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Similarity and Distance in Information Spatializations
Sara Irina Fabrikant & Daniel R. Montello
Department of Geography, University of California Santa Barbara,
Santa Barbara, CA 93106, Email: {sara, montello}
Information spatializations are spatial displays—visualizations—of the semantic content of
nonspatial information, such as news stories or library documents. Spatialization relies on
locating information items in a graphic display based on item similarity. When inspecting a
point-display spatialization of news stories, for instance, one would expect to find highly
related news stories clustered together. We have coined this spatialization principle the
distance-similarity metaphor (Montello et al., 2003). The distance-similarity metaphor is
reminiscent of Tobler’s “first law of geography” (Tobler, 1970), which contends that one can
predict the similarity of geographic features based on their distances to other features on the
Earth’s surface. According to the first law, distance determines similarity. In essence the
distance-similarity metaphor is the inverse of the first law of geography, because similarity
typically determines distance in spatializations. Thus we have referred to the “first law of
cognitive geography” (Montello et al., 2003)—people believe that closer features are more
similar than distant features. To the extent that this principle is true, it provides theoretical
justification for the distance-similarity metaphor as a principle of spatialization design.
Both the physical and cognitive versions of the first law of geography depend on
distance. But the information visualization literature gives no insight as to which type of
distance people do employ or should employ when assessing similarity between spatialized
information objects. Our previous studies have produced empirical evidence of how distance
operates in the context of spatializations (Fabrikant, 2003; Fabrikant et al., 2002, 2004;
Fabrikant and Montello, 2004; Montello et al., 2003). In these studies, participants have
rated the similarity between documents depicted as points in spatialized displays. Four types
of spatialization displays have been examined in these studies: (1) point displays, (2) network
displays linking the points, (3) black-and-white regions containing the points, and (4)
colored regions containing the points. In the point displays, participants based judgments of
the relative similarity of two pairs of document points primarily on direct (straight-line or “as
the crow flies”) metric distances between points, but concentrations of points in the display
led to the emergence of visual features in the display, such as lines or clusters, that
considerably moderated the operation of the first law of cognitive geography. In the network
Fabrikant, S. I. and Montello, D. R. (2004). Similarity and Distance in Information Spatializations.
GIScience 2004, Adelphi, MD, Oct. 20-24, 2004: 279-281.
displays, participants based similarity judgments on metric distances along network links,
even though they also had available direct distances across network links and topological
separations (numbers of nodes or links connecting points). In the region displays,
participants based similarity judgments primarily on region membership so that comparison
documents within a region were judged as more similar than documents in different regions,
even if the latter were closer in direct distance. Coloring the regions produced thematically
based judgments of similarity that could strengthen or weaken regional membership effects,
depending on whether region hues matched or not.
In the present study, we directly investigated the relationship of perceived distances to
judged similarities between document points, within various spatialization types. We further
investigated how participants interpret instructions to judge distances when those
instructions do not specify the type of distance; that is, what are participants’ default
interpretations of distance? Like the studies summarized above, we showed participants four
blocks of point, network, black-and-white region, and colored region displays. We asked
one group of participants (n = 24) to judge the relative similarity between two pairs of
document points, just as in our earlier studies. A second group (n = 25) judged the relative
distance between the pairs of document points (distance type being unspecified), and a third
group (n = 24) judged the relative direct or straight-line distance between the pairs.
The study replicates the findings we reported in the papers cited above, but it also
provides more direct and precise information on how similarity judgments relate to default
distance and direct distance judgments. No matter the type of spatialization display, there
are no significant differences between people’s default and direct judgments of relative
distance; people clearly interpret default distance instructions to refer to direct (straight-line)
distance. Also, we find that well-known optical illusions such as the vertical illusion
(Gregory, 1978) and the space-filling interval illusion (Thorndyke, 1981) affect distance
judgments in spatializations, and can thus affect the operation of the first law of cognitive
In point displays, judgments of similarity parallel judgments of direct distance (default
distance too, of course), at least in the ordinal sense that greater distance differences between
the two pairs of document points generally result in greater similarity differences. However,
we find that similarity judgments are much more variable than distance judgments. People
do not judge relative similarities as consistently as they do relative distances, so that two
participants who both see one pair of points as being much closer than the other pair tend
not to agree as much about the relative similarity of the pairs. This suggests that the
distance-similarity metaphor is not as self-evident to people viewing information displays as
is commonly assumed in the information visualization literature (Card et al, 1999). We also
confirm with point displays that emergent point features act oppositely on distance
judgments to how they act on similarity judgments—emergent features make points appear
further apart but more similar. Points belonging to a common emergent feature are
interpreted to be more similar even if they are seen as further apart, essentially a variation on
the region effect.
In network and region displays, judgments of similarity mostly diverge from judgments
of direct distance, as we expected. Replicating our earlier studies, similarity judgments in
network displays correspond to distance along links rather than direct distance across links.
Distance judgments reflect direct distance across links. Likewise, similarity judgments in
region displays mostly correspond to region membership rather than direct distance within
or across regions, and are strengthened or weakened appropriately by region hues. Distance
judgments more-or-less ignore region membership and hue, with the caveat that region
membership in displays of points has been shown to affect distance judgments (Steiner,
2001), and they do so to some degree in our results. Distance across region boundaries
appears a little longer as compared to the same distance within regions. In agreement with
the results for point displays, however, similarity judgments in network and region displays
are more variable than distance judgments.
Our findings provide much needed empirical evidence on the conditions under which
people employ distance when assessing similarity between data objects in spatialized views,
and when they do, which type of distance. That is, the findings provide evidence on the
effectiveness and operation of the distance-similarity metaphor in the design of different
types of spatialization. They may also give initial insight into how the first law of cognitive
geography operates when people explore the similarity of geographic features depicted in
cartographic maps or GIS displays.
Funding by the National Geospatial-Intelligence Agency (NMA-201-00-1-2005) is greatly
appreciated. We thank Marco Ruocco, Richard Middleton and Amy Linker for their
assistance in designing and running the experiments. We are also grateful for David Mark’s
continued insightful input, discussion and brainstorming since the inception of this project.
Card, S. K., Mackinlay, J. D., and Shneiderman, B. (1999). Readings in Information
Visualization. Using Vision to Think, Morgan Kaufmann, San Francisco, CA.
Fabrikant, S. I. (2003). Distanz als Raummetapher für die Informationsvisualierung.
Distance as a spatial metaphor for the visualisation of information. Kartographische
Nachrichten, vol. 52, no. 6: 276-282.
Fabrikant, S. I., and Montello, D. R. (2004). The Distance-Similarity Metaphor in RegionDisplay Spatializations. Manuscript in preparation, University of California, Santa
Fabrikant, S. I., Montello, D. R., Ruocco, M., and Middleton, R. (2004). The DistanceSimilarity Metaphor in Network-Display Spatializations. Manuscript submitted for
publication, University of California, Santa Barbara.
Fabrikant, S. I., Ruocco, M., Middleton, R., Montello, D. R., and Jörgensen, C. (2002).
The First Law of Cognitive Geography: Distance and Similarity in Semantic Space.
Proceedings, GIScience 2002, Boulder, CO: 31-33.
Gregory, R. L. (1978). Eye and Brain: The Psychology of Seeing (3rd ed.). McGraw-Hill, New
Montello, D. R., Fabrikant, S. I., Ruocco, M., and Middleton, R. S. (2003). Spatialization:
Testing the First Law of Cognitive Geography on Point-Spatialization Displays. In:
Kuhn, W., Worboys, M. F., and Timpf, S., (eds.), Spatial Information Theory:
Foundations of Geographic Information Science. Conference on Spatial Information Theory
(COSIT) 2003, Lecture Notes in Computer Science, Springer Verlag, Berlin, Germany:
Steiner, E. B. (2001). Region Representation and Cognitive Distance Distortion. Unpublished
Master of Science, The Pennsylvania State University.
Thorndyke, P. W. (1981). Distance Estimation from Cognitive Maps. Cognitive Psychology,
vol. 13: 526-550.
Tobler, W. R. (1970). A Computer Movie Simulating Urban Growth in the Detroit Region.
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