exploring geovisualization the distance- similarity metaphor

Exploring Geovisualization

34 July/August 2006 Published by the IEEE Computer Society 0272-1716/06/$20.00 © 2006 IEEE

S patial metaphors are a popular approachto visualizing information in such forms as

information worlds, information spaces, and cyberspaces.Spatial metaphors can also describe user interactionswith these products—for example, navigating the WWW,traversing document spaces, and flying over informationlandscapes. These expressions reflect an intuition thatusers can explore and understand abstract informationspaces as if they were real geographic spaces.

According to the distance-similarity metaphor1⎯oneof the most popular spatial metaphors in information

visualization⎯similar entities in adisplay should be placed closertogether because users will interpretcloser entities as being more similar.Explicit or implicit belief in the dis-tance-similarity metaphor justifiesthe notion that more similar docu-ments should be placed near eachother in a spatialized documentarchive. Figure 1 illustrates this prin-ciple. It depicts a portion of theOpen Directory Project (ODP), alarge human-edited Web site direc-tory that uses a treemap spatializa-tion method.2 A treemap’s purposeis to help people visually explorehierarchically organized data, suchas file and directory structures oncomputer operating systems, or var-ious hierarchical databases avail-able through the Internet. Using the

distance-similarity metaphor, Web sites depicted in Fig-ure 1 (red and white dots) whose contents are more sim-ilar are closer together in the display, whereas lesssimilar sites are farther apart.

Another spatial metaphor at work in Figure 1 is theregion metaphor, which reflects the data’s hierarchicalnature. Grouping similar documents into homogeneousthematic zones or clusters emphasizes them visually. Theclusters, spatially semicontiguous zones in various colorshades, show the themes at a particular hierarchical level.Thematically different regions are shaded in different hues(blue and green, for example). We call any spatialized dis-

play that applies the region metaphor a region-display spa-tialization. Cartographers use color hue to depict categor-ical differences in geographic data, such as in soil andelection maps (see the “Background in Spatialization”sidebar on page 36). However, as Figure 1 shows, categor-ically different region pairs—“computers” and “society,”for example—share the same color hues. This violates thecartographic principle for thematic maps that unique sym-bols should denote category membership.

Our previous studies showed how the distance-simi-larity metaphor operates in the context of point,1 net-work,3 and surface display spatializations.4 This articlereports results of our empirical investigations of themetaphor’s effectiveness in region-display spatializa-tions. We try to shed light on how the spatial metaphorof region membership (in monochrome regions) andthe nonspatial metaphor of color hue (that is, coloredregions) can affect the distance-similarity metaphor’soperation in spatialized region displays.

ExperimentsWe conducted two experiments on nonexpert users’

interpretation of the distance-similarity metaphor inregion-display spatializations such as those shown inFigure 1. Each point in the display represents an infor-mation-bearing entity such as a book, Web site, or newsstory. Their organization within regions might or mightnot suggest something to users about their interrelation-ships. In different trials, participants made similarityjudgments while viewing region displays that varied thedistance relationship of two pairs of comparison points(documents), the context provided by the display’sregion structure, and the visual characteristics of theregion boundaries and polygons. We were specificallyinterested in how viewers balance or coordinate theimplications of distance relationships in the displayswith the implications of region membership relation-ships to infer similarity between documents. We alsoinvestigated how hue⎯a nonspatial visual variable⎯in-fluences people’s similarity assessments.

Experiment 1Our first experiment investigated how nonexpert users

interpret simple black-and-white region-display spatial-

Region-display spatializationsrepresent documentsmetaphorically as points withinregions. Semanticinterrelatedness is expressed bysome combination of interpointdistance and regionmembership. In twoexperiments, the authorsinvestigate judgments ofdocument similarity as afunction of these variables.Distance matters, but regionmembership largely determinesjudged similarity; hue furthermodifies it.

Sara Irina FabrikantUniversity of Zurich

Daniel R. MontelloUniversity of California at Santa Barbara

David M. Mark University at Buffalo, SUNY

The Distance-Similarity Metaphorin Region-DisplaySpatializations

izations. We showed research participants computer dis-plays of points overlaid with planar-enforced polygon cov-erage so each point was within exactly one 2D polygonalregion. We explained that the points represented docu-ments, with three of the document points labeled A, 1,and 2 (see Figure 2). We asked participants to comparethe similarity of A and 1 to the similarity of A and 2 usinga 9-point scale. That is, we asked participants to comparethe relative similarity of two pairs of document pointswith various regional membership relations.

Independently of regional membership, the relativelocations of the three comparison points varied so thatthe direct (straight-line) metric distances between thetwo pairs (A and 1 and A and 2) were equal, or differedto varying degrees. In addition to the region trials, thisexperiment also tested other spatialization metaphors,namely points without regions and points within net-works. Other articles report results from trials involv-ing point spatializations1 and results involving networkspatializations.3 Here we focus exclusively on resultsfrom the region displays.

Method. Participating in the experiment were 44students (25 male and 19 female) from an undergrad-uate regional geography class, with a mean age of 21.0years. The test sample represented the desired noviceuser population: most participants weren’t geographymajors; rated their map reading ability as average; hadused maps only occasionally; and had no training in car-tography, geographic information systems (GISs), com-puter graphics, or graphic design.

The participants viewed computer displays createdusing ESRI ArcMap and composed of black points con-tained within regions formed by surface tessellation into2D polygons (both convex and concave) with blackboundaries. These were inspired by region displays sim-ilar to that in Figure 1 but weren’t actual treemap out-puts. Each point represented a single document in a

digital database. In each display, we used red text to labelthree points (A, 1, and 2) for participants to compare forsimilarity (see Figure 2). The display prompted partici-pants to “compare the similarity between document Aand document 1 with the similarity between documentA and document 2.” Participants rated similarity on a 9-point scale ranging left to right from 5 to 1 and then backup to 5 (see Figure 2). In this article, we refer to the pairof documents A and 1 as A:1 and A and 2 as A:2.

Participants viewed 10 region trials in a block (theyalso viewed 30 additional trials involving other displaymetaphors). We varied the region displays to allowcomparisons of distance relationship effects on judged

IEEE Computer Graphics and Applications 35

1 A region-display spatialization.

2 Sample screenshot from a trial in the first experiment showing display,similarity question, and rating scale as they appeared to participants.

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similarity to region membership effects. Either one pairwas closer than the other pair, or they were the samedistance apart. At the same time, either one pair was inthe same region and the third point was in a neighbor-ing region, or all three points were in different regions.We varied graphical elements that we didn’t expect toaffect similarity judgments (such as the absolute loca-tion of a point on the screen) nonsystematically.

Three practice trials at the beginning of the test intro-duced participants to the concept of similarity, the trialstyle, and the response scale format. To avoid primingany particular equivalence between distance and simi-larity, the practice trials prompted nondistance similar-ity judgments (for example, by asking participants tocompare the similarity of images of a dog, cat, and tiger).

Participants also responded to 11 pretest questions abouttheir personal backgrounds, including questions on age,gender, and any visual impairments (including colorblindness), as well as their formal experiences in partic-ular areas such as cartography and GIS. After the maintest questions, participants responded to 28 posttestquestions that asked, for example, how useful theythought each display type was for rating similarity andhow easy it was to judge similarities for each display type.Participants also indicated how they had judged similar-ity and whether the displays reminded them of anything.

We administered the experiment using a Windows2000 Pentium III personal computer. We programmedthe interface using Microsoft Visual Basic 6.0, and pro-jected images onto a back-projection screen using an


36 July/August 2006

Background in SpatializationFew nonexpert spatialization users know how

spatializations are created, and, because spatializations rarelyinclude legends or other traditional map marginalia, theydon’t provide these users with information on how tointerpret spatialized display aspects such as distance, region,or scale.

A fundamental assumption in information visualization isthat spatialized displays work because users can understandthem intuitively.1,2 If this assumption is generally true,understanding the fundamentals of geographic space (themetaphors’ source domain) as understood by display userswill help you construct cognitively adequate informationdisplays based on meaningful spatial metaphors (targetdomains). Location and distance on the Earth’s surface areamong the most fundamental geographic primitives, andboth are reflected in the distance-similarity metaphor.

The distance-similarity metaphor is essentially the inverseof the empirical principle of the first law of geography.3 Thefirst law of geography suggests that you can predict thesimilarity of geographic features based on their relativelocations on the Earth’s surface. You can measure the law’seffect using spatial autocorrelation indices—that is, indicesshowing the strength with which the characteristics of aparticular location in space correspond to surroundinglocations’ characteristics.

Geographic regionalization—the discontinuouspartitioning of space—is a fundamental task that hasoccupied geographers for centuries. Some geographicphenomena vary more or less smoothly over space whileothers exhibit extreme discontinuities, which appears toviolate the first law.4 In fact, regionalization typically dependson the decay of similarity over distance suggested by the firstlaw, insofar as regions consist of spatially proximate andthematically similar locations.5

Figure A shows a common geographic region display inwhich a discrete graphic model renders the more continuousreality. Area-class or categorical-coverage maps can depictregions.

These maps categorize each point in geographic space,and the regions visually emerge. The map in Figure Aclassifies the land area into terrestrial ecoregions representingzones of relatively homogeneous land cover properties.

In this map, same-colored zones identify areas on theEarth’s surface that share similar ecological characteristics, asthe map legend indicates. If the first law were the onlyprinciple operating, we’d expect the land-cover type“deserts and xeric shrublands” at place A to be more similarto the type “tropical and subtropical grasslands” at place 1than to the identical type “deserts and xeric shrublands” atthe more distant place 2. Geographers resolve this apparentcontradiction by considering two additional spatial

primitives: scale and aggregation.The scale at which one is exploringgeographic space will determinehow regular or irregular certaingeographic phenomena appear onEarth’s surface. As a general rule,geographic data exhibit increasedvariability with increasing distance.4

Even if distance remains constant,depending on the context, there aremany ways to aggregate individuallocations into geographic areas.Consequently, you can’t make(error-free) inferences aboutindividual locations’ characteristicsbased only on regionalrelationships⎯an example of thecross-level fallacy.

Map legend

Countryboundaries

Coastline

Habitat typeMangroves

Flooded grasslands

Tropical andsubtropicalgrasslands, andshrublands

Tropical andsubtropicalconiferous forestsWater

Unknown

Other

Tundra

Tropical andsubtropical drybroadleaf forests

Tropical andsubtropical moistbroadleaf forestsSnow, ice,glaciers, and rock

Deserts and xericshrublands

Mediterraneanscrub

A Terrestrial ecoregions.

(Map used with permission of the National Geographic Society)

RGB color projector, generating a 1.8-meter-wide and1.4-meter-high image at 0.6 meters above the floor. Par-ticipants sat at a viewing table 2.7 meters away from thescreen, resulting in an approximately 37-degree hori-zontal viewing angle. They used a standard mouse andkeyboard to answer questions. The system recordedanswers automatically and stored them digitally, includ-ing the time required to make similarity judgments. Wemeasured response time as the elapsed time in milli-seconds between the trial display appearing on thescreen and the participant proceeding to the next trial.

We told participants that the display would present aseries of trials about “diagrams that show an informa-tion collection from our computer database,” which con-tains documents such as news stories, books, and

journal articles, and that the display would present eachdocument as a single point. We gave them no informa-tion on how to judge similarity, and attached no mean-ing to the graphical elements other than the points. Weassured participants that there were no right or wronganswers, and asked them not to waste time, as we wouldtime their answers.

After answering the pretest questions and perform-ing the practice trials, participants responded to themain test trials organized into blocks (the block ofregion displays plus blocks of the other display types),rating all trials of one display type before turning toanother type. Trials within each block appeared in a dif-ferent randomized order for each participant. Finally,participants answered the posttest questions.


The scale issue, combined with the aggregation problem,gives rise to the modifiable areal unit problem (MAUP).4 Forexample, land cover and surface characteristics measured ona soil patch of a few square meters in size (that is, highresolution or fine spatial scale) might not be evident at acoarser (that is, lower-resolution) scale, because thephenomenon might not be distributed evenly over thedomain (in other words, it might exhibit high spatialheterogeneity).

A choropleth map is another type of discrete regiondisplay, arguably one of the most commonly used (andabused) methods of mapping. Contrary to area-class maps,the boundaries delineating regions in a choropleth maparen’t data derived. The boundaries typically separateadministrative regions such as census enumeration units orcountries. Choropleth maps often depict intangible, abstractthemes of the environment, such as health statistics,economic activities, or political events. In terms ofabstraction level, they’re more closely related to informationvisualization displays than to area-class maps (see Figure A).

The choropleth map in Figure B depicts the proportions ofobese people per state in the US in 2000. Obesity rates arerendered with varying color shades—the darker the shade,the higher the ratio of obese people in the state. Spatialautocorrelation (that is, the first law) appears to be evidentin this purely human health and dietary phenomenon, whenmapped at the aggregation level of US states. Contiguousstates in the South seem to have higher rates than adjacentstates in the Midwest, for example. Despite this fact, theobesity rate for Michigan (A) is more similar to Texas (2) thanto Minnesota (1), which is in fact closer.

Humans have great difficulty conceptualizing the n-dimensional reality of, for example, health phenomena.Aggregation and categorization are fundamentalorganizational principles of human cognition6 that extend togeographical phenomena.5 This might explain thepopularity of area-class and choropleth maps, and whypeople seem to have no problem resolving spatialcontradictions when using these maps. In fact, we couldeven conjecture that choropleth maps’ popularity is due totheir high cognitive adequacy⎯that is, they representcontinuous properties of space discretely because this is howhumans make sense of the environment. The question arisesas to whether the interpretation of metaphorical region

displays (such as in Figure 1 in the main article) might differfrom the interpretation of area-class or choropleth maps ofreal-world regions or statistical phenomena. Could peopleinterpret metaphorical displays more variably becausethey’re less tied to assumptions about real space?Considering that people can somehow resolve apparentdistance-similarity contradictions on choropleth maps, howdo they resolve potential contradictions between thedistance-similarity metaphor and other spatial metaphorssuch as aggregation (region membership), or nonspatialmetaphors such as color hue?

References1. S. Card, K. Mackinlay, and B. Shneiderman, “Readings in Informa-

tion Visualization,” Using Vision to Think, Morgan Kaufmann, 1999.2. T.A. Wise, “Visualizing the Non-Visual: Spatial Analysis and Inter-

action with Information from Text Documents,” Proc. IEEE Infor-mation Visualization, IEEE CS Press, 1995, pp. 51-58.

3. W.R. Tobler, “A Computer Movie Simulating Urban Growth in theDetroit Region,” Economic Geography, vol. 46, no. 2, 1970, pp.234-240.

4. P.A. Longley et al., Geographic Information Systems and Science,Wiley, 2005.

5. D.R. Montello, “Regions in Geography: Process and Content,”Foundations of Geographic Information Science, M. Duckham et al.,eds., Taylor & Francis, 2003, pp. 173-189.

6. E.E. Smith and D.L. Medin, Categories and Concepts, Harvard Univ.Press, 1981.

A1

2

Percent obesity(BMI > 30)

13.8 - 17.217.3 - 18.818.9 - 20.720.8 - 21.621.7 - 24.3

B Obesity rates per US state in 2000.

Results. We treated similarity ratings as 9-point inter-val scales by scoring a response of 5 to the far left (A and1 are much more similar) as a 1, a response of 5 to the farright (A and 2 are much more similar) as a 9, and aresponse of 1 in the middle (1 and 2 are equally similar toA) as a 5 (see Figure 2). Thus, a mean rating less than 5.0indicates that participants saw A:1 as more similar, where-as a mean rating greater than 5.0 indicates that they sawA:2 as more similar. We then tested differences from equalsimilarity between A:1 and A:2 with t-scores based on thedifference of the mean similarity rating from 5.0.

To examine the effects of direct distance and regionmembership on similarity judgments for the two pairs ofcomparison documents, A:1 and A:2, we examined sev-eral subsets of trials:

■ One trial depicted the relative distance relationshipsas working against region membership relationships⎯that is, the document in the same region as A wasfurther from A, while the other document was closerbut in a neighboring region (see Figure 3a).

■ Two trials depicted the relative distance relationshipsas equal but not the region membership relationships⎯that is, the documents were the same distance fromA, but one was in the same region while the other wasin a neighboring region (see Figure 3b).

■ One trial depicted the relative distance relationshipsas reinforcing the region membership relationships⎯that is, one document was both closer to and in thesame region as A, while the other document was in adifferent region (see Figure 3c).

■ Three trials depicted both distance and region mem-bership relations as equal (see Figure 3d).

■ One trial examined whether distance would affectsimilarity when region membership was equal⎯thatis, one document was closer to A but region member-ship relationships were equal (see Figure 3e).

■ Finally, two trials examined whether region member-ship proximity would affect similarity⎯that is, bothdocuments were equally close to A and in differentregions from A, but one neighbored A’s region and theother was one region removed (see Figure 3f).

We aggregated these trial subsets (when there wasmore than one trial), reverse-scoring trials when appro-priate so that a mean score above 5.0 would reflectregion membership’s effect on similarity for all trials.

The participants gave the one trial in subset 1 a meansimilarity rating of 5.6, t(43) = 1.74 (not significant).When region membership contradicted distance, itweakened but didn’t eliminate distance’s effect on sim-ilarity.

In contrast, for subset 2, participants gave the two tri-als a mean similarity rating of 6.1, t(43) = 4.89 (p <0.0001). When distance relationships didn’t differenti-ate the pairs of documents, region membership deter-mined similarity.

Participants gave the one trial in subset 3 a mean sim-ilarity rating of 3.4, t(43) = −5.60 (p < 0.0001). In thissubset, distance and region membership relationshipsapparently reinforced each other.

For subset 4, participants gave the three trials a meansimilarity rating of 5.2, t(43) = 1.45 (not significant).When distance and region membership relationshipswere equal, similarity ratings were equal. Ostensibly noother visual variable was available on which to judgesimilarity.

They gave the one trial in subset 5 a mean similarityrating of 4.4, t(43) = −2.50 (p < 0.05). In this subset, dis-tance across region boundaries affected similarity rat-ings when region membership relationships were equal.

Finally, participants gave the two trials in subset 6 amean similarity rating of 5.2, t(43) = 0.88 (not signifi-cant). When distance relationships were equal and nei-


38 July/August 2006

3 Example display types for our first experiment. The mean ratings were (a) 5.6 (not significant); (b) 6.1 (p < 0.0001); (c) 3.4 (p <0.0001); (d) 5.2 (not significant); (e) 4.4 (p < 0.05); and (f) 5.2 (not significant).

(a) (b) (c)

(d) (e) (f)

ther document shared a region with the comparisondocument, similarity ratings were again equal. Appar-ently being one region removed was no different frombeing more than one region removed; topological prox-imity between regions didn’t operate according to aproximity/similarity metaphor.

We compared response times and similarity ratingsas a function of trial block order and gender. Participantsresponded significantly more slowly during the firstblock of region trials (mean of 16.5 seconds per trial)than during the second (10.2 seconds per trial) or thirdblocks (11.4 seconds per trial)⎯F(2, 41) = 4.75 (p <0.05). As we expected, however, mean similarity ratingsdidn’t differ as a function of trial block order⎯F(2, 41)= 2.07 (not significant). Response times also didn’t sig-nificantly differ as a function of participant gender:women responded in an average of 11.9 seconds pertrial, and men an average of 11.7 seconds per tri-al⎯t(42) = 0.11. Participant gender didn’t influencemean similarity ratings either: women rated the pairsof comparison documents a 5.1, on average, while menrated them a 4.9, t(42) = 0.97 (not significant).

Experiment 2Our second experiment attempted to replicate and

extend the results we obtained with region-display spa-tializations in our first experiment. First, we wanted tofind out if our finding from the first experiment aboutregion membership’s effect on similarity judgments,over and above direct distance’s effect, would replicatewith a new set of black-and-white displays viewed by anew set of participants. We also wanted to examine howcolor hue affected judgments of similarity in region dis-plays. We expected that region hue could compound orweaken region membership’s effects. For instance, weexpected that documents in separate regions might stillbe seen as similar if the two regions were of the same oreven similar hues.

We varied hue in two ways. In one type of trial, wecolored all regions in one of four hues, with the provisothat neighboring regions were always of a different hue.Thus, several regions were the same hue in these dis-plays. We call these classed hues because we suspectedthat the hues might suggest to users membership in athematic class. In the other type of hue trial, we coloredeach region a (somewhat) different hue, so the numberof hues in the display equaled the number of regions.We call these unclassed hues.

In addition to region hue, we also used a black bor-der around regions. On half of the hue trials, the coloredregions were surrounded by a black border (like the bor-ders in the black-and-white trials); on the other half, thecolored regions simply abutted each other, with thecolor transitions signaling region boundaries. This way,we could determine whether clear borders (like thosein the black-and-white trials) were necessary for theregion effect to occur, or at least whether clear borderswould strengthen or otherwise influence any region orhue effects.

Finally, we varied the size of the viewed displays. Wereported elsewhere1 that participants who viewed pointdisplays projected at the relatively large size used in the

first experiment rated similarity differences betweenthe two pairs of documents more strongly than did par-ticipants who viewed displays projected at a smaller size.Here we examine whether display size influences ratedsimilarity in region displays.

Method. Participants in this experiment were 48 stu-dents (27 male and 21 female) from an undergraduateintroductory human geography class, with a mean ageof 21.5. None had participated in the first experiment.They also received a small amount of course credit inreturn for their participation. We again judged the testsample to be a good sample of the desired novice userpopulation.

As in the first experiment, participants viewed com-puter displays composed of different graphical ele-ments. However, this experiment tested only region andpoint displays (other work discusses the point displaytrials1). All displays included black points, with threepoints (labeled A, 1, and 2) described as documents tobe compared for similarity. Participants performed thesame similarity judgments using the same scale as in thefirst experiment.

We varied the region displays according to three vari-ables:

■ hue presence (black-and-white versus coloredregions),

■ border (black borders versus no borders, applied onlyto colored regions), and

■ hue class (classed versus unclassed hues, applied onlyto colored regions).

We presented participants with 78 region trials,which, with the 16 point trials reported elsewhere, gaveus a total of 94 trials. We divided the 78 region trials into10 trials of black-and-white regions (like those in thefirst experiment) and 68 trials of colored regions. Wedivided the 68 colored regions into 34 with borders and34 without borders; and the two sets of 34 regions into24 with classed hues and 10 with unclassed hues. Weused more classed-hue than unclassed-hue trialsbecause the classed trials offered more characteristicsto vary. In particular, we could contrast trials with com-parison points in different regions of the same hue totrials with points in regions of different hue in variousways. Figure 4a (next page) shows a bordered unclasseddisplay; Figure 4b shows an unbordered unclassed dis-play; and Figure 4c shows a bordered classed display.

We organized the region trials into three blocks accord-ing to the hue presence and border variables. We didn’tuse the hue class to structure trial blocks; rather, we ran-domly intermixed classed and unclassed hue trials with-in their respective blocks (bordered or unbordered).

Participants responded to five practice trials in thisexperiment, similar to those from the first experimentbut including two dealing with color. After the main testtrials, participants answered 56 posttest questions,including the 11 questions from the first experimentabout their personal backgrounds. We adapted the addi-tional posttest questions from the first experiment toaccount for the new display types.


We used the same equipment and setup as in the firstexperiment with one important addition. In this exper-iment, we varied the displays’ projected image size. Halfof the participants viewed a small image from a distanceof 1.6 meters, projected to be 0.6 meters wide and 0.4meters high at a height of 1.2 meters above the floor.This resulted in a horizontal viewing angle of approxi-mately 20 degrees. The other half of the participantsviewed a large image, projected (as in the first experi-ment) to be 1.8 meters wide and 1.4 meters high at 0.6meters above the floor. Viewed from 2.7 meters in frontof the screen, the horizontal viewing angle was approx-imately 37 degrees. We chose these sizes to provide areasonable size contrast.

We tested participants as in the first experiment, pre-senting the three region blocks (black-and-white, bor-dered colored, and unbordered colored), along with theblock of point trials, in counterbalanced orders. We pre-sented trials within blocks in different random ordersfor each participant.

Results. We again treated similarity ratings as 9-point interval scales, so that a mean rating less than 5.0indicates that participants saw A:1 as more similar,while a mean rating greater than 5.0 indicates that theysaw A:2 as more similar. We first examined the black-and-white trials to determine whether we replicated ourfindings from the first experiment on the effects of directdistance and region membership on similarity judg-ments. We aggregated trials into subsets as in the firstexperiment’s analysis.

For subset 1, one trial depicted the relative distancerelationships as working against region membershiprelationships. Participants gave the trial a mean simi-larity rating of 6.5, t(47) = 6.54 (p < 0.0001). In thisexperiment, when region membership contradicted dis-tance, region membership’s effect weakened the dis-tance effect so much that it essentially eliminated it.

For subset 2, one trial depicted the relative distancerelationships of the two pairs as equal, but only one ofthe comparison documents was in the same region asA. Participants gave this trial a mean similarity rating of6.6, t(47) = 6.54 (p < 0.0001). Region membership againdetermined similarity when distance relationships did-n’t differentiate the pairs of documents.

For subset 3, one trial depicted the relative distancerelationships as reinforcing region membership relation-ships. Participants gave this trial a mean similarity rat-

ing of 6.9, t(47) = 7.85 (p < 0.0001). Again, distance andregion membership relationships reinforced each other.

For subset 4, two trials depicted both distance andregion membership relations as equal. Participants gavethese trials a mean similarity rating of 4.9, t(47) = −1.77(not significant). Again, when distance and region mem-bership relationships were equal, similarity ratings wereequal.

For subset 5, five trials examined whether distancewould affect similarity when region membership wasequal. We used several trials to examine this effect herebecause in the first experiment, we based our findingthat distance mattered when region membership wasequal on only one trial. Participants gave the five trialsa mean similarity rating of 3.9, t(47) = −8.71 (p <0.0001). Clearly, distance across region boundariesaffected similarity ratings when region membershiprelationships were equal.

Finally, this experiment had no subset 6 trials con-trasting region proximity while holding distance equal.

In sum, results for the monochrome region trials inthe second experiment are largely consistent with theresults of the first. That is, we again show that regionmembership in region-display spatializations largely, butnot completely, overrides distance’s effects on similarity.

We next analyzed the colored region displays. We start-ed with the unclassed trials because they presented thesame 10 display patterns as the black-and-white trials,with the addition of unique colors to each region. We firstanalyzed bordered trials, as they were most similar to theblack-and-white trials. We aggregated bordered unclassedtrials into the same subsets as the black-and-white trials.

Participants gave one subset 1 trial a mean similarityrating of 6.7, t(47) = 5.55 (p < 0.0001). As with black-and-white displays (at least in the second experiment),when region membership contradicted distance, it elim-inated distance’s effect on similarity.

Participants gave one subset 2 trial a mean similarityrating of 7.3, t(47) = 11.51 (p < 0.0001). Again, regionmembership determined similarity when distance rela-tionships didn’t differentiate the pairs of documents.

The one trial in subset 3 depicted the relative distancerelationships as reinforcing the region membership rela-tionships. Participants gave that trial a mean similarityrating of 7.8, t(47) = 14.86 (p < 0.0001).

The two trials in subset 4 depicted distance and regionmembership relations as equal. Participants gave thesetrials a mean similarity rating of 5.0, t(47) = −0.53 (not


40 July/August 2006

4 Example display types for the second experiment: (a) bordered unclassed display, (b) unbordered unclassed display, and (c) bordered classed display.

(a) (b) (c)

significant). Again, when distance and region member-ship relationships were equal, similarity ratings wereequal.

Finally, for subset 5, five trials examined whether dis-tance would affect similarity when region membershipwas equal. Participants gave the five trials a mean sim-ilarity rating of 4.5, t(47) = −3.57 (p < 0.001). Clearly,distance across region boundaries again affected simi-larity ratings when region membership relationshipswere equal.

Directly comparing these effects to those found in theblack-and-white trials revealed that filling the regionswith colors strengthened region membership’s effectson similarity ratings. Although trial subset 1 didn’t dif-fer much between the black-and-white and colored ver-sions, subsets 2 and 3, which revealed significant regioneffects with black-and-white regions, did so even morestrongly with unclassed colored regions. Repeated-mea-sures comparisons of black and white with borderedunclassed colored trials were significant for subsets 2and 3: t(46) = 3.05 (p < 0.01) and t(46) = 3.63 (p <0.001). Trial subset 5 showed a distance effect on simi-larity when region membership was equal; however, theeffect was significantly weaker with bordered unclassedcolored regions: t(46) = 4.77 (p < 0.0001). Essentially,colored regions overrode distance relationships morethan did black-and-white regions, perhaps because colorprovided a stronger differentiation between regions.

The absence of borders around the unclassed coloredregions didn’t weaken or otherwise modify the regioneffects. Mean similarity ratings for unbordered trialswere close to those for bordered trials and didn’t signif-icantly differ for any trial subset. (Because of a designerror, one unbordered trial was displayed with differ-ent color hues than its corresponding bordered trial, butwe excluded these trials from this analysis.) A repeat-ed-measures analysis of all unclassed trials revealed thata border had no main effect on similarity ratings (F(1,47) = 1.92 (not significant)), nor did an interaction existbetween the border’s presence and specific questions(F(8, 40) = 0.85 (not significant)).

Finally, we analyzed the results for the classed col-ored region displays. We again analyzed bordered tri-als first. The spatial patterns of five of the classed trialswere copies of five of the unclassed trials. We coulddirectly compare these trials because they displayed twoof the three comparison documents as being within thesame region and the third as being in another region ofa different hue. In fact, these classed trials produced vir-tually the same effect pattern as did the correspondingunclassed trials. There was neither a main effect ofclassed-unclassed (F(1, 47) = 2.50 (not significant)) noran interaction between classed-unclassed and specificquestions (F(4, 44) = 0.92 (not significant)). Hence, theuse of a classed color scheme per se apparently didn’talter similarity judgments, as compared to an unclassedcolor scheme. As we’ll show, however, classed colorschemes did make a difference when documents beingcompared were in different regions that could be of thesame hue.

The remaining 19 classed trials with borders dis-played the three comparison documents in threeregions. (We didn’t test pairs of documents within thesame region in these trials, because documents in thesame region would necessarily be in regions of the samehue.) In some of these trials, two of the three regionswere the same hue; in others, all three were differenthues. As we did with the black-and-white and unclassedtrials, we aggregated these remaining classed trials intosubsets of trials that displayed the two pairs of compar-ison documents⎯A:1 and A:2⎯according to similarrelationships (in this case, relationships of relative dis-tance and relative region hue). We used five subsets:

■ One trial depicted the relative distance relationshipsas equal, but only one comparison document’s regionhue matched A’s region hue (see Figure 5a).

■ Four trials depicted the relative distance relationshipsas working against region hue relationships⎯that is,the document closer to A was in a region of a differ-ent hue, whereas the other document was in a regionof the same hue as A (see Figure 5b).


5 Examples of bordered and classedcolored display types for the secondexperiment. For these display types, themean ratings were: (a) 6.8 (p < 0.0001),(b) 5.7 (p < 0.01), (c) 7.4 (p < 0.0001), (d) 5.0 (not significant), and (e) 4.1 (p <0.0001).

(a) (b) (c)

(d) (e)

■ Four trials depicted the relative distance relationshipsas reinforcing the region hue relationships⎯that is,one document was both closer to A and in a region ofthe same hue (see Figure 5c).

■ Two trials depicted distance and region hue relationsas equal (see Figure 5d).

■ Eight trials examined whether distance would affectsimilarity when region hue was equal⎯that is, onedocument was closer to A but neither document wasin a region of the same hue as A (see Figure 5e).

We aggregated these trial subsets (when there wasmore than one trial), reverse scoring trials when appro-priate so that a mean score above 5.0 would reflect theeffect of region hue on similarity for all trials.

Participants gave one subset 1 trial a mean similar-ity rating of 6.8, t(47) = 8.51 (p < 0.0001). When we held distance across regionsequal, participants interpretedmatched region hues as indicat-ing greater similarity.

For subset 2, four trials depict-ed the relative distance relation-ships as contradicting region huerelationships. Participants gavethose trials a mean similarity rat-ing of 5.7, t(47) = 2.80 (p < 0.01).Thus, they were more likely tointerpret matched region hues asindicating similarity than theywere closer distance (across regions), although anexamination of individual responses showed that sev-eral participants saw distance as equally or more rele-vant to similarity in this condition.

Participants gave the four trials in subset 3 a meansimilarity rating of 7.4, t(47) = 15.43 (p < 0.0001). Dis-tance and region hue relationships clearly reinforcedeach other.

Participants gave the two trials in subset 4 a meansimilarity rating of 5.0, t(47) = −0.52 (not significant).When distance and region hue relationships were equal,similarity ratings were equal.

Finally, for subset 5, participants gave the eight trialsa mean similarity rating of 4.1, t(47) = −7.70 (p <0.0001). Distance across region boundaries affectedsimilarity ratings when region hue relationships wereequal.

As with the unclassed colored regions, the absence ofborders around the classed colored regions had noobservable effect on similarity ratings. Mean similarityratings for unbordered trials were similar to those forbordered trials, and didn’t significantly differ for any ofthe trial subsets. (Because of a design error similar tothat made on the unclassed trials, one unborderedclassed trial was displayed with different color hues thanits corresponding bordered trial. We excluded both tri-als from this analysis.) A repeated-measures analysis ofall classed trials revealed that the border’s presence hadno main effect on similarity ratings⎯F(1, 47) = 0.22(not significant)⎯nor an interaction between the bor-der’s presence and specific questions⎯F(22, 26) = 1.17(not significant).

Response time and similarity as a functionof block order and gender. As in the first experi-ment, we compared response times as a function of trialblock order and gender. Participants responded to black-and-white region trials significantly more slowly whenthey occurred during the first trial block (mean of 15.8seconds per trial) than during the second (9.2 secondsper trial), third (8.1 seconds per trial), or fourth blocks(7.0 seconds per trial)⎯F(3, 44) = 8.38 (p < 0.001). Aswe expected, mean similarity ratings didn’t differ as afunction of trial block order, F(3, 44) = 1.05 (not signif-icant). Response times also didn’t significantly differ asa function of participant gender: women responded inan average of 10.6 seconds per trial, men in an averageof 9.4 seconds per trial, t(46) = 0.75 (not significant).Participant gender didn’t influence mean similarity rat-ings either: on average, women rated the pairs of com-

parison documents a 4.5,whereas men rated them a 4.6,t(46) = −0.74 (not significant).

On colored regions, whetherbordered or unbordered, partic-ipants responded to trials signif-icantly more slowly when theyoccurred during the first trialblock (mean of 10.5 seconds pertrial, both for bordered andunbordered regions) than duringthe second (8.3 and 9.9 secondsper trial), third (8.6 and 7.7 sec-

onds per trial), or fourth blocks (7.2 and 7.2 seconds pertrial). These differences didn’t reach statistical signifi-cance, however⎯F(3, 44) = 1.78 and 2.14. As we expect-ed, mean similarity ratings didn’t differ as a function oftrial block order for either bordered or unborderedregions⎯F(3, 44) = 0.51 and 1.29 (not significant).

Response times also didn’t significantly differ as afunction of participant gender: women responded in anaverage of 8.6 seconds per trial on bordered regions and9.5 seconds per trial on unbordered regions; menresponded in an average of 8.8 seconds per trial on bor-dered regions and 8.3 seconds per trial on unborderedregions. Neither of these reached statistical significance,t(46) = −0.22 and 1.00.

Participant gender didn’t influence mean similarityratings either. On average, both men and women ratedthe pairs of comparison documents on bordered regionsa 4.5, t(46) = 0.03 (not significant). Women rated thepairs of comparison documents on unbordered regionsa 4.4, on average, whereas men rated them a 4.6, t(46)= −1.00 (not significant).

Display scale. As we report elsewhere,1 the rela-tionship between distance and similarity (as expressedby a correlation) in point displays was significantlystronger with the large display than with the small dis-play. To test the possible effect of display size on judgedsimilarity in region displays in the second experiment,we compared the size of mean differences reported inthe two display size conditions. We tested each groupof trials (black-and-white, unclassed colored, andclassed colored) in repeated-measures analyses with


42 July/August 2006

The relationship between

distance and similarity in point

displays was significantly

stronger with the large display

than with the small display.

display size as a between-participant factor, and ques-tion and border (when appropriate) as repeated factors.The main effect of display size didn’t reach significancefor any trial group, nor did any size interactions withquestion or border.

In point-display spatializations, similarity is essential-ly a matter of metric distance, with some exceptionssuch as clusters. Changes in display scale directly affectapparent metric size and distance relationships. How-ever, as our empirical results suggest, image scale seemsless important in region-display spatializations becauseregion membership, region hue, and so on largelyaccount for similarity, and not metric distance.

Region enclosureRegion enclosure relations influence participants’

judgments of the relative similarity of document pointsin an information display.When interpoint distanceswere equal but one pair wasin the same region and theother pair spanned a regionboundary, most participantsused region enclosure as abasis for making relative sim-ilarity judgments. This wasthe case for monochrome dis-plays and also for multihueddisplays, whether or not bor-der lines explicitly markedthe region boundaries. When region enclosure relationscontradicted interpoint distances, the region relationsweakened, cancelled, or even reversed similarity judg-ments that participants likely would have made basedon interpoint distances alone. Also, in colored displays,when all three points were in different regions, pointsin regions of the same color were judged to be more sim-ilar, other things being equal. These results aren’t thatsurprising given knowledge of established principles ofcartographic design. However, the results we report hereare the first to confirm these design principles empiri-cally in the context of point similarity judgments on dia-grams divided into regions.

In cartographic displays of real geographic informa-tion (that is, information about Earth’s surface), geo-graphic reality at least partially determines thelocations of points and region boundaries. Cartogra-phers have some flexibility in their choice of colors, lineweights, and other design elements, but not much flex-ibility in feature or boundary positions. The resultsreported here thus both confirm cartographic designpractice and suggest possible unintended consequencesof some design choices. For example, users might inter-pret similar or identical colors of regions on politicalmaps as indicating semantic similarity, even if that isn’tthe designer’s intention. The design implications of thisstudy are more substantial in the context of informa-tion displays where nonspatial information is spatial-ized for presentation, and where networks, regions, andeven positions are adjustable design elements ratherthan representations of features with positions in thereal world.

Design implications for region displayspatializations

Together with empirical findings from point, network,and surface display spatializations, our experimentalresults on region displays fully support a theoretical spa-tialization framework grounded on GIScience, includingcognitive, perceptual, and experiential principles.5 Ourresults confirm that the spatial metaphor region is a use-ful concept for depicting clusters of similar documentsin an information space. The results also suggest thatthe interpretation of metaphorical region displays oper-ates akin to regions depicted in area-class maps or choro-pleth maps of real-world phenomena. If interpointdistance is meant to fully capture and present documentsimilarity, display designers should avoid adding regionsto the display, because, as this study’s results clearlydemonstrate, region enclosure relations and region

color similarity will modify judg-ments that participants would havemade based on interpoint distancesalone. If, however, similarity indicat-ed by the display is meant to be of amore qualitative nature, addingregions around groups of similarpoints and coloring semanticallysimilar regions with similar hueswill reinforce the similarity judg-ments that viewers are likely tomake from point displays alone.Regions help structure space and

can help users navigate through a hierarchically orga-nized information space. However, if similarity is meantto be communicated entirely via regional membership,our results suggest that interpoint distances continue toinfluence perceived similarity even in region displays.

Our results for the nonspatial color hue metaphorconfirm the pattern found for colored network-displayspatializations3 in suggesting the utility of long-estab-lished cartographic design principles for spatialization.Cartographers use color hues to depict qualitativeinformation about geographic features. Hue differ-ences are mapped onto categorical differences (thatis, at the nominal level of measurement) such as soiltypes, land-use zones, or animal habitats. Haphazarduse of color could lead to misinterpretation⎯for exam-ple, if the same color represents different categories(as Figure 1 shows). Designers of the region spatial-ization in Figure 1 might have attempted a colorscheme typically found on political maps, where asmall number of hues (typically four or five) areassigned to countries such that no two adjacent coun-tries have the same color. In this example, hue is sim-ply used for aesthetics and perceptual distinctiveness,and doesn’t signify a semantic category membership.According to our findings, we suggest redesigning thedisplay using a set of distinctly different color hues forthe hierarchy’s top-level categories and varying colorsaturation or value within the chosen hue to show dif-ferent depth levels within the hierarchy branches. Acolor selection tool such as the ColorBrewer (seehttp://www.colorbrewer.org) provides cartographi-cally sound color schemes.


Our results confirm that the

spatial metaphor region is a

useful concept for depicting

clusters of similar documents in

an information space.

Designers can also use region labels as graphic sym-bols to reinforce category membership, as the extract ofa news-article spatialization in Figure 6 shows. Carto-graphically informed labeling can help reduce the needfor additional map legends.

Conclusion and outlookTaken with our earlier results, our findings for points

within regions provide a comprehensive picture of howother information display design elements influencejudgments of the similarities of pairs of points in suchdisplays. Interestingly, in point displays, clustering oralignment of groups of points has some effect on simi-larity judgments, introducing into the visual field whatamount to implicit lines or regions. Thus, avoiding net-works or regions won’t necessarily avoid network andregion effects, because point patterns can induce line-like and region-like effects. Color hue can enhance theregion effect or hinder it. These examples demonstratehow the use of cartographic design principles providesa sound design framework for better controlling percep-

tual and cognitive effects of design choices for spatializa-tion displays. ■

References1. D.R. Montello et al., “Spatialization: Testing the First Law

of Cognitive Geography on Point-Spatialization Displays,”Spatial Information Theory: Foundations of GeographicInformation Science, Conf. Spatial Information Theory(COSIT), W. Kuhn, M.F. Worboys, and S. Timpf, eds., LNCS2205, Springer-Verlag, 2003, pp. 335-351.

2. B. Johnson and B. Shneiderman, “Treemaps: A Space-Fill-ing Approach to the Visualization of Hierarchical Informa-tion Structures,” Proc. 2nd Int’l IEEE Visualization Conf.,IEEE CS Press, 1991, pp. 284-291.

3. S.I. Fabrikant et al., “The Distance-Similarity Metaphor inNetwork-Display Spatializations,” Cartography and Geo-graphic Information Science, vol. 31, no. 4, 2004, pp. 237-252.

4. S.I. Fabrikant, “Distanz als Raummetapher für die Infor-mationsvisualisierung [Distance as a Spatial Metaphor forthe Visualization of Information],” KartographischeNachrichten, vol. 52, no. 6, 2003, pp. 276-282.

5. S.I. Fabrikant and A. Skupin, “Cognitively Plausible Infor-mation Visualization,” Exploring Geovisualization, J. Dykes,A.M. MacEachren, and M.J. Kraak, eds., Elsevier, 2005,pp. 667-690.

Sara Irina Fabrikant is an associ-ate professor and head of the Geo-graphic Visualization and AnalysisDivision in the Department of Geog-raphy at the University of Zurich. Herresearch interests include geographicinformation visualization, GIS scienceand cognition, and graphical user-

interface design, including dynamic cartography andhypermedia. Fabrikant has a PhD in geography from theUniversity of Colorado-Boulder. Contact her at [email protected]

Daniel R. Montello is a professorin the Department of Geography andan affiliated professor in the Depart-ment of Psychology at the Universityof California at Santa Barbara. Hisresearch interests include spatial andgeographic perception, cognition, andbehavior, including cognitive issues in

cartography and GIS. Montello has a PhD in environmen-tal psychology from Arizona State University.

David M. Mark is a professor in theDepartment of Geography at the Uni-versity at Buffalo, SUNY, where healso is director of the Buffalo office ofthe US National Center for Geograph-ic Information and Analysis. Hisresearch interests include geospatialontology, spatial cognition, geograph-

ic information science, and indigenous GIS. Mark has aPhD in geography from Simon Fraser University.


44 July/August 2006

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6 Region spatialization of news stories with region labels.

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publishes over 150 conference publications a year.

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publishes over 150 conference publications a year.

For a preview of the latest papers in your field, visit

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