Flow maps are effective tools to represent connections and interactions volume between geographical regions [1
], and are widely applied to research related to spatial trajectory and interactions, such as migration [2
], transportation [3
], population movement [4
], disease spread [5
], and social communication flows [6
]. Researchers use various methods to generate flow, such as force-directed edges [6
], bundled edges [8
], and 3D curves [9
]. Current theories and techniques related to geographical information systems (GIS) to produce flow maps are still immature [10
]. Researchers have been attempting to solve the cartographical problems that influence human cognition, such as overlapping or intersecting symbols and inappropriate color and size of symbols [7
]. Therefore, it is important to evaluate and improve the usability of flow maps, which can allow users to perform certain tasks more accurately and rapidly.
The usability of flow maps influences the effectiveness and efficiency of map users processing and interpreting cartographical flow information. Shape, color, and size are three important visual variables in cartography [12
]. Previous cartographical studies have demonstrated the influence on effectiveness and efficiency in maps caused by shape, color, and size [14
]. Researchers have also conducted experiments to evaluate the representation of these three visual variables in flow maps [1
]. We believe that these three visual variables have significant influences on the usability of flow maps. However, these studies did not reach consistent conclusions on the effectiveness and efficiency of flow shapes. In addition, the differences in usability between using line thicknesses and color gradients to represent flow volume remain to be studied.
In this study, we used eye-tracking and questionnaire methods to evaluate the usability of flow maps. We mainly focused on comparisons between (a) straight lines and curves to indicate flows and (b) line thicknesses and color gradients to indicate the flow volume. We also explored how users react to flow maps with different combinations of visual variables (a) and (b). This study will examine flow maps as research objects from the perspective of user cognition for the map visual variables, and it will probe into the flow map design principles through the process of visualization via an eye tracking experiment. This study seeks to answer questions regarding how visual variables for flow maps affect people’s understanding of geographic information and how the usability of flow maps should be evaluated. Specifically, we address the following questions:
To indicate flows, do straight lines and curves influence the usability of a flow map?
To represent flow volume, do line thicknesses and color gradients have different impacts on the usability of a flow map?
The remainder of this article mainly includes five sections. In Section 2
, the research background of flow maps and usability studies using eye tracking are reviewed. In Section 3
, we describe the design of the experiment. Section 4
presents the analysis indices and results of our experiment. In Section 5
, the experimental results are analyzed and discussed regarding the influences of line shape, line thickness, and line color gradient on the usability of flow maps. Finally, in Section 6
, we make a brief conclusion and provide suggestions for the future.
2. Related Work
] suggested the use of multiple parallel lines or icons in addition to lines to represent the data type, volume, and flow speed. Dent, Torguson and Hodler [20
] noted that the design principles used to create flow maps include the placement of small flows over larger flows if overlapping is inevitable, the use of arrows to indicate the flow direction, the application of varying line thicknesses to show different data quantities, and the drawing of arrows proportionally to the line thicknesses. The two aforementioned studies both employed curves in the map to represent the data flow, but they did not prove that a curve is more effective than a straight line. Scholars have produced different findings with regard to this issue. Xu et al. [21
] conducted a user study of curved edges in graph visualization. They asked participants to complete network tasks, including the determination of connectivity, shortest path, node degree, and common neighbors, and to provide subjective ratings of the aesthetics of different edge types. They found that users perform more efficiently and accurately with maps containing straight lines than with maps possessing curves. Meanwhile, Purchase et al. [22
] also presented tasks, including the shortest path, vertex degree, and common neighbor. They discovered that users performed better with straight lines, although they preferred curved graphs. However, Jenny et al. [1
] found that curved flows are more effective than straight flows, arrows indicate direction more effectively than tapered line thicknesses, and flows between nodes are more effective than flows between areas. Furthermore, through a literature review, experimental data analysis, and questionnaire survey methods, they derived several design principles about flow maps, including reducing curve overlap, avoiding excessive curvature, and avoiding curves of unconnected nodes. Studies on the usability of flow maps have mostly utilized indices of the accuracy, task time, or user preference; however, few studies have involved the users’ visual perception while reading a flow map.
Eye tracking provides a great deal of assistance for cognitive research on cartography [23
] by recording real-time fixation, saccade, and duration data, and analyzing eye movement behavior to research visual information processing and to guide map design endeavors [24
]. Based on the eye tracking method, many scholars have conducted thorough research on map interface design [26
], in addition to visual query strategies and map interpretation [28
]. Dong [30
] found that enhanced remote sensing images have a higher usability than the original images based on eye tracking data and that the effects of size, color, and frequency are related to the display resolution in dynamic maps. Popelka and Brychtova [31
] compared the human perception of contour lines and 3D terrain, and they found that users have different strategies of cognition according to scan path. H Liao et al. [32
] studied the influence of label density on maps, and they found that both response time for visual search tasks and visual complexity are positively correlated with label density. Therefore, exploring flow maps of geo-data and the differences among the visual variables based on eye-tracking technology is feasible, which may induce cognition patterns in users reading flow maps. Recently, eye tracking has been adopted to evaluate the usability of different types of maps, such as WebMaps [33
], interactive maps [27
], and animated maps [34
], which can provide more direct cues to users’ visual cognition of maps and has potential for evaluating the usability of flow maps.
However, few studies have employed eye-tracking to evaluate the usability of flow maps. Hsin-Yang Ho, et al. [35
] conducted an eye tracking experiment to explore the influences of five different two-dimensional flow visualization methods on the visual perception of the user. They obtained several new findings that were not observed in previous studies. For example, they found that users are more likely to focus on key points or on highly variable regions and that the average gaze distance can be utilized to help find differences in the performances among different flow visualization methods. Blascheck et al. [36
] proposed an approach to explore eye movements in node-link graphs with different layouts, and to generate and adjust node-link graphs with eye movements data. Netzel et al. [37
] used eye tracking to compare the visualization of node-link trajectories between different ways to represent link types, nodes, and depth sorting for overlaps. However, they did not test the influence of the shape, color, and size of flows.
3.1. Experimental Design
We performed an indoor eye tracking experiment using a desktop eye tracker to record the eye movement data of the participants. During the experiment, the participants were placed in a silent, distraction-free environment. They were required to read the provided flow map that appeared on the screen and subsequently answer the preset questions. To ensure that the participants maintained a relaxed state in consideration of the task duration, we paused the process between every two maps to allow the participants to rest, during which time they were able to record their answers. In addition, to minimize the impact of nontask-related actions on the eye movements of the participants, a simple human-computer interaction process consisting of a single mouse click for switching the map was designed. Finally, we evaluated the impacts of shape, size (line thickness), and color (color gradient) on visualizing the flow on user cognition through the results of the tasks and eye movement data.
In addition to the eye tracking experiment, we conducted a test of participants using questionnaires with identical flow maps. We required the participants to give scores for two parts: (a) the visual quality of the connections between nodes in maps with straight lines and curves (b) and the visual quality of the flow volume between nodes in maps with different line thicknesses or color gradients. A five-grade marking system was used: 1 = very unclear, 2 = unclear, 3 = normal, 4 = clear, and 5 = very clear. In part 1, participants were asked to evaluate from several perspectives, including the simplicity of judging the flow directions, the number of overlapping or intersecting features, and the ability to express details. In part 2, they were asked to evaluate the ability to discern the difference in flow quantities.
In total, the experiment involved 40 participants and the questionnaire test involved another 42 participants. All the participants were between 20 and 23 years old, and they were undergraduates in the Faculty of Geographical Science, Beijing Normal University. They were assigned to two groups to accomplish different tasks. Each group size (N = 20) was consistent with those of other eye tracking cartography studies [26
]. None of the participants possessed an eye disease or color vision deficiency. It is noted that the participants have homogeneity due to the limitation of available sources of participants. The homogeneity may influence universality of experimental results, but it will also increase the statistical effectiveness. The selection of participants is considered to be acceptable because our study focuses more on how different visual variables in flow maps influence users’ performance, rather than how different users perform when reading flow maps.
This experiment used a Tobii T120 Eye Tracker (www.tobii.com
) with a sampling frequency of 60 Hz. The eye tracker was connected to a 17-inch monitor with a screen resolution of 1280 × 1024. Tobii Studio 3.2, the corresponding software, was installed on a Lenovo PC.
In this paper, we used four mobile communication datasets collected from Northeast China as the origin data for the flow maps. The origin data were provided from a communication operator, and all data that may have included private information were encrypted. We used straight lines and arc curves to represent the flow of data. In the material flow maps, different line thicknesses and color gradients were used to indicate the flow volume, and their effects on the usability of the maps were compared. Line thicknesses and color gradients were both divided into five levels to represent the flow volume. We chose a red gradient for the color aspect and divided it into five levels. It should be noted that the base map had a gray tone; therefore, to avoid color confusion, we chose a red gradient rather than a gray gradient. Linear features were generated based on the abovementioned method and were then symbolized using line thicknesses and color gradients, after which we were finally able to complete the visualization of the flow of geo-data. Figure 1
shows samples of the experimental materials.
Normally, point size represents quantized attributes of locations in flow maps [1
]. In material maps, point features that represent cities do not have the same size because the size variable is used to represent the total volume of flow in each city. In our experiment, we do not focus on the effects on the usability of flow maps caused by point size. To reduce the point size influence on the results of the experiment, the meaning of point size is not displayed in the legends and was presented to participants before the experiment, and the difference in point size did not help participants to finish preset tasks.
As shown in Figure 2
, the participants were equally divided into two groups. For group A, line thicknesses were used to indicate the flow volume of maps. For group B, color gradients were used to indicate the flow volume of maps. We used four basic flow datasets to generate material flow maps. Each group had four maps using straight lines and four maps using curves.
First, we introduced the instructions and procedure of the experiment to the participants, who were then given 1 to 3 min to familiarize themselves with the functions and operations of the interface.
Then, the participants were asked to read the maps shown on the screen and complete the given tasks. The main tasks in the experiment were to search for a target feature and to compare the flow volume. Participants were asked one question before each map was displayed, and they needed to give the answer after reading each map. Both group A and B used the same order of maps and the same questions for each map. To offset the learning effect of the participants, we allowed half the participants to read the maps in a normal order and the other half to read the maps in reverse order in each group. All questions were based on the three questions shown below. The order of maps and settings of relevant questions are shown in Table 1
Q1: Among the outflows from city A, to which city does the flow have the largest (smallest) volume?
Q2: Among the inflows to city A, from which city does the flow have the largest (smallest) volume?
Q3: The largest (smallest) data flow occurs between which two cities?
Notably, using straight lines to represent flows in maps will cause overlaps of flow and make it difficult for users to distinguish flows. This problem also existed in our material flow maps. To ensure that participants were able to complete preset tasks, we purposely adjusted the questions to avoid these overlapping flows as correct answers and tried to maintain the difficulty of the questions. For example, we selected a proper city as city A, such as Dalian in Figure 1
, and chose a more visually salient flow from the largest flow and the smallest flow as the answer to the question.
The eye movement data and response accuracies were recorded for further analysis. The experiment duration for each participant was 10 to 15 min. A participant sampling rate exceeding 80 percent was considered acceptable for data analysis. After the eye tracking experiment, we conducted a test using questionnaires and asked the participants to score the material flow maps.
3.6. Analysis Indices
The analysis of the eye tracking data included effectiveness and efficiency indices. The effectiveness indices included the fixation count, percentage of fixations in area of interests (AOIs), and accuracy, while the efficiency indices included the finish time and time to first fixation. Their interpretations are listed in Table 2
Five indices (Table 2
) were selected to analyze the efficiency and effectiveness of users’ performance when using flow maps to finish preset tasks. Two task indices (Table 2
) directly measured users’ performance: (1) accuracy (correctness), which reflects the effectiveness of users’ performance, where a high accuracy indicates a high effectiveness; and (2) finish time, which reflects the efficiency of users’ performance, where a short time to finish all tasks indicates a high efficiency.
Three statistical eye-tracking indices (Table 2
) were selected to measure user gaze behaviors statistically: (1) The first was fixation count (number of fixations), which indicates users’ efforts in processing information during reading maps. More fixations means users are distracted with nontarget areas when searching for targets [38
]. A poorly designed flow map may hamper users’ searching efficiency and lead to more fixations; (2) the second was the percentage of fixations in AOIs (the ratio of on target), which reflects users’ attention on target AOIs and indicates the searching efficiency for targets [38
]. Fixation count is correlative with the number of components that the user is required to process. If the numbers of components in two maps are quite different, then the percentage of fixations in AOIs is the better metric for indicating searching efficiency. A low percentage of fixations in AOIs indicates a low searching efficiency; (3) the third index was the time to first fixation, which indicates how long the users need to identify targets from a complex map [39
]. A well designed flow map should quickly guide users’ visual attention.
We used independent-sample Mann-Whitney U tests to analyze the differences between the abovementioned five indices of the effectiveness and efficiency between straight lines and curves and between line thicknesses and color gradients. To process the percentage of fixations in AOIs and time to first fixation, we defined AOIs as flows that match the correct answers for each map’s question and constructed them in Tobii Studio. Each AOI was constructed using a buffer area of original flow due to the inaccuracy of the eye tracker. The maximum deviation from a gaze point that eye trackers can locate is 0.5°, which is approximately equivalent to 25 pixels on the screen of the eye trackers. Thus, we chose 25 pixels as the buffer distance. Figure A1
shows samples of the experimental materials covered by AOIs. We used gaze opacity maps to show where and for how long users fixated. These gaze opacity maps were generated in Tobii Studio from the fixation count of all participants with a radius of 50 pixels. In addition, we used Pearson chi-squared tests to analyze the data of the questionnaires, to test the difference between straight lines and curves, and between line thicknesses and color gradients.
4.1. Straight Lines and Curves
With regard to the task indices, as shown in Table 3
and Figure 3
, the accuracy for the maps with straight lines (M
= 6.76, SD = 0.62) was significantly smaller than that for the maps with curves (M
= 7.43, SD = 0.81, U
= −3.085, p
= 0.002 < 0.01). The finish time for the maps with straight lines (M
= 5.10 s, SD = 2.68) was significantly shorter than that for the maps with curves (M
= 7.58 s, SD = 2.56, U
= −2.981, p
= 0.003 < 0.01).
With regard to the statistical eye tracking indices, the fixation count for the maps with straight lines (M = 25.99, SD = 11.31) was significantly less than that for the maps with curves (M = 37.47, SD = 9.36, U = −3.283, p = 0.001 < 0.01). The percentage of fixations in AOIs for the maps with straight lines (M = 0.20, SD = 0.07) was significantly smaller than that for the maps with curves (M = 0.26, SD = 0.09, U = −2.428, p = 0.015 < 0.05). The time to first fixation for the maps with straight lines (M = 2.27 s, SD = 0.69) was insignificantly longer than that for the maps with curves (M = 2.07 s, SD = 0.84, U = 1.094, p = 0.274).
To conclude, using curved features to indicate the flow of data in maps was more effective than using straight lines, and thus, the participants could focus more on an effective area within the map to acquire accurate information. In terms of the efficiency, the finish times for the straight-line maps were shorter than those for the curve maps, although the times to first fixation were longer.
4.2. Line Thicknesses and Color Gradients
The experimental results (Table 4
and Figure 4
) show that with regard to task indices, the accuracy for the line-thickness maps (M
= 6.75, SD = 0.71) was significantly smaller than that for the color-gradient maps (M
= 7.52, SD = 0.60, U
= −3.341, p
= 0.001 < 0.05). The difference in the finish times between the maps with different line thicknesses (M
= 6.50 s, SD = 3.30) and the color-gradient maps (M
= 6.35 s, SD = 3.46, U
= 0.183, p
= 0.855) was insignificant.
With regard to the statistical eye-tracking indices, the difference in the fixation counts between the maps using different line thicknesses (M = 32.74, SD = 12.89) and the maps using color gradients (M = 31.28, SD = 13.37, U = 0.574, p = 0.566) was insignificant. The percentage of fixations in AOIs for the maps using different line thicknesses (M = 0.23, SD = 0.07) was lower than that for the maps using color gradients (M = 0.28, SD = 0.08, U = −1.956, p = 0.050), although the difference was insignificant. Similarly, with regard to the time to first fixation, the difference between the line-thickness maps (M = 1.99 s, SD = 0.56) and the color-gradient maps (M = 1.96 s, SD = 0.73, U = 0.365, p = 0.715) was also insignificant.
To conclude, the difference between the use of line thicknesses and color gradients is mainly embodied by a change in the map effectiveness. When using color gradients to indicate the flow volume, the percentage of fixations in AOIs and the number of correct answers were significantly larger, indicating that the participants were able to focus more efficiently on target areas with valid information in the maps and acquire correct answers more easily. However, there was no significant difference in the efficiency for map reading and searching tasks between these two mechanisms for indicating the flow volume.
The questionnaire results are shown in Figure 5
, and the Pearson chi-squared test results are shown in Table 5
. In terms of different line shapes (Figure 5
a), the difference between maps using straight lines and curves was significant (p
= 0.000 < 0.01). For straight lines, 19.4% of the participants indicated that the maps were unclear because there were too many overlapping and intersecting lines that made them barely distinguishable. For curves, only 8.1% of participants rated the map as unclear. Neither maps with straight lines nor those with curves were rated as being very unclear. Curves were generally thought to be more complex due to excessive curvature. In addition, maps using the two types of line features received a similar percentage of normal evaluation (straight line = 37.8% and curves = 39.1%). The participants rated these maps as being nearly usable, but with some problems mentioned above. Furthermore, for straight lines, 35.0% and 7.8% rated them as clear and very clear, respectively (42.8% in all). For curves, the percentage was much higher—38.4% and 14.4% rated them as clear and very clear, respectively (52.8% in all). Maps using curves were rated as being clearer than those with straight lines. To conclude, compared to straight lines, curves can effectively avoid overlapping and intersecting and are less likely to make the maps misunderstood.
The difference between maps using line thicknesses and color gradients was also significant (p
= 0.000 < 0.01). In terms of different methods to visualize flow volumes (Figure 5
b), for different line thicknesses, 29.0% and 7.1% rated the maps as clear and very clear (36.1% in all), while for color gradients, 48.1% and 16.3% rated them as clear and very clear (64.4% in all). Most participants indicated that it was much harder to judge the flow volume from maps using different line thicknesses than it was from maps using color gradients. Thus, using color gradients is a better choice than using different line thicknesses to visualize flow quantities.
6. Conclusions and Future Work
This study was intended to explore the effects of visual variables on the usability of flow maps. The results of indoor eye tracking experiments show that the use of curves instead of straight lines to visualize flows benefits the effectiveness of flow maps because using curves reduces the number of overlapping and intersecting features, thus improving the clarity of maps. For maps using curves, participants paid more attention to effective areas while performing tasks that involved reading the maps and searching for information, and they were more likely to collect accurate information. However, straight-line maps tend to exhibit more overlapping and intersecting features, which could hinder the perception of accurate information and even cause maps to be misread. In addition, the use of color gradients could significantly improve the effectiveness of maps compared to the use of different line thicknesses.
Notably, our study only provides a comparison between a single color gradient and different line thicknesses. Therefore, the influence of other color gradients and relevant variables on the usability of flow maps should be tested in further investigations with larger datasets that contain more nodes and flows and more participants with different backgrounds.