The “Map” in the mental map: Experimental results in dynamic graph drawing

https://doi.org/10.1016/j.ijhcs.2013.08.004Get rights and content

Highlights

  • We summarize experiments that test mental map preservation in dynamic graph drawing.

  • No experiment has found a positive effect of the mental map on undirected graphs.

  • More than 3–5 elements should be involved to offload mental effort to the diagram.

  • Tasks that require orientation in the information space should be tested.

  • Mental map preservation may be more related to task than previously thought.

Abstract

Preserving the mental map is frequently cited by dynamic graph drawing algorithm designers as an important optimization criterion. There have been a number of definitions for mental map preservation and many different algorithmic approaches to drive dynamic graph drawing to satisfy these definitions. One of the most frequently used definitions is that of Coleman and Parker where “the placement of existing nodes and edges should change as little as possible when a change is made to the graph.” A number of experiments have been run to test the effectiveness of this definition from a usability perspective. To date, no experiment has found conclusive evidence that supports the effectiveness of the mental map in the comprehension of a dynamic graph series. In this paper, we summarize the experiments conducted on this definition of mental map preservation and provide recommendations to designers and researchers to fully understand when the mental map supports user tasks.

Introduction

This paper summarizes and critiques empirical results relating to the problem known as preserving the mental map in dynamic graph drawing. A graph consists of a set of nodes V, together with a set of edges E which represent relationships between the nodes. Graph drawing is the process of assigning co-ordinates to the nodes so that a node-link representation of the graph can be depicted in a two-dimensional plane. Dynamic graph drawing deals with graphs that evolve over time, whereby the structure of the graph changes as nodes and edges are added or removed. The dynamic graph is often divided into several timeslices that are snapshots of the graph at specific time intervals. The algorithms assign coordinates to the nodes present in these timeslices. Several algorithms have been proposed to draw an evolving graph with data structured in this way (Brandes et al., 2011). These algorithms have many application areas, including but not limited to: sociology (van Duijn et al., 2003) and social networks (Brandes et al., 2011), software engineering (Burch et al., 2011), computer networks (Boitmanis et al., 2007), social media analysis (Java et al., 2007, Kwak et al., 2010), and systems biology (Barsky et al., 2008).

In dynamic graph drawing, it is generally assumed that the presentation of the information should be as stable as possible as the graph evolves. This preservation of the mental map feature is often cited as a desired criterion for a successful dynamic graph drawing algorithm. Intuitively, the idea of mental map preservation is to keep the positions of the nodes as stable as possible as the graph changes. It is conjectured that drawing stability allows the person interpreting the diagram to offload cognitive effort by using an external visual representation instead of relying solely on memory and supports their ability to comprehend the information space – in this case, the dynamic graph. Thus, preserving the mental map is closely related to cognitive maps in psychology and overviews in information visualization.

The notion of a mental map has a long history in other disciplines, such as geography (Kitchin, 1994) and psychology with varied names for the same idea. Tolman (1948) provides one of the first definitions of what he calls a cognitive map to describe how rats, and by analogy humans, navigate an environment. The definition of mental map in this research is an internal representation of the physical environment to enable navigation. Maps are entities that externalize this information and help support this internal representation so that the human does not need to rely entirely on memory for the full representation of an object or physical space.

In the field of psychology, research into these internal representations has existed for many years using varied terminology do describe this concept. Johnson-Laird (1983) proposed the existence of mental models of logical propositions that facilitate reasoning and explanation, and subsequent research has mostly furthered this area along these lines (eg. Stenning, 2002). Shepard and Metzler (1971) demonstrated that internal models of diagrams were not, however, internally represented as propositions, but were instead mental images. Kosslyn and Pomerantz (1977) nicely summarize some of the central ideas of this theory. Quoting from this paper, we can see the possible limitations that humans have when generating mental models and the need to externalize them:

“… An image is a spatial representation like that underlying the experience of seeing an object during visual perception. These images may be generated from underlying abstract representations, but the contents of these underlying representations are accessible only via generation of a surface (experienced) image. … Only a finite processing capacity is available for constructing and representing images. This limits the amount of detail that may be activated at any one moment.”

Palmer (1978) states that we cannot know the actual form of this internal representation and defines informational equivalence as the extent that two representations (internal and/or external) embody the same information. Subsequent research has investigated the use of such internal diagrammatic representations in reasoning/problem solving (Glasgow et al., 1995, Stenning, 2002), and the benefit of externalizing these models for learning (Cox and Brna, 1995, Ainsworth, 2006) and thinking (Blackwell, 2001, Brna et al., 2001). Asking users to externalize their mental models, usually by drawing them, provides a way we can observe the form of these models, acknowledging that the transcription process may be imprecise (Palmer, 1978).

In the field of psychology, most of this research has concentrated on cognitive models of physical environments or objects. In the field of information visualization and graph drawing, the internal representation is not based on objects in the physical world, but rather it is based on data in an abstract information space. Still, the concept of building a cognitive map, or mental model, of this information space is still relevant as users of these systems would like to understand the information landscape. Thus, it is reasonable to discuss the notion of cognitive models of an information space for the purposes of visualization. These models are related to the concept of overviews which can be viewed as an external representations, or maps, of data. The famous information seeking mantra of Shneiderman (1996) “Overview first, zoom and filter, then details on demand” emphasizes the need for supporting the cognitive map, or this internal representation, when browsing information. Hornbaek and Hertzum (2011) generalize Shneiderman's notion of an overview and provide a survey of overviews as used in information visualization research. The survey finds qualitative support for overviews but impact on task performance is less clear.

For dynamic data, the concept of mental models and cognitive maps is further complicated by the fact that the information space is not static and evolves over time. However, there is still a need for the internal representation to provide an overview that is consistent over time. This concept of information stability is equivalent to the concept of preserving the mental map in dynamic graph drawing. It is not enough for algorithm designers to include a mental map preservation feature in their dynamic graph layout algorithm; the effect of these features in supporting the comprehension of the information needs to be evaluated, usually through human-centred, empirical studies. These studies have typically been conducted by researchers in information visualization and graph drawing community versed in methods for empirically evaluating readability and usability (Purchase et al., 1996, Purchase, 1997, Ware et al., 2002, Tory et al., 2007) and memorability (Lam et al., 2006, Tory et al., 2009) of techniques in these domains. In the human–computer interaction experiments conducted on dynamic graphs, a common and repeated conclusion was that no significant positive effect was found between conditions that preserved the mental map and conditions that did not, over a variety of different tasks in the area of undirected, dynamic graph drawing. In other words, choosing to preserve the mental map did not improve the performance of participants in the experiment, either in terms of response time or error rate, when compared to a representation of the dynamic graph whereby each and every timeslice was drawn independently (Purchase and Samra, 2008, Saffrey and Purchase, 2008, Archambault et al., 2011, Archambault and Purchase, 2012). These results therefore contradict the intuition of algorithm designers who expect that the preservation of the mental map should, in some way, improve the ability of the user to understand changes to a dynamic graph.

The principal contribution of this paper is an examination of these experiments in an attempt to understand why this surprising result has been replicated in several experiments and to provide recommendations to designers and researchers alike. We seek some inspiration from the fields of psychology and geography to explain why these previous experiments have not revealed a benefit for the preservation of the mental map. We believe that in order to benefit from mental map preservation, tasks should rely heavily on the map properties of the dynamic data: tasks that require orientation and navigation through the data. These tasks rely heavily on external representations of the dynamic graph because they are too complicated for the participant to accomplish relying solely on their cognitive map of the information space. This notion is difficult to define in graph drawing as dynamic graphs are often abstract entities.

In this paper, we define this map as properties of the dynamic graph drawing that help support the orientation of the user in the data. These properties can differ from readability and memorability as they rely on the ability of the user to navigate and locate information in the larger data set relative to other information. Implicit in this definition, we suggest that for the mental map to be beneficial, the number of data elements considered in the tasks tested in our experiments should be large. This summary focuses on experiments that deal with human factors in dynamic graph drawing rather than algorithmic considerations. Further discussion of algorithmic considerations and other aesthetic criteria can be found in book chapters and surveys on the topic (Branke, 2001, Brandes et al., 2011).

Section snippets

The mental map and dynamic graph drawing

In Section 2.1, we precisely define the types of dynamic graphs considered in this paper. Section 2.2 presents the definition of mental map preservation used. In Section 2.3, we discuss the types of mental map preservation algorithms used and present a study that sheds some light on which ones perform best with respect to the chosen definition of mental map preservation. Finally, we present the results of experiments that test the effectiveness of mental map preservation with users in Section

Where mental map preservation may help

In dynamic graph drawing, the environment is often an abstract information space that is evolving over time. A direct application of this navigational definition of map is therefore not always possible. Thus, the experiments to test the utility of preserving the mental map in dynamic graph drawing have stemmed from a tradition of information visualization and graph drawing readability and usability studies (Purchase et al., 1996, Purchase, 1997, Ware et al., 2002, Tory et al., 2007) as well as

Possible explanations for experimental results

In this section, we describe possible limitations of the ability of previous experiments to find a positive effect of mental map preservation and suggest future avenues of research.

Revisiting the definition of the mental map

In this paper, we have argued that using the definition of Coleman and Parker (1996) preservation of the mental map will most likely be useful in situations where information must be offloaded to the drawing. This occurs in local tasks when the number of independently moving areas of the graph used in the task is high and for global tasks when the number of distinguishable nodes/edges used in the task is high. However, Coleman and Parker (1996) preserves all three mathematical models as defined

Recommendations for designers

In this paper, we present evidence that preserving the mental map is not always helpful when performing tasks on dynamic graphs. For local tasks, the number of nodes, edges, or subgraphs considered needs to be high. For global tasks, the number of distinguishable nodes and edges used in the task needs to be high. In general, preserving the mental map may not support graph interpretation (Purchase and Samra, 2008, Archambault et al., 2011, Saffrey and Purchase, 2008), change (Purchase et al.,

Acknowledgments

The first author would like to acknowledge the support of the Clique Strategic Research Cluster funded by Science Foundation Ireland (SFI) Grant no. 08/SRC/I140. We would also like to thank John Hamer and Bruno Pinaud for all their help with our experiments. We would like to thank all of the participants who took part in our experiments on this topic. Finally, we would like to thank the anonymous reviewers of this journal for their helpful comments and revisions.

References (67)

  • Bederson, B.B., Boltman, A., 1999. Does animation help users build mental maps of spatial information? In: Proceedings...
  • S. Bender-deMoll et al.

    The art and science of dynamic network visualization

    Journal of Social Structure

    (2006)
  • Boitmanis, K., Brandes, U., Pich, C., 2007. Visualizing internet evolution on the autonomous systems level. In:...
  • Brandes, U., Fleischer, D., Puppe, T., 2005. Dynamic spectral layout of small worlds. In: Proceedings of Graph Drawing...
  • U. Brandes et al.

    Visualization methods for longitudinal social networks and stochastic actor-oriented modeling

    Social Networks

    (2011)
  • Brandes, U., Mader, M., 2011. A quantitative comparison of stress-minimization approaches for offline dynamic graph...
  • Brandes, U., Pich, C., 2008. An experimental study on distance-based graph drawing. In: Proceedings of Graph Drawing...
  • Brandes, U., Wagner, D., 1997. A bayesian paradigm for dynamic graph layout. In: Proceedings of Graph Drawing (GD...
  • Branke, J., 2001. Drawing graphs: methods and models. In: Dynamic Graph Drawing, vol. 2025 of LNCS. Springer-Verlag...
  • Bridgeman, S., Tamassia, R., 1998. Difference metrics for interactive orthogonal graph drawing algorithms. In:...
  • P. Brna et al.

    Learning to think and communicate with diagrams14 questions to consider

    Artificial Intelligence Review

    (2001)
  • M. Burch et al.

    Parallel edge splatting for scalable dynamic graph visualization

    IEEE Transactions on Visualization and Computer Graphics

    (2011)
  • Cohen, R. F., Battista, G. D., Tollis, I. G., Cohen, R. F., Tamassia, R., Tollis, I. G., 1992. A framework for dynamic...
  • M.K. Coleman et al.

    Aesthetics-based graph layout for human consumption

    Software – Practice and Experience

    (1996)
  • R. Cox et al.

    Supporting the use of external representations in problem solvingthe need for flexible learning environments

    Journal of Artificial Intelligence in Education

    (1995)
  • Diehl, S., Görg, C., 2002. Graphs, they are a changing – dynamic graph drawing for a sequence of graphs. In:...
  • Eades, P., Lai, W., Misue, K., Sugiyama, K., 1991. Preserving the mental map of a diagram. In: Proceedings of...
  • Erten, C., Harding, P.J., Kobourov, S., Wampler, K., Yee, G.V., 2003. GraphAEL: graph animations with evolving layouts....
  • M. Farrugia et al.

    Effective temporal graph layouta comparative study of animation versus static display methods

    Journal of Information Visualization

    (2011)
  • Frishman, Y., Tal, A., 2004. Dynamic drawing of clustered graphs. In: Proceedings of IEEE Symposium on Information...
  • Y. Frishman et al.

    Online dynamic graph drawing

    IEEE Transactions on Visualization and Computer Graphics

    (2008)
  • Gansner, E., Koren, Y., North, S., 2004. Graph drawing by stress majorization. In: Proceedings of Graph Drawing (GD...
  • Cited by (0)

    View full text