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Article Excerpt
Abstract
Most of the recent research in data visualization has focused on technical and aesthetic issues involved in the manipulation of graphs, specifically on features that facilitate data exploration to make graphs interactive and dynamic. The present research identifies a gap in the existing knowledge of graph construction, namely potential problems in both 3D and 2D graphs that will impede comprehension of information when three or more variables are used in a graphical representation. Based on theories regarding perceptual issues of graph construction (Bertin 1981; Pinker 1991), we evaluate specific cases where 3D graphs may out-perform 2D graphs, and vice-versa. Two experiments have been conducted to test these hypotheses, and 3D graphs have been found to consistently outperform 2D graphs in all of our experimental scenarios. A third experiment has been conducted to identify situations where 2D graphs might perform at least as well as 3D graphs, but its results suggest that 3D graphs outperform 2D graphs even for simple tasks, thus leading to the conclusion that 3D graphs perform better than 2D graphs under all task conditions with more than two variables.
Keywords: Computer graphics, 3-D graphics, human information processing, information presentation, information retrieval, information characteristics, information processing
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Introduction
The development of sophisticated data mining and data presentation applications in the last 10 years have led to a new level of interest in the field of data visualization, the art and science of visually representing n-dimensional data. Data visualization consists of two distinct phases: (1) graph construction, including all decisions that go into the construction of a graph and (2) graph manipulation, comprising all decisions that go into the interactive modification and manipulation of graphs by end-users (Buja et al. 1996). Until the mid-1990s, a considerable amount of research investigated effective methods of representing information in two-dimensional graphs (Bennett and Toms 1993; Dickson et al. 1986; Jarvenpaa and Dickson 1988; Spence 1990; Tan and Benbasat 1990). While most of this work focused on constructing 2D graphs, some research in scientific data visualization has also addressed information representation and manipulation using n-dimensional graphs (Colet and Aaronson 1995; Wickens and Carswell 1995; Wickens et al. 1994). More recently, several researchers have addressed image construction methods for visualizing multidimensional managerial data (Jones 1994; Zhang 1996, 1998).
In general, recent research has shifted away from the production of static images and toward features that make graphs more interactive. Indeed, most of the recent data visualization research has focused more on the manipulation of graphs (e.g., filtering, querying and interface design) rather than on graph construction (Buja et al. 1996; Cook et al. 1995; Hurley and Buja 1990; Swayne et al. 1998). Almost invariably, all of these studies have involved high density and high dimensional data (Sutherland et al. 2000). Some of this research has focused on the design of user interfaces, advocating the use of motion or animation as another channel to convey information (Baecker and Small 1990; Bartram 1997; Ware 2000).
Notwithstanding these studies, there is still a surprising paucity of cumulative empirical research concerning the graph construction stage, specifically on information representation using 3D graphs (Card et al. 1999). Past research on information representation using 3D graphs has yielded equivocal results in terms of performance differences among 2D graphs, 3D graphs, and tables (Dull and Teagarden 1999; Meyer et al. 1997; Sollenberger and Milgarm 1993); therefore, the present paper seeks more empirical results by focusing on the first step of the data visualization process: graph construction. In this research we identify relationship encoding, where some relationships are more readily available for comprehension than others, as a limitation that will have an impact on the performance of 2D graphs (Shah and Carpenter 1995). We also believe that relationship encoding will bring into question some of the past research on 2D graphs, specifically research that posits that line graphs are better than bar graphs to understand trends. On the other hand, previous research has noted ambiguity of depth perceptions as a major limitation of 3D graphs (Sollenberger and Milgarm 1993; Wickens et al. 1994). In addition, familiarity and complexity have been known to have strong impacts on graph comprehension (Kennedy et al. 1998; Meyer et al. 1997). Familiar graphs typically take less time to comprehend than unfamiliar graphs. However, the effect of complexity on graph comprehension has yielded mixed results (Meyer et al. 1997). Thus, our objective is to predict conditions where 3D graphs might outperform 2D Cartesian graphs, and vice-versa, and to test these predictions in a series of laboratory experiments.
In the next section, we briefly review past literature on data visualization and introduce a model of the intellectual processes involved in reading and understanding graphs, as discussed by Pinker (1991). We then attempt to situate our research in a broader context, by expanding on the work of Bertin (1981). The limitations of 2D and 3D graphs are briefly discussed. Our research hypotheses, based on the theories outlined and developed in the previous sections, are then enumerated. The general research methodology is described. The three sections that follow present the results of our three experiments. The results of the study are discussed and our conclusions presented.
Literature Review
Background
A taxonomy of previous research is sketched in Table 1, with the two primary areas of data visualization (graph construction and graph manipulation) and the two general streams of previous research (technical concerns and perceptual and cognitive processes). Researchers working on the technical concerns area (popularly known as the computer graphics field) have typically focused on the technical grammar involved in constructing and manipulating graphs, while work on perceptual and cognitive processes involved understanding graph comprehension. We argue that there is still a gap in the graph construction stage in that not enough research has been done to study the perceptual and cognitive ramifications of information representation using 3D graphs (cell 3 in Table 1). Most of the empirical research cited in that cell has primarily investigated information representation using 2D graphs.
Among the work done in cell 3, some researchers have focused on rules for graph construction (Bertin 1981; Zhang 1998), while others have developed frameworks for the graphical elements used in displays (Cleveland and McGill 1984; Simkin and Hastie 1987; Spence 1990). Past empirical research in cell 3 has focused primarily on Cartesian 2D graphs and the relationships between two variables. Sometimes, researchers have included information about a third variable, categorical in nature, in the 2D graphs, using legends. However, when more than two components are to be represented, more options are available than before in constructing graphs. For example, users can choose either a single 3D graph or two 2D graphs to represent the same information. Within these two broad types, users have innumerable ways of representing information (bar charts, line charts, scatter plots, etc.), even given the restrictive assumption that a Cartesian graph is preferable to other forms of graphical representation. Even though some research has investigated information representation using 3D graphs (Dull and Teagarden 1999; Wickens et al. 1994; Yu and Behrens 1995), there is a dearth of empirical research on when to use 3D graphs rather than 2D graphs when more than two components are to be represented (Card et al. 1999). This paper addresses the gap that currently exists in this area.
Pinker's Theory of Graph Comprehension
A graph, according to Pinker (1991), is a representation that tries to communicate to readers a set of n-tuples of values in mathematical scales, using objects whose visual dimensions (e.g., length, position, lightness, and shape) correspond to the respective scales in the representation (nominal, ordinal, interval, or ratio-scales), and whose values on each dimension (i.e., an object's particular length, position, and so on) correlate with the values on the corresponding scales. A graph reader must do two things to comprehend a graph, according to Pinker. First, the reader must mentally represent the objects in the graph in a certain way. For example, in a bar graph, one must think of the bars in terms of their heights and their positions along the x-axis, but not necessarily in terms of the jagged edges formed by the tops of the bars. Pinker introduces the concept of visual descriptions to accomplish the first task. This visual description is the output of the mechanisms of visual perception that shows the identity of the scene's parts and their relationship among them (see Figure 1). When a reader looks at a graph, the information from a graph arrives at his/her nervous system as a two-dimensional pattern of intensities, referred to as visual array, on the retina. This raw information from the visual array is converted to memory representations signifying knowledge of what the visual marks of the graphs mean through visual descriptions.
Subsequently, graph readers must remember, or deduce, which aspects of the visual constituents of the graph stand for each of the mathematical scales that the graph represents. According to Pinker, the correct correlations are made through graph schema, which are remembered knowledge in some domain, consisting of descriptions that contain slots or parameters for as yet unknown information. Readers use these visual descriptions and graph schema to extract the information from a graph. In order to accomplish these two things, readers must first form visual descriptions of graphs by some appropriate visual encoding mechanisms. However, to be useful, any theory of graph comprehension must be able to restrict the visual descriptions that will be generated. Principles such as the Gestalt laws of grouping (Wertheimer 1938), grounded in basic perceptual research, naturally constrain the form of visual descriptions, according to Pinker. Simultaneously, the limited processing capacity of humans is another factor that limits the extent and quantity of visual descriptions.
Graph-readers now need to translate information from the visual descriptions into conceptual messages and translate questions into forms that can be answered through visual descriptions. These types of cognitive connections are made by instantiating graph schema, according to Pinker. This involves particular processes (see Figure 1).
[FIGURE 1 OMITTED]
* Matching: identification of a graph as belonging to a particular graph type.
* Message assembly: creation of a conceptual message out of the instantiated graph schema. It is important to remember that not all information on a graph is necessarily translated directly into conceptual messages due to short-term memory capacity limitations, noise in the match process, and bad construction of graphs that highlights unimportant information, among other reasons.
* Interrogation: retrieval and codification of new information based on conceptual questions. This process happens when a reader needs some piece of information that is not already in the conceptual message. This initiates a top-down search to find the desired information.
* Inferential processes: application of mathematical and logical rules to the entries of conceptual message.
An important implication of the theory is that if the desired information is not in the conceptual message, it will have to be generated by the top-down interrogation process or the inferential process. For a limited-capacity system, such as the human mind, this would mean that a particular type of information would be harder to extract from a given graph to the extent that inferential processes and top-down encoding processes, as opposed to conceptual message look-up, must be used. Clearly, this implies cognitive costs for the graph reader. Thus, extracting information from a graph is easiest when a visual description has those predicates that directly answer the conceptual question asked of the reader. For example, line graphs should be best for illustrating trends and interactions, since there exist many visual predicates for line shapes.
Graph Construction with Three Components
While Pinker's work provides a foundation for understanding how users comprehend graphs, there is still a need to understand whether it is possible to use certain fundamental principles to construct graphs that portray n-dimensional data sets. Bertin (1981) makes a case for using the level of organization of the information component--nominal, ordinal, interval, and ratio--as the basis for construction of graphs. A graphic system has eight visual variables to represent these components of information, according to Bertin: the two dimensions of the plane of the graph, in addition to the size, value, texture, color, orientation, and shape of the graph. The visual variables chosen to represent the individual components of information must be at least at the same level of organization as the components they represent. For example, if an information component is ratio-level in nature,...
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