Do 3D Visualizations Fail? An Empirical Discussionon 2D and 3D Representations of the

Spatio-temporal Data

Erdem Kaya∗, M. Tolga Eren†, Candemir Doger‡, and Selim Balcisoy§Sabanci University Tuzla, Istanbul 34956

∗erdemkaya@sabanciuniv.edu†mustafae@sabanciuniv.edu‡cdoger@sabanciuniv.edu§balcisoy@sabanciuniv.edu

Abstract—Having particular aspects diverging from otherkinds of data, spatio-temporal data may require conventionalvisualization techniques and tools to be modified and tailored foranalysis purposes. However, there could be a number of pitfallsfor the design of such analysis tools that completely relies on thewell-known techniques with well-known limitations possibly dueto the intrinsic characteristics of the data at hand. In this paper,we present an experimental study to empirically testify whetheradvantages and limitations of 2D and 3D representations are validfor the spatio-temporal data visualization. To form the basis forour experimental design, we interviewed domain experts from alocation-based services company and identified different cases ofspatio-temporal data analysis. Furthermore, we implemented twosimple representations, namely density map and density cube, andconducted a laboratory experiment to compare aforementionedtechniques from time and correctness perspectives.

Results of our experiment revealed that care must be takenwhile applying highly accepted well-understood properties of 2Dand 3D visualizations to the spatio-temporal data. On one hand,none of the techniques was superior to the other in terms oftask completion time except for some particular cases. On theother hand, our 2D density map implementation led to moreaccurate inferences for tasks related to trend detection andmaking comparisons, as vastly suggested by the previous work. Assuggested by these examples, the validity of the generally acceptedaspects of 2D and 3D visualization needs to be reconsidered forthe analysis of spatio-temporal data, hence the purpose of ourstudy.

I. INTRODUCTION

Over the past few years, visualization community haveworked on problems closely related to the cartographic andgeographic information system (GIS) communities. The crossdisciplinary connection between these fields facilitates thevisual display and interactive exploration of geospatial dataand the information derived from it. Analysis of geographicinformation in time and space is becoming an important subjectwith the increasing use of location data in everyday life. Somekey challenges are understanding dynamics of data in timeand space, identifying spatial and temporal data patterns, andcorrelating spatio-temporal data to other data such as sales.

In their extensive work, Andrienko and Andrienko empha-size the need of visualization techniques and analytical toolsthat will support spatio-temporal thinking and contribute tosolving a large range of problems [1]. Nevertheless, due to the

sophisticated nature of spatio-temporal data analysis, currentvisualization techniques and analytical tools [2] are not fullyeffective and need to be improved.

In this work we are not proposing novel visualizationtechniques for spatio-temporal data. Instead, we propose thatwhether well-known aspects of 2D and 3D representations arealso valid in spatio-temporal visualization. To support our find-ings we conducted an experiment with highly representativescenarios and tasks that could be used in spatio-temporal dataanalysis.

The main contribution of this work is a novel empiricalstudy leading to the conclusion that 3D visualizations shouldbe considered as a valid option in spatio-temporal data visu-alizations. To our knowledge this is the first work providingevidence opposing the findings of the previous research against3D techniques on this domain. A particular kind of visualiza-tion technique is not completely advantageous compared toothers as suggested by previous work [3], [1], [4], [5], [6]. Onthe contrary, 2D and 3D visualizations seem to be counterpartscompleting each other. The advantages of 2D representationsover 3D for various kinds of data seems to be well-understoodwhich might mislead to the understanding that 3D has moredrawbacks than 2D in spatio-temporal visualization. Based onour study and [6], it appears to be the fact that there is enoughevidence to reject the idea that 3D visualization should only beconsidered as secondary option in the visualization of spatio-temporal data.

We have analyzed 2D and 3D density visualization tech-niques, namely density map (Figure 1a and 1b), and densitycube (Figure 1c). Before designing our evaluation method-ology, we have interviewed system administrators from alocation based services (LBS) company and identified mostlikely scenarios based on which we performed a laboratory ex-periment to compare density map and density cube techniquesfrom time (to complete the tasks) and correctness perspectives.

Based on the scenario-wise analysis of our collected data,we found out that participants were able to analyze the datafaster with density cube technique in the cases where theyneed to view a given data window as a whole (e.g. trenddetection). However, they were able to answer the questionsmore accurately in overall when they viewed the data withdensity map technique. Particularly, density map technique

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(a) (b) (c)

Fig. 1: Views from our experimental tool showing the 2D and 3D visualization of the spatio-temporal data from a commercial friend finder application. (a) 2DDensity Map, (b) Zoomed Density Map, and (c) 3D Density Cube. Note that the third dimension for the Density Cube is time.

was significantly better than the density cube technique inthe case of cluttered data. Density map technique assistedparticipants better in terms of accuracy in minimum-maximum,and comparison questions, while no significant differencewas observed for trend questions. Our scenario-wise analysisrevealed that density cube and density map techniques weresuperior to each other depending on the scenario. These resultssuggest the reconsideration of well-known properties of 2Dand 3D representations particularly when the data to analyzeis spatio-temporal.

The paper is organized as follows. Previous work (Section2) gives a brief background about the 2D and 3D represen-tations along with spatio-temporal data and its visualization.After the specification of the data and the techniques (Section3), the experiment methodology is reported (Section 4). Andfinally, after a discussion on the results of our experiment(Section 5), we conclude (Section 6).

II. PREVIOUS WORK

A. Properties of 2D and 3D Representations

The choice of 2D or 3D representations in informationvisualization seems to be a highly debatable and complextask. Furthermore, previous body of work suggests that well-understood commonly accepted advantages and drawbacks ofone representation over the other may depend on the contextand data analysis objectives. For example, as Munzner states[4], selecting 3D becomes meaningful when the 3D represen-tation is implicit in the dataset and when that representationfits to the mental model of the user about the phenomenon.

It would be a subject of a different work to enumerateall the studies comparing the 2D and 3D representations.Common known properties of these representations will brieflybe explained with a few example studies.

The effectiveness of 2D representations in terms of botheffectiveness (e.g. time to complete task) and accuracy (e.g.error rate) have also been reported in a number of studies. Forexample, users were able to locate regions of interest more ef-fectively and accurately when they view the blood flow visual-ization with 2D representations [7]. In their experimental study,Hicks et al. [3] compared various performance levels of 2D and3D visualizations of e-mail usage log, which they consider as

temporal data. They reported that 3D representations poorlyperformed in terms of task completion time whereas the verysame representation aided their participants in answering thecomparison questions more accurately where the participantshad to view the whole data. Their findings differ from ourspossibly due to the natural differences between temporal andspatio-temporal data, which we discuss in Section 5.

Another property of the 2D visualizations is related to spa-tial memory as suggested by previous work. In their study [8],Cockburn et al. suggest that their subjects’ ability to quicklylocate web page images deteriorated as their freedom to use thethird dimension increased. Case studies and formal user studiesdemonstrated that 2D data encodings and representations aregenerally more effective than 3D for tasks involving spatialmemory, spatial identification, and precision.

The advantage of the 3D representations becomes clearwith the tasks requiring the holistic view of the data [9],[3], [5]. As Hicks et al. state, cognitive error degrades whenthe users are to view the data as a whole. The experimentalfindings of Kjellin et al. also supports this idea as theirparticipants were able to better track multiple vehicles whenthey were equipped with 3D visualization techniques [6].Nevertheless, the holistic view might bring its own issues suchas occlusion, one of the common problems associated with3D representations [3]. Perspective foreshortening is anotherproblem with the 3D representations. Users might suffer fromjustifying the measures of the objects in the 3D visualizationsdue to the perspective projection while performing trend com-parison tasks.

B. Spatio-temporal Data

In their extensive work [10], [11], [12], MacEachren andKraak explore different techniques and the research chal-lenges in geovisualization field. They address the importantpoints of geovisualization such as representation of geospatialinformation, integration of visualisation with computationalmethods, interface design for geovisualization environmentsand cognitive/usability aspects of geovisualization. Differentcartographic techniques have been used to represent geospa-tial information. Among many other visualizations that usegeographic maps, thematic mapping [13] techniques are de-signed to show a particular theme connected with a specific

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geographic area. Density map [14] technique is also adoptedfor geographic data visualization and data analysis in severalimportant examples. Fisher proposes an interactive heat mapsystem [15] that visualizes the geographic areas with high userattention in order to understand the use of online maps. Mehleret. al also use a geographic visualization technique similar toheat map [16] in which they geographically analyze the newssources. Another interactive framework taking advantage ofheat maps is introduced by Scheepens et al.[17] in which theyaim to visualize the trajectory data of vessels. The density mapimplementation employed in our experimental study is heavilyinfluenced by heat map visualization technique.

Perhaps one of the most important and ubiquitous datatypes is the one with references to both time and space,usually referred to as spatio-temporal data. The concept ofspatio-temporal data is defined in both geographic informationsystems (GIS) [18], data mining [19], and visualization [20].Visualization of spatio-temporal data involves the direct de-piction of each record in a data set so as to allow the analystto extract noteworthy patterns by viewing the representationson the displays and interacting with those representations.Increasing number of studies on management [21] and analysis[1], [22] of spatio-temporal data in the last decade indicatethe importance of the analysis of this data type. The analysisof such data with references both in space and in time is achallenging research topic. Major research challenges include[23] scale, as it is often necessary to consider spatio-temporaldata at different spatio-temporal scales; the uncertainty ofthe data as data are often incomplete, interpolated, collectedat different times, or based upon different assumptions; thecomplexity of geographical space and time, since in additionto metric properties of space and time and topological/temporalrelations between objects, it is necessary to take into accountthe heterogeneity of the space and structure of time; and finallythe complexity of spatial decision making processes, sincea decision process may involve actors with different roles,interests, levels of knowledge of the problem domain and theterritory.

When the spatio-temporal data sets are very large andcomplex, existing techniques may not be effective to allowthe analyst to extract important patterns. Users may also havedifficulty in perceiving, tracking and comprehending numerousvisual elements that change simultaneously. One way to dealwith this problem would be the aggregation or summarizationof data prior to graphical representation and visualization [24],[25], [26].

Infinitely many visualization studies have been conductedregarding spatio-temporal data visualizations. For visualizingthe spatial change over time in data, Scheepens et al. proposean interactive visualization framework, which analyzes thetrajectory data of vessels to understand their behavior and risks[26]. After the space-time cube method has been revisited forthe analysis of geographic data in many works [12], [15], ithas been used frequently in visualizing spatio-temporal data[27], [28]. The space-time cube approach bore the idea ofusing the third axis for representing time. 3D visualizationtechniques have been used on visualizing hierarchies thatchange over time in a geo-spatial context [29]. Several time-oriented visualization methods are also presented [30], [31]to analyze and support effective allocation of resources in a

spatio-temporal context. In their analytic review, Andrienkoet al. [20] discuss various visualization techniques for spatio-temporal data, with a focus on exploration. They categorizethe techniques by what kind of data they can be used for andthe kinds of exploration questions can be asked.

Being a very brief summary of existing literature, theseworks include evaluations of the visualizations to some par-ticular extend; however, when and if their findings for thespatio-temporal data apply also to other types of data seemsto be rather unheeded. Effects of the representation typemay be different than expected when the data to explore isspatio-temporal, where the dimensionality inherently increases.Kjellin et al. [6] reports different cases how 2D and 3D rep-resentations outperform each other. Their 2D representationsof movement plots assisted the participants to perform betterwhile they were trying to estimate the intersection of twovehicles. Contrarily, 3D representation helped the users betterwhen they had to estimate a similar measure for more vehicles,supporting our idea that the nature of the spatio-temporaldata might effect the generally accepted drawbacks of the 3Drepresentations.

III. DOMAIN PROBLEM SPECIFICATION

Many spatio-temporal visualization techniques and toolshave been designed for the analysis of trajectory data. How-ever, the geographic data employed in our visualizations arespatial events with GPS-accuracy geographic coordinates anda seconds-precision timestamp. In other words, we do nothave any trajectories and our analysis of spatio-temporal datasolely depends on the spatial correlation between regions ofconsecutive density representations. Our methods are designedconsidering these characteristics of the data.

A. Data Description

1) Real Data: The geographic data employed in our studycomprises spatial event records with geographic coordinateswith GPS-accuracy as well as a seconds-precision timestamp.Approximately 2.5 millions of such records have been col-lected by a LBS company. Each data record corresponds towhen and where a mobile phone application was invoked.Dataset involves records saved between February 2nd, 2011and April 1st, 2012 from almost all provinces of Turkey. Eventhough the density of the data adequately enabled us to inferpossible interesting trends, we opted to use fictious data so thatwe could generate a number of patterns that were not existentin our real data.

2) Artificially Generated Data: For our experimental study,we decided employing artificial data merely to generate a widerspectrum of different scenarios that were not available in thereal data.

A data generator has been designed to reflect the nature ofspatio-temporal data. For a given region centered at LC anda specific time interval T , the generator creates data recordseach of which corresponds to a point L in the data spacewith latitude (LC,Lat), longitude (LC,Long), and time (LC,T )dimensions.

For a given time period T , i sub-intervals with evendurations are created such that the duration of each sub interval

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t = T/i. Based on the requirements of a predefined scenario, adistribution function f [t] is defined as the planned total numberof data points per sub interval t. The actual total number ofdata points per sub interval is calculated as

Nt = R(f [t](1− α), f [t](1 + α))

where α (0 6 α 6 0.5) is the noise parameter controlling thedistortion of the number of the data points to be generated,and the function R(a,b) selects a random value between a andb.

Point Generation—The following equations are employedto generate data points LG(LG,Lat, LG,Long, LG,T ) each ofwhich are comprised of tuples of latitude, longitude, andtimestamp.

LG,Lat = rcosθ + L0,Lat

LG,Long = rsinθ + L0,Long

LG,T = R(tm, tn)

where r = R(Ra, Rb), θ = R(0, 2π), L0 is the origin pointon which the data generation calculation based on (Please seeFigure 2a). In principle, the data generator is provided withthe region center LC before the data generation process. Theregion center LC is slightly shifted to a randomly created point(L0) to add noise to the data generation. The calculation ofL0 will be explained in the next subsection. tm and tn arethe beginning and the ending times, respectively, of a givensub interval t. Being the inner and outer radii of the selectedannular subarea, Ra and Rb, will be explained further in thenext section.

Scatter of the Generated Points—The geographical scat-ter of the generated data points was based on the “LotteryScheduling Algorithm” developed by Waldsburger et al. [32]In the lottery scheduling algorithm, each process to be run ona CPU is assigned a number of tickets. At the beginning ofeach run period, scheduler picks a ticket randomly and selectsthe process holding this ticket. Apparently, the process holdingmore tickets than the other rivaling processes will have morechance to be scheduled on the CPU. Our data generator toolbenefited from this algorithm for the scatter of data. Such that,the area of interest is divided into C concentric annular nested

(a) (b)

Fig. 2: Given an origin point L0, (a) a data point is generated with randomizedθ angle and a radius selected from the interval [Ra, Rb], (b) which specifiesthe inner and outer radii of the selected annular area cj .

areas as in Figure 2b, and each area is assigned a number oftickets ωj , in other words, scatter parameters, associated witharea cj . The number of tickets, ωj , defines the probability ofa data point to be generated in area cj . For a group of sub-intervals [ta, ..., tb], the scatter of the data can be arrangedby simply modifying ωj scatter parameters. The number ofscatter parameters (and also the number of nested areas), j, isspecified manually depending on the requirements of the taskscenario. The selected area cj is defined by two radii, Ra andRb, which is calculated as Ra = D(j−1)

C and Rb =DjC , where

D is the diameter of the circular area for which the data willbe generated.

Scatter Noise—To generate data looking more real, weconsidered another noise factor β, namely scatter noise.Scatter noise parameter creates distortions on the scatter ofthe data by randomizing the latitude and longitude valuesof the origin point L0 within a predefined limited area.L0(L0,Lat, L0,Long, L0,T ) is calculated before the generationof each data point with following formulae,

L0,Lat = rrcosθ + LC,Lat

L0,Long = rrsinθ + LC,Long

L0,T = 0

where rr = R(0, D/β), θ = R(0, 2π), LC is the centralpoint of region with a radius D selected by the experimentersaccording to the requirements of the scenarios.

B. Spatio-temporal Data Analysis Needs

We conducted interviews with system operators at a LBScompany in order to form a practical basis for our experimentalstudy. We found out that two spatial analysis cases were oftheir firm’s critical importance: (a) Measuring the effectivenessof a service promotion (e.g. analyzing the effects of a promo-tion for a particular period of time after the advertisement)and (b) identification of local service disruptions (e.g. beingable to find of 30-minute-long disruption in a week-longworth of data). It was important for them to quantify theeffective breadth and duration of a promotion to understand themarket dynamics. Fast and correct spatial analysis of servicedisruption cases was found out to be crucial. For example, alocal service drop could trigger a false alarm which may leadto a legal dispute in particular cases. Even though tracing backfrom the usage logs of the service might be considered as areasonable approach, the process had usually been evaluatedas exhaustive and unfruitful.

It was also important to locate and identify the generalusage patterns, customer behavior patterns, and user profilesfor the service providers, since the data specifically tailoredfor some special user groups might bring potential benefits.

Yet another important aspect of the data at hand was thatcorrelating the data with spatial (e.g. business district, touristsite, shopping area) and temporal landmarks (e.g. days ofweek, holidays, tax time). Such information would requirespatio-temporal data to be correlated with other data and wouldadd further challenges. Despite these challenges, such correla-tions would significantly improve customer segmentation andwould lead to improved effectiveness of services.

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t5

t4

t3

t2

t1

t0

[t4 – t5]

Interval 5

[t3 – t4]

Interval 4

[t2 – t3]

Interval 3

[t1 – t2]

Interval 2

[t0 – t1]

Interval 1

Fig. 3: Generation of 3D texture by stacking density maps: Density mapsare generated for each time interval with the data lying in the correspondinginterval. Then, these density maps are stacked according to the order of thetime intervals to generate the 3D texture.

C. Visualization Techniques

In order to represent 2D and 3D techniques in our exper-imental study, density map and density cube representationswere implemented.

Density Map Animation—Density map animation has beenimplemented as the sequential animation of raster images.Firstly, the density map of the artificial data has been cre-ated by making use of kernel density estimation. Calculatedintensity values of pixels were scaled into the range of 0-255 to produce a gray-scale intensity map image. Upon thecalculation, we modeled each geographic location as a radialgradient, a filled circle having a gradually descending intensityas the distance from the center increases. To calculate theintensity of each pixel with this method, additive blendingtechnique has been utilized where the intensity values of geo-graphical points occupying the same pixel have been summedup. Consequently, at the beginning of the colorization process,gray-scale maps have been created by scaling the intensityvalues of each pixel between 0-255. Finally, appropriate colorschemes have been chosen to be applied on the gray-scaleintensity maps [17]. The still images generated with thismethod are used as the frames for the animation.

Density Cube—As a time-space cube variant for spatio-temporal data visualization, density cube represents the dataof interest as a whole on the display so that the cognitive loadon analysts is reduced by obviating the need for rememberingthe previous frames for tracking the changes. Density cubetechnique overcomes this limitation by utilizing a 3D texture,which actually is a stacked version of consecutive density maps(Figure 3). The 3D texture is then rendered by employing aGPU ray-caster to visualize all time slices in a single frame.Similar visualization techniques have been used in medicalimaging field in recent years [33]. Imitation of the 3D textureconveys the continuity of the data. Since the frames has readily

been created for density map animation technique, densitycube required less computation load. As for interaction, theparticipant was able to change the orientation of the cube tobetter analyze the desired portions of the data. The participantcould also change the time scale which would either compressor extend the visualization along the time axis (axis-y in Figure3).

IV. EXPERIMENT

The methodology to analyze the effectiveness of visual-ization techniques has benefited much from Munzner’s NestedModel for visualization design and validation[34]. While manystudies on information visualization demonstrates how theymeasure potential usability of their techniques, we consideredit useful to specify which evaluation method should be em-ployed based on the contribution category of our findings.As Munzner states, the contribution of an information visu-alization study should be well defined since each contributionvenue requires a different evaluation technique. According toher evaluation model, possible contributions of informationvisualization studies can be classified as (a) domain problemcharacterization, (b) operation and data type abstraction, (c)visual encoding and interaction design, and (d) algorithmdesign. In order to assist readers to comprehend how ourstudy fits in the existing literature, we defined the level ofthe possible contributions of our study. The density map anddensity cube techniques have been implemented to aid theusers to notice the possible trends and outliers in spatio-temporal data. On the one hand, the change in the data isabstracted to particular visual formations, which could bevisually analyzed by the users. On the other hand, users areprovided a number of interactions with the assistance of whichthey can rotate, manipulate, and scale the visualization to makemore sense of the data.

A. Methodology

Much research has been done to investigate how effectivedifferent venues of visualization techniques are to aid the anal-ysis. While many researchers suggested that 2D representationsshould not be the only technique of choice [5], [35], there areconsiderable number of studies suspecting potential benefitsof 3D representations. We believe that the reconsiderationof well-known characteristics of 2D (e.g. reasonable levelof detail) and 3D (e.g. occlusion) representations when thespatio-temporal data visualization is considered might yieldunexpected results. That is in other words, we aim to empiri-cally evidence whether the commonly accepted characteristicsof this two classes of representations are also valid in thespatio-temporal data visualization. The typical metrics for theperformance of a visualization technique could be the timespent by a user on a given task and could be the correctness rateof the inferences made based on the observed data. From thisvantage point, a study aiming to explore possible advantages ofone technique over another might benefit from these metrics.

1) Experimental Design: To explore the advantages ofthe visualization techniques, we designed a within-subjectexperiment with a single independent factor (Type of thevisualization technique: Density map vs. Density cube). Asimplied by the design of the experiment, each participantviewed the same scenario twice with different visualization

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Scenario 1

Density Map Visualization

Dataset 1A

Scenario 2

Dataset 2A

Scenario 3

Dataset 3A

Scenario 4

Dataset 4A

Scenario 5

Dataset 5A

Section 1

Task 1 Task 2 Task 3 Task 4 Task 5

Scenario 1

Density Cube Visualization

Dataset 1B

Scenario 2

Dataset 2B

Scenario 3

Dataset 3B

Scenario 4

Dataset 4B

Scenario 5

Dataset 5B

Section 2

Task 6 Task 7 Task 8 Task 9 Task 10

Fig. 4: Scenarios, tasks, and datasets: Task sequence for experiment Group 1. Sequences for other groups can be derived from Figure 6.

technique. The performance of the participants was measuredin terms of time and correctness rate.

We have conducted interviews with three data analyst in alocation-based services company in order to formulate our ex-perimental scenarios and tasks. To better simulate the cases thatmight exist in real data, five scenarios were created. As can beseen in Figure 4, the experiment comprised two sections, eachof which included five tasks and was dedicated to one of thetwo visualization techniques, namely density map or densitycube. According to our experimental design, participants wereexpected to finish both sections which include tasks generatedbased on the same scenarios, which could have caused learningeffect1. To prevent possible learning effects, each scenario wasrealized with two datasets sharing the same data formationbut generated for different location and sampling frequency.For example, if scenario 1 emphasizes an increasing trend inthe data, two datasets (dataset 1A and 1B) generated for thisscenario must have the same trend, but the datasets shouldbe generated for different locations, and should span acrossdifferent periods of time.

The order of the visualization techniques viewed by theparticipants was of importance to prevent bias on the collecteddata. Furthermore, the dataset-visualization technique combi-nation had to be counter-balanced such that each combinationhad to be viewed by the participants with the same frequency.To address these problems, we generated four participantgroups. As shown in Figure 6, dataset-visualization techniquecombination and the ordering has been fully stratified. Forexample, participants in Group 1 viewed the scenarios realizedwith Datasets A and visualized with density map technique inthe first half of the experiment, while they viewed the samescenarios realized with Datasets B and visualized with densitycube technique. Similarly, participants in Group 2 viewed thesame sequence except for the order of the datasets.

Scenarios—We believed that evaluation of visualizationtechniques should benefit from the formations (e.g. trends)that could exist in a real-world data. Such formations couldinform the generation of scenarios that would be used duringthe experiments. After examination of the real data and theresults derived from interview, we established five scenarioswhose characteristics were, we believe, capable and diverse

1Learning effect is a case where the participants gain ability to accomplishtasks with better performance metrics as a result of repeatedly working onsimilar tasks.

enough to aid us in investigating how and in which ways avisualization technique would outperform the other.

Five scenarios employed in the experiments are demon-strated in Figure 5. In the first scenario, the usage of theapplication in a city has been demonstrated. By employingthis scenario we aimed to facilitate an evaluation setting whereusers were expected to locate different levels of increase inthe usage of the LBS service. The first scenario dictated datageneration process with a moderate increase followed by anexponential one.

A typical workday in a city’s downtown and suburban areashas been simulated in the second scenario. Moreover, a servicefailure in the downtown area between 12-3pm has been addedto the scenario design. As can be seen in the Figure 5, a steepincrease in the usage rate between 3-9pm implies a commoncase where the application is used more frequently at the endof a work day. In the suburban area, a sudden increase in theusage rate at around 3pm is shown.

The third scenario, similar to the second scenario, demon-strates a usage rate pattern in a city’s downtown and suburbanareas. However, in this scenario a weekend day has been simu-lated where the usage rate in downtown increased consistentlyduring the day. A slight increase followed by a decrease in thesuburban area has also been added to the design.

Commute of farmers from their villages to farm fieldsin rural areas was simulated in the fourth scenario. In thisscenario, the usage rate decrease in all villages earlier in theday followed by an increase in the afternoon was demonstrated.The usage rate peak around 1pm in the farm field has beengenerated to give the insight that farmers could use theapplication more often while they work in the field.

Finally in the last scenario, participants were expected toinfer a periodical trend of the usage rate in a city of moderatesize. A typical work day usage rate trend has been repeatedthree times with random noise added to the slope of the trend.

Datasets—To demonstrate the scenarios in the experimentaltool, we generated datasets with our data generator explainedin Section 3. Our design dictates that participants will vieweach scenario twice; however, with different visualizationtechniques and datasets combinations (Figure 4). To preventpossible learning effects, two separate datasets, hereinaftertwin datasets, for each scenario has been generated. The twindatasets share the same data formation specified according

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to the corresponding scenarios. However, they differ in thenoise they include, the location and time information whereand when the scenario takes place, and finally the length ofthe time period along which the scenario spans. For example,twin datasets 1A and 1B have the same trends as specifiedby Scenario 1. However, the scenario takes place in the citiesGonen and Tomarza in October 2011 and November 2012 indatasets 1A and 1B, respectively.

Tasks and Groups—As illustrated in Figure 4, each runof the experiment was comprised of 10 tasks, each of whichis a combination of a scenario, an accompanying dataset,and the technique to visualize the dataset. The order of thescenarios was specified as shown in the Figure 4, and this orderwas never modified throughout the experiments. However, thedataset and the accompanying visualization technique that willbe used for a given task was determined according to theexperiment groups (Figure 6), which were created to preventlearning effect. For example, participants in Group 1 viewedtasks 1 through 5 which were created with datasets 1A through5A visualized with density map technique while they viewedtasks 6 through 10 generated with datasets 1B through 5Bvisualized with density cube technique. All possible datasetand technique orderings were stratified among these fourexperiment groups.

Questions—In each task, users were expected to answerfour or five multiple-choice questions. Please see Figure 7 forthe number of questions asked in each task. We asked threetypes of questions to our participants during the experiment:

• MinMax, finding the minimum or maximum usage ratein the data set,

Q) In which of the following time periods was the service usedmost?

a) May 10th, 2011 – May 14th, 2011b) May 22nd, 2011 – May 26th, 2011c) June 4th, 2011 – June 8th, 2011d) June 8th, 2011 – June 12th, 2011e) This tool is not informative enough to answer this

question.

• Comparison, comparing the usage rates at two differenttime stamps,

Q) Which of the following is true?a) The usage rate on July 13th, 2011 is higher than the

one on July 18th, 2011.b) The usage rate on July 18th, 2011 is higher than the

one on July 13th, 2011.c) The usage rates on July 18th, 2011 and July 13th,

2011 are almost at the same level.d) This tool is not informative enough to answer this

question.

• Trend, detecting trends in the data,

Q) Which of the following is correct about the usage ratevariances around city shown to you?

a) The usage rate moderately increases during the firsthalf of the period. During the second half of the period,usage rate increases much more faster than it does in thefirst half of the period.

b) The usage rate moderately decreases during the firsthalf of the period. During the second half of the period,usage rate increases saliently.

c) The usage rate moderately decreases during the firsthalf of the period. During the second half of the period,usage rate remains at an almost constant level.

d) The usage rate moderately increases with a constantacceleration during the whole period.

e) This tool is not informative enough to answer thisquestion.

In total, the participants answered 46 multiple-choice ques-tions (23 for both density map and density cube techniques)during the experiment.

2) Procedure: Experimental procedure is shown in Figure6. At the beginning of the experiment, participants were shortlybriefed about the experiment followed by a visual capabilitytest. Upon the completion of the test, participants were ran-domly assigned to one of the experiment groups. Dependingon the experiment group, the first section of the experimentstarted with an instruction part for either density map or densitycube technique. In instruction part, each participant receivedabout 10 minute of training with our tool so that they hadadequate amount of time to explore a small example dataset.Every question asked by the participants were answered by theexperimenter to ensure that they understood the functioning ofthe tool and gained sense of how the data should be interpreted.Following the instruction part, participants were shown thefirst five tasks with the sequence explained in the previoussubsection. For example (Figure 6), a participant in Group 2took a training about the density map technique and completedfive tasks generated with datasets B and visualized with densitymap technique. The second section of the experiment has beencompleted with the same sequence of processes.

3) Measures: Our measures included both objective andsubjective data. We defined the descriptiveness capability ofeach technique in terms of time to solve the questions and thecorrectness value indicating how accurately the participantsanswered the questions. The time measure was collected foreach task separately. The correctness value, collected both astask-based and as total, has been normalized so that it wasranged between 0 and 100.

4) Participants: 14 participants (4 female), graduate andundergraduate students in a university in Turkey, volunteeredfor the experiment. Nevertheless, one of the cases was dis-carded due to the color vision deficiency (CVD) [36] of oneof the participants.

B. Results

Analysis of the collected data was conducted in three steps;(1) effects of 3D visual capability baseline, (2) analysis of taskcompletion time, and finally (3) analysis of correctness rate. Tocomply with the question types discussed in the previous sub-section, analysis of task completion time and correctness rate

7

Scenarios 1...5

Experiment Briefing

Visual Capability Test

Density Map

Dataset A

Post-study Questionnaire

Density Map

Dataset B

Density Cube

Dataset A

Density Cube

Dataset B

Density Cube

Density Map

Instructions

Density Cube

Dataset B

Density Cube

Dataset A

Density Map

Dataset B

Density Map

Dataset A

Post-study Questionnaire

Group 1

Group 2

Group 3

Group 4

Group Selection

Density Map

Density Cube

Instructions Tasks 1...5

Scenarios 1...5

Tasks 6...10

Section 1 Section 2

Fig. 6: Experiment Conduct Flow

was evaluated separately for minimum-maximum, comparison,and trend questions.

1) Effects of 3D Visual Capability Baseline: We performedgeneral linear model (GLM) repeated measures in order toanalyze the variance of the correctness and time along withthe 3D visual capability as the covariate. As the result of ouranalysis, we found out that visual capability did not have aneffect on time measure, F (1, 6) = 1.82, p < .23, while itwas marginally effective2 on correctness measure, F (1, 6) =4.652, p < .1, implying an opportunity for further investigationwith visual capability as a factor of interest.

2) Analysis of Task Completion Time: Task completiontime performance of our participants was evaluated separatelyfor minimum-maximum, comparison and trend questions. Foreach question type, analysis of each sceanario (3 x 5 pairedt-tests) and total time spent across all scenarios (3 x 1 pairedt-tests) was conducted.

The comparison of the total time periods spent on eachtechnique (for each question type) showed that neither tech-nique assisted participants in solving the tasks in less time thanthe other technique did as demonstrated in Table 9. However, anotable exception occurred for the minimum-maximum ques-tions of the second scenario, t(12) = 1.862, p < .1, wherethe density cube technique (M = 18.95, SD = 14.85) outper-formed the density map technique (M = 35.58, SD = 31.2)(Figure 8a). Another exceptional case existed for the compar-ison questions of the fifth scenario, t(12) = −1.861, p < .1,where the density map technique (M = 25.72, SD = 11.07)aided users to better compare the usage rates than the densitycube technique did (M = 37.97, SD = 21.33) (Figure 8b).

3) Analysis of Correctness Measure: Analysis of correct-ness measure revealed significant findings about how visualiza-tion technique was predictive on our participants’ success. Foreach question type (trend, minimum-maximum, and compari-son), analysis of overall success rate of our participants wasconducted. According to the results of paired t-tests appliedon the correctness measures, we found out that participantswere able to answer both trend (t(12) = 2.215, p < .05)(Figure 11) and comparison (t(12) = 3.482, p < .01) (Figure12) questions more correctly when they viewed the data withdensity map technique. Statistical results are presented in

2While reporting the statistical results, marginal effect is referred to the pvalue between 0.05 and 0.1.

Table 10. However, there was no significant difference betweenthe correctness measures of the two visualization techniques(t(12) = 1.443, p > .1) for minimum-maximum question type.

V. DISCUSSION

Listing the benefits and drawbacks of 2D and 3D repre-sentations for each kind of data and task is out of scope ofthis work. We believe that there exists enough evidence inorder to argue that 3D representations in the visualization ofspatio-temporal data should remain as a valid option as 2Drepresentations are accepted to be by the existing literature.This is to say that, some common and well-known drawbacksof 3D visualizations seems not to be significantly present whenthe spatial and temporal data is to be analyzed. Even more, 3Drepresentations of spatial and temporal activities can aid theusers perform significantly better in particular tasks where 2Drepresentations accepted as the de facto leading option [6].

The analytical use cases that can occur in spatio-temporaldata are inexhaustible in terms of the possible formations(i.e. patterns), and tasks to be performed. The setup for thevisualization and the role of the users of the visualization areother factors contributing to this variety. In our experiment,we were able to cover only five of them that were found tobe the best representatives of LBS data analysis by the fieldexperts. As suggested by Andrienko and Andrienko [1], thetasks remain analogous across various visualizations, hencetheir task typology divided into two main groups as elementaryand synoptic tasks. Some tasks may require a holistic view ofdata, while some others might lead users to make analysisbased on a particular point in the visualization. According tothis typology [1], our minimum-maximum, comparison, andtrend questions correspond to inverse comparison, direct com-parison, and pattern identification, respectively, task groups.This correspondence forms a basis for our discussion onwhether and why 2D and 3D representations fail for particulartasks in spatio-temporal data visualization compared to thevisualizations of other data types.

While analyzing the data represented in the second sce-nario, users observed the whole dataset as a set of 3D objectsin our experimental tool enabling them to draw decisions morequickly than they did with density map animation. This ishighly likely due to the fact that users tend to model thedata in their mind as a whole rather than interpreting datain smaller chunks, causing them to browse through all data as

8

Map

City

Scenario 1

City

Scenario 2

City

Scenario 3

09:00 12:00 15:00 18:00 21:00 00:00 03:00 06:00

Map

Map

Suburban

09:00 12:00 15:00 18:00 21:00 00:00 03:00 06:00

Suburban

Field

Scenario 4

Map

Village A

Village C

Village B

Village D

07:00 09:00 11:00 13:00 15:00 17:00 19:00

Map

City

Scenario 5

14:00 16:00 18:00 20:00

City

City

Suburban

City

City

Suburban

Field

Villages

Usage Rate

Usage Rate

Usage Rate

Usage Rate

Usage Rate

Fig. 5: Scenarios and accompanying trends: Five scenarios created for theexperiment. In the left column of the figure, general spatial distribution ofthe data is shown. In the right column, noise-free trends of application usagerate as a function of time has been depicted. The actual data represented inthe experimental tool includes some level of noise in order to complicate thetasks and to imitate the real-world data.

fast as possible [9]. Similar findings have also been reportedin [3], [5]. Hicks et al. claim that computational offload3 thatoccurs during the holistic observation of the data assists tocomplete the undirected comparison tasks in less time. Earlier

3Computational offload refers to the gain in the cognitive effort of theparticipants in their experiment.

Scenario Tasks Number of questions

MinMax Comp. Trend TOTAL

1 Task 1 Task 6 2 1 2 5

2 Task 2 Task 7 2 1 1 4

3 Task 3 Task 8 2 1 2 5

4 Task 4 Task 9 2 1 2 5

5 Task 5 Task 10 2 1 1 4

Fig. 7: The number of questions asked per task is demonstrated. Participantswere expected to answer four or five questions in total for each task: TwoMinMax questions, one Comparison question, and finally one or two questionsrelated to Trend analysis.

works of Tversky et al.[37] and Baudisch et al.[38] implythat the static representation of motion may be more effectivethan animation. Robertson et al. stated that static depictionsof trends appear to be more effective, supporting our findingsabout the density cube visualization, which is actually a staticrepresentation of all the data for a given time period and region.According to the previous work along with our findings, theholistic overview capability of 3D representations suggestedin these studies seems to be valid also for the spatio-temporaldata visualization.

In their experimental study, Hicks et al. [3] report variousperformance levels of 2D graph, 3D plot, and 3D helix visual-izations of e-mail usage log, which they consider as temporaldata. They conducted a laboratory experiment to compare theperformances of these visualizations against three groups oftasks, namely information retrieval, directed, and undirectedcomparisons which can be classified as information lookup, direct comparison, and inverse comparison, respectively,according to [1]. They reported that 3D representations poorlyperformed in terms of overall task completion time comparedto 2D graph. However, in our experiment, we were not able toobserve any significant superiority of 2D representation over3D in terms of overall task completion time. The scenario-wise

p < .1

0

20

40

60

80

Density Map Density Cube

Task

Co

mp

leti

on

Tim

e (s

ec)

(a) Min-max, Scenario 2

p < .1

Density Map Density Cube

Task

Co

mp

leti

on

Tim

e (s

ec)

0

10

20

30

40

50

60

(b) Comparison, Scenario 5

Fig. 8: Exceptional cases in the analysis of task completion time: (a) Taskcompletion time analysis of minimum-maximum questions of the secondscenario: Participants answered the questions faster in minimum-maximumquestion category when using density cube visualization. (b) Task completiontime analysis of comparison questions of the fifth scenario: Participantsanswered the questions faster in comparison question category when usingdensity map visualization.

9

Question Type

Visualization Technique

Means and Standard Deviations

Significance Levels

Trend Density Map M=53.3, SD=18.5

t(12) = 1.283, p > .1 Density Cube M=38.5, SD=31.9

Minimum-Maximum

Density Map M=38.0, SD=17.6 t(12) = .054, p > .1

Density Cube M=37.6, SD=18.6

Comparison Density Map M=21.1, SD=18.6

t(12) = -.276, p > .1 Density Cube M=23.0, SD=22.8

Fig. 9: Statistical results for analysis of overall time measure for each questiontype: No significant difference could be found between the task completiontime measures of the two visualization techniques (all ps > .1) (Means oftask completion times are in seconds.).

Question Type

Visualization Technique

Means and Standard Deviations

Significance Levels

Trend Density Map M=74.62, SD=12.66

t(12) = 2.215, p* < .05 Density Cube M=59.23, SD=21.78

Minimum-Maximum

Density Map M=70.00, SD=19.15 t(12) = 1.443, p > .1

Density Cube M=58.46, SD=18.64

Comparison Density Map M=80.00, SD=20.00

t(12) = 3.482, p** < .01 Density Cube M=58.46, SD=20.75

Fig. 10: Statistical results for analysis of overall correctness measure foreach question type: A zero value means that all users answered the questionswrong, where a value of 100 demonstrates the opposite. Participants answeredthe questions more accurately when they viewed the data with density mapanimation technique for trend and comparison question types. Please note thatp values for trend and comparison questions are significant.

Density Map Density Cube

Co

rrec

tnes

s R

ate

(%)

0

20

40

60

80

100 p* < .05

Fig. 11: Comparison of density map and density cube techniques accordingto overall correctness rate in trend questions: Participants were able to answertrend questions more accurately when they viewed the data with density maptechnique.

task completion times of the two representations also were notsignificantly different. The fact that 2D representation were notable to outperform 3D could potentially be due to the higherdimensionality of our spatio-temporal data compared to 2Dtemporal data used in [3]. Our participants spent more effortwhile analyzing with density map technique probably sincethey had to navigate to the other timestamps of the animation.On the other hand, participants were able to partially view the2D temporal data used in [3]. Density map animation techniqueleads analysts to focus on a representation of data for a unique

Density Map Density Cube

Co

rrec

tnes

s R

ate

(%)

0

20

40

60

80

100 p** < .01

Fig. 12: Comparison of density map and density cube techniques accordingto overall correctness rate in comparison questions: Participants were able toanswer comparison questions more accurately when they viewed the data withdensity map technique.

(a)

(b)

Fig. 13: (a) A frame from density cube visualization: The problematicocclusion in Scenario 4 is depicted. (b) The density map animation of thesame scenario: Occluded regions are viewed more clearly.

moment of time causing the need for traversing back andforth in time dimension of the visualization tool during the

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analysis process, which was also reported in [5]. Kjellin et al.also reported that 2D visualization of spatio-temporal data ledto a better analysis performance particularly when the tasksrequired detect structures in the visualization were invariantto Euclidean and similarity transformations [6]. Nevertheless,we could rarely observe the significant superiority of the 2Drepresentation in terms of either time or accuracy during ourexperiment.

As Hicks et al. reported, 3D plot of the temporal datafacilitates convenience and accuracy with the undirected com-parison tasks [3]. Nevertheless, we did not observe similarresults in our experiments where our participants were ableto make more accurate inferences with density map technique(our 2D implementation). Particularly, they completed the taskswith more accurate answers while they were analyzing thefourth scenario where the data were more cluttered comparedto other scenarios. As seen in Figure 13, locating minimumor maximum usage rates (inverse comparison task) with 3Drepresentation has been a challenging task due to occlusion asreported by both our participants and the experiment results.On the other hand, density map technique as our 2D represen-tation implementation allowed users to delve into the detailsof the data and draw more accurate conclusions. The occlusionproblem inherent in 3D visualizations is more apparent inthe visualization of spatio-temporal data possibly due to theincreased dimensionality compared to temporal data.

Another difficulty with 3D visualization is complexity ofmaking accurate size estimate due to the perspective fore-shortening [4], [39]. Heights and widths that are at differ-ent distances from the user complicates comparing patterns(categorized as behavior comparison in [1]) as suggested by[40]. Our participants were able to locate trends (as behavioridentification in [1]) significantly more accurately with the 2Drepresentation of the location-based services data. This resultis inline with [40], [39], [1] suggesting that the perspectiveprojection effect in 3D representation is also a deterious effectin the visualization of spatio-temporal data.

Subtle regular patterns (e.g. periodically repeating forma-tion as in our fifth scenario and information retrieval tasks in[3]) might aid revealing invaluable inferences with prominentimportance to the analysts. As suggested by our results and[3], 3D techniques might better unveil subtly changing pat-terns over time. However, the choice of 3D technique is ofimportance since not all kinds of 3D representations could aidthe detection of regular patterns without introducing occlusion.

As discussed above, the inferences previously made aboutthe visualization techniques seem to be failing for the visual-ization of the spatio-temporal data. Due to its intrinsic proper-ties, given the findings of our experiment, analysis of spatio-temporal data requires reconsideration of the widely acceptedproperties of 2D and 3D representations. Nevertheless, moreresearch has to be done to investigate how and in which tasks2D and 3D representations are effective.

VI. CONCLUSION

Visualization of spatio-temporal data still remains as adaunting problem not only because of the variability of thecases that could be observed, but also due to the fact thatparticular cases usually require their intrinsic approaches. Even

more, well-known aspects of 2D and 3D representations invisualizations of other kinds of data might not directly beapplied when the data at hand is spatio-temporal. Given thecomplexity of the visualization context space comprising thetask type, data type, and the user role, it is almost infeasibleto cover all research space in order to conclude that 2Drepresentations should be the first option to be considered [4].We conducted an experiment where we treated our participantswith five scenarios defined by field experts each of which isvisualized with both density map and density cube techniques,relatively simple examples of 2D and 3D representations.Based on the findings of our experimental study, along withthe findings of the previous work [6], [3], we claim that thereis enough evidence that 2D representations seems not to besignificantly better than 3D representations while analyzingspatio-temporal data.

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