovisitproximateplacesinaradioof3km,0.5kmand1kmrespec-
expresses a belief in people going to nearby tracts with a high
tively.ClustersC1,C4,C6andC7showpreferenceonvisitingthe
percentage of white people living there. In the column Overall
surroundingsofTimesSquareinaradioof0.5km,0.5km,0.01Km
ofTable4,weshowtherankingofhypothesesevaluatedoverthe
and0.01kmrespectively. Finally,taxiridesinclusterC5tendto
wholedataset,tocomparewiththeresultsobtainedfortheindividual
visitplacesneartheFlatironbuildinginaradioof0.5km.
clusters. Theuniformhypothesisisabaselinewhichallowsusto
verifywhetherahypothesiscanbeagoodexplanationofhuman Foursquare.Taxiridesintheoveralldatasetaremorelikelytovisit
mobilityornot.Greencellsinthetableindicatethatahypothesis verydenseareascontainingworkplaces, restaurants, discosand
performedbetterthantheuniformhypothesisinthatcluster. bars.Similarly,clustersC1,C4andC5whichhappentobemorning
Tocharacterizethedifferentpatternsinhumanmobility(i.e.,the ridesaround7−9am,prefertogototractscontainingworkplaces
clusterresultsoftheNTFstep),weinspecttheobtainedrankings suchasbuildingsandoffices. TaxiridesinclusterC6gototracts
forthedifferentclusters. Inparticular,weareinterestedinwhich dominatedbyrecreationplacessuchasparksandotheroutdoors
hypothesesperformexceptionallywell(i.e.,haveatoprankindi- intheeveningsaround6pm.ClusterC3canbebestcharacterized
catedbyasmallnumber)intheclusterbothonanabsolutescale bythepartyhypothesiswhichmeansthattaxiridestendtovisit
andincomparisontotherankingobtainedfromtheoveralldataset. tractscontainingnightlifespots(onweekendnights—inferredwith
Forexample,considerClusterC3thatcapturestimeframesatthe NTF).Likewise,inclusterC7peopletendtovisittractscontaining
weekendnights.Forthiscluster,wecanobserveveryhighranksfor popularplacessuchasrestaurantsandnightlifespots.Notethatall
thegravitationalhypothesesParty,Popularity(check-ins),Foodand hypothesesinthisgroupperformbetterthantheuniformhypothesis
Recreation. inallclusters,demonstratingtheoverallhighexplanatorypowerof
Insummary,clustersC1,C2andC3(showninFigure1)canbe suchdatasourceswithrespecttohumanmobility.
characterizedasfollows.ClusterC1predominantlyrepresentstaxi
ridesaround9amonworkdays.Peopleinthisclusterprefertogo Census. From the overall data, we can infer that users tend to
tonearbytractscontainingpopularplacessuchasworkplacesand visitclosebytractswithhighpercentageofwhitepeoplelivingin
restaurantsnearTimesSquareinaradioof0.5km.ClusterC2groups them.Wecanalsoobservethatingeneraltaxiridesarenotgoingto
taxiridesgoingtobigtractscontainingartgalleries,museumsand residentialareasbuttocommercialzones,whichisalsothecaseof
parks. Transitionsinthisgroupusuallyleavetractswithasmall clustersC1,C3andC7,oppositetoclustersC2,C4andC5whereit
numberofvenuesonworkdaysaround6pm. Finally, clusterC3 ismorelikelytovisittractscontainingartgalleriesandmuseums.In
identifiesalltaxiridesonFridaysandSaturdaysnightaround1am. clusterC6wecandeducethatpeopletendtovisittractscontaining
parksratherthanresidentialzones.
Table4: RankingofHypotheses. Thistableshowstherankingof23outof70hypothesesevaluatedwithHypTrailsover3different
groups.Overallrepresentsall143MtaxiridesinManhattan2013,clustersCiareclustersidentifiedbyNTF.Numericcellsrepresent
theranksofthehypothesesinrespectiveclusters.Forthedistance-basedhypotheses,weonlyshowresultsforthebestparameterof
thestandarddeviationσ (parameterinparentheses).Greencellshighlightallhypothesesthatoutperformtheuniformhypothesis.
Overall C1 C2 C3 C4 C5 C6 C7
HYPOTHESES Workdays Workdays Weekends Workdays Workdays Mo-Sa6pm Workdays
2013
9am 6pm 1am 7am 9am,6pm Sa-Su2pm 6pm
Baseline
Uniform 42 56 56 56 56 55 62 59
Distance-based(σ)
Proximity 14(3.0) 7(1.0) 2(0.5) 14(1.0) 10(1.0) 19(1.0) 10(0.01) 13(1.0)
Centroid(GeographicalCenter) 38(5.0) 50(5.0) 25(1.0) 58(5.0) 52(5.0) 58(5.0) 51(3.0) 51(5.0)
Centroid(FlatironBuilding) 29(5.0) 32(2.0) 51(5.0) 17(1.0) 2(0.01) 4(0.5) 44(3.0) 20(0.5)
Centroid(TimesSquare) 22(3.0) 1(0.5) 43(3.0) 46(3.0) 1(0.5) 43(2.0) 2(0.01) 1(0.01)
Foursquare
Gravitational(Allvenues) 1 12 14 10 14 10 14 9
Gravitational(Check-ins) 9 3 30 2 11 5 4 3
Gravitational(Work) 2 5 12 24 8 6 13 11
Gravitational(Food) 5 4 31 4 12 15 11 4
Gravitational(Party) 7 17 37 1 19 9 20 5
Gravitational(Recreation) 15 21 10 9 17 13 7 33
VenueSimilarity 39 53 53 53 53 52 58 53
Census
Gravitational(Population) 21 61 28 20 59 46 42 25
Gravitational(TractArea) 23 34 8 26 24 20 24 38
Gravitational(%Whitepeople) 6 24 13 28 28 27 35 27
Gravitational(Residentialzoning) 50 65 19 35 65 61 67 49
Gravitational(Commercialzoning) 13 8 32 22 9 24 19 15
Gravitational(ArtGalleries) 46 23 1 38 5 2 52 54
Gravitational(Museums) 54 13 3 40 6 7 26 58
Gravitational(Parks) 63 62 4 44 63 59 6 64
RaceSimilarity 32 48 50 52 50 50 59 50
PovertySimilarity 37 55 52 54 55 53 61 56
EmploymentSimilarity 40 57 54 55 58 54 60 58
6. DISCUSSION clusteringapproachisexchangeableandcouldbereplacedbyany
Inthiswork,wehaveshownthatspatio-temporaldynamicsin otherclusteringtechnique.
humanbehaviorcanpotentiallybebetterexplainedbyconsidering Statespace. Sinceourapproachrequiresadiscretestatespace,it
parts of the data separately. We identified clusters of taxi rides isnecessarytoaggregatepick-upanddrop-offlocationsofthetaxi
andutilizedopenlyavailabledatafromtheWebtoexplainthem. ridesinanarea. Thechoiceoftheseaggregationalunits(i.e.,the
However,therearesomeaspectsthatneedtobetakenintoaccount statesinourstatespace)canpotentiallyinfluencetheresults.Thisis
forthecurrentapproach. knowninliteratureastheModifiablearealunitproblem[28].Inthis
paper,wechosetractsforthelevelofouranalysisasitallowedfor
Concentrationparameterk.Asdiscussedin[33],theHypTrails thedirectintegrationofinformationfromcensusdata.Experiments
approach requires setting a parameter k to elicit Dirichlet priors withdifferentstatespacesaresubjectsoffuturework.
fromhypotheses.Highervaluesofkexpressstrongerbelievesinthe
Multipledimensions. Inthispaper,weclustertaxitripswithre-
respectivehypotheses.Technically,largervaluesofkimplyhigher
specttotime,pick-upanddrop-offlocation.However,ourapproach
valuesofthehyperparameters(pseudocounts)oftheDirichletdis-
allowstoextendthesebyadditionalinformation,e.g.,numberof
tributions.Inourexperiments,wetriedseveralvaluesofkfrom0to
passengers.Inthiscase,ahigherdimensionaltensorwouldbeused
100;overallverysimilarresults.Thereportedresultsinthispaper
byNTF,buttheresultingclusterscouldalsobeexplainedwithhelp
useanintermediatevalueofk=10.
oftheHypTrailsapproach.Thescaleofthesedimensionscouldalso
Correlationsintheexplanations.UsingHypTrailstoexplainclus- suggestmorefine-grainedmobilitybehaviors.Forinstance,inthis
terswillnotbeabletoidentifycausesofmovementpatterns,but workwedefinedthetimedimensionasall168hoursofaweekin
onlycorrelations.Asanexample,forClusterC2inourcasestudy ordertodistinguishpatternsonworkdaysandweekends.
theArtGallerieshypothesisperformsbest.Thisofcoursedoesnot Normalization. Theexternalonlinedataweuseforconstructing
meanthattaxitripsinthatclusterprominentlyhaveartgalleriesas mobilityhypothesesmightnotbeevenlydistributedacrossalltracts
destinations,butthatpeoplegotoplacesthatalsohavenearbyart (e.g.,#ofchurchesvs.#ofrestaurants).ThereforetheHypTrailsap-
galleries.Inthatdirection,wealsointendtointegrateacorrelation proachnormalizeseachbeliefmatrixtobeabletocomparedifferent
analysisbetweentheusedhypothesesinfutureworkinorderto hypothesestoeachother.
identifyexplanationsthataresimilartoeachother.
7. RELATEDWORK
Clustering method. In this paper, we use HypTrails to explain
clustersobtainedbyNon-negativetensorfactorization.WhileNTF Humanmobilityresearch.Humanmobilityisaphenomenonthat
is a reliable and established method in this line of research, the has attracted the attention of governments and researchers from
differentfields.Studyingthemovementofpeople(e.g.,migration correlatingmobilitypatternsandenergyconsumptiontoprovide
orcommuting)fromasocialscienceperspectivehashelpedusto bettersustainableurbanforms[20],andbymeasuringtheirinflu-
understandwho,whereandwhypeoplemove[2,24,35,40]aswell enceintheworldonattractingvisitors[21],andbyquantifyingtheir
aswhatconsequencessuchmovementcarries, bymeansofe.g., resiliencetoextremeevents[7].In[4,9],theauthorsimplemented
demographic,socio-economicandland-usefactors. Inliterature, visualizationtoolstounderstandurbanflowsacrosstimeandspace
theyarealsoreferredtoasactivity-basedanalysis.Naturalsciences, fromtaxiridesandsocialmedia.
ontheotherhand,haveshownusthatuniversalpatternsexistand Thenoveltyofourapproachreliesonthreefactors:(1)amulti-
aremodelledbymovement-basedtechniqueswhichcanpredicthu- dimensionalpatternrecognitionprocessusingNTF[5]toidentify
mandynamics[25,32].Tothebestofourknowledge,thereexists differentmobilitybehaviorsintaxidata,(2)theexpansionofthe
littleresearchonexplaininghumanmobilitybycombiningboth activity-based human mobility behavior into a hypothesis-based
movement-basedapproachesandactivity-basedanalyses.Further- schemabuiltuponhumanbeliefsand(3)quantifyingtheplausibil-
more,theyarenotabletocaptureoccasionalorseasonalbehaviors ityofbeliefsforeverymobilitybehaviorusingHypTrails[33]—a
thatoccuronlyatcertainperiodsoftime. Bayesianapproachforexpressingandcomparinghypothesesabout
humantrails.
Ubiquitousdata. Duetothelackofopenandupdatedinforma-
tion at global scale (e.g., surveys or census data), and thanks to
8. CONCLUSIONS
theriseofubiquitoustechnologiessuchasmobilephonedataand
GPS,researcherscangetaccesstohumantrailswhichfacilitates Inthispaper,wehavepresentedaninnovativeapproachfordis-
thestudyofhumanmovements. Thereexistseveralstudiesthat coveringandcharacterizingpatternsinhumanmobilitybehavior.It
haverevealedspatio-temporalpatternsindifferentcitiesbasedon combines(i)theclusteringoftransitiondatautilizingnon-negative
mobilephonecalldetailrecords(CDR)[17,38],taxitrips[3,6,23] tensorfactorization(NTF)withbothtimeandspacedimensions
andbikerides[19,31]. Therapidemergeofsocialnetworkshas and(ii)characterizingtheseclustersusingtheBayesianHypTrails
alsobenefitedthestudyofhumanmobilitybasedongeo-tagged method.InourexperimentsontaxidatafromManhattan,wewere
data.Forinstance,theworkbyJurdaketal.[18]studiesTwitteras abletoidentifyseveralinterestingfacetsofhumanmobilityand
aproxyofhumanmovement,byusinguniversalindicatorssuchas characterizethemusingcensusdataandadditionalinformationcol-
displacementdistributionandgyrationradiusdistributionthatmea- lectedfromFoursquare.Asoneexample,wediscoveredagroupof
surehowfarindividualstypicallymovebasedongeo-locatedtweets. taxiridesthatendatlocationswithahighdensityofpartyvenueson
Similarly,theauthorsin[27]proposedanetworkofplacesbuilt weekendnights.Thestrengthofthisapproachreliesonthefactthat
uponFoursquare’svenuesandmodelhumanmobilitybyconsider- theinterpretationoftheclusteringresultscanbeeasilycharacterized
ingtemporalandnetworkdynamicsinferredfromuser’scheck-ins. withhighlevelhypothesesusingHypTrails.
Gabrielli et al. [10] proposed a technique to analyze human tra- Ourworkextendsrecentresearchconcernedwithabetterunder-
jectoriesofresidentsandtouristsbysemanticallylabelingsource standingofhumanmobility. We have demonstrated thathuman
anddestinationspots.Basedontime-evolvingnetworks,thework mobilityisnotone-dimensionalbutrathercontainsdifferentfacets
in[11]identifiesandrankscollectivefeaturesforepidemicspread. including(butnotlimitedto)timeandspace.Futureresearchcan
Thisisamoreintrusivewayoftrackinghumanmovement,sinceit benefit from our methodological and experimental concepts pre-
requirestheuseofwearablesensors. sentedinthiswork.Amorefine-grainedviewonhumanmobility
canalsofacilitatee.g.,cityplanners,trafficcontrol,location-based
Activity-basedhumanbehavior. Comparedtothispaper, other
recommendersystemsoreventplanning.
works have identified and explained periodical movement-based
Inthefuture,weaimtogeneralizeourfindingsbystudyingsimilar
patternsasactivity-basedhumanbehaviors. In [41],theauthors
data(e.g.,biketripsorgeo-taggedtweets)availableforNewYork
proposedamodeltorepresentthetransitionprobabilityoftravel
andothercities.Indoingso,wecouldnotonlyunveilnovelgeneral
demandsduringatimeintervalandsuggestedthattraveldemands
patternsofmobility,butalsodiscoversimilaritiesanddifferences
canbeassociatedwithfixedlocationsundersomecircumstances.
betweencities.
Jiangetal.[16]explainedwhen,whereandhowindividualsinteract
Acknowledgments. ThisworkwaspartiallyfundedbyDFGGer-
with places in metropolitan areas based on activity survey data
manScienceFundresearchprojects“KonSKOE”and“PoSTsII”.
in Chicago. The work shows daily patterns as eigenvectors and
employsK-meansclusteringtoidentifygroupsofindividualsbased
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