THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF GEOGRAPHY

Transcription

1 THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF GEOGRAPHY ASSESSING THE COGNITVE ADEQUACY OF TOPOLOGICAL CALCULI: TRANSLATION VS. SCALING JINLONG YANG Spring 2011 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Geography with honors in Geography Reviewed and approved* by the following: Alexander Klippel Assistant Professor of Geography Thesis Supervisor Roger M. Downs Professor of Geography Honors Adviser * Signatures are on file in the Schreyer Honors College.

2 i ABSTRACT Movement patterns at the geographic scale are pervasive in the world we live in. Developing formalisms for capturing the spatial-temporal information of such movement patterns is becoming a central focus in spatial information science. To facilitate the meaningful interpretation of movement patterns, it is critical to design formalisms that are similar to humans conceptualization of space for both static and dynamically changing spatial relations. The research reported in this thesis focuses on cognitively assessing the adequacy of topological calculi in the capture of translation and scaling movements. The results show that topology plays a dominant role in conceptualizing geographic movement patterns, but that domain semantics influences the saliency of topologically distinguished ending relations.

3 ii TABLE OF CONTENTS LIST OF FIGURES... iii LIST OF TABLES... iv ACKNOWLEDGEMENTS... v Chapter 1 Introduction... 1 Chapter 2 Experiments... 6 Materials... 7 Participants... 9 Procedure Data Collection Chapter 3 Results Basic statistics Cluster analysis Multi-dimensional scaling Grouping raw frequencies Linguistic Analysis Chapter 4 Conclusions Bibliography Appendix A. ANOVA of the number of groups created over eight scenarios Appendix B. ANOVA of the amount of time that participants spent on the grouping task over eight scenarios Appendix C. Dendrograms of average linkage and complete linkage... 45

4 iii LIST OF FIGURES Figure 1. Conceptual neighborhood graph Figure 2. Design layout of icons in hurricane scenario and lake scenario Figure 3. Screenshots of the grouping interface of CatScan Figure 4. Box plots of the number of groups created by participants in the eight scenarios Figure 5. Box plot of the amount of time that participants spent on the grouping task over eight scenarios Figure 6. Dendrograms of four translation movement scenarios Figure 7. Dendrograms of four scaling movement scenarios Figure 8. MDS plots of four translation movement scenarios Figure 9. MDS plots of four scaling movement scenarios Figure 10. Screenshot of the KlipArt tool Figure 11. Line chart of the number of participants who placed all eight topological equivalence icons into the same group for each topologically distinguished ending relation over four translation scenarios Figure 12. Line chart of the number of participants who placed all eight topological equivalence icons into the same group for each topologically distinguished ending relation over four scaling scenarios

5 iv LIST OF TABLES Table 1 The design of icons in translation movement scenarios Table 2 The design of icons in scaling movement scenarios Table 3. An overview of participant information over eight scenarios Table 4. The number (and percentage) of participants who using terms relating to topology or domain semantics in each scenario

6 v ACKNOWLEDGEMENTS The completion of this research would not have been possible without the support of many people. I would first like to thank my parents who provided love, support, and encouragement through my study. I am heartily thankful to my thesis supervisor, Dr. Alexander Klippel for his continuous guidance, support, and encouragement in the past two years. I want to especially thank my honors advisor, Dr. Roger Downs for his comments on my thesis. I am indebted to my colleagues, Rui Li who ran experiments and exchanged ideas with me, and Frank Hardisty who supplying me with technical support I owe special thanks Ping Zhao for lending me a laptop when my own one was out of function.

7 1 Chapter 1 Introduction Humans live in a dynamic spatial world. It is, therefore, important to develop an understanding of how humans think about space and time and about situations in which tools such as maps and computers (e.g., GPS and GIS) provide assistance to spatio-temporal thinking processes. However, computers characterize space in a quantitative way (e.g., object A, a chair, is 3.45 meters from object B, the door), while humans tend to characterize space in a qualitative manner (e.g. object A is near object B). To bridge this gap, it is essential to develop formalisms that are similar to humans characterizations of space. The study reported in this thesis focuses on assessing the cognitive adequacy of topology a qualitative calculus for characterizing spatial relations to model conceptualizations of two of the three major types of movements identified by Egenhofer and Al-Taha (1992) - translation movement (e.g., a hurricane moving toward/across a peninsula) and scaling movement (e.g., a lake extending and shrinking due to rainfall). Topology plays a central role in understanding the formal and cognitive characterization of movement patterns (Kurata & Egenhofer, 2009). On the one hand, it provides a way to filter out unnecessary details from humans conceptualizations of spatial relations. On the other hand, topology has shown potential to be an essential cognitive invariant in geographic event conceptualization (Egenhofer & Mark, 1995). Topological distinguished relations can be formally arranged in so-called conceptual neighborhood graphs (CNG) (Freksa, 1992). Research from cognitive science has shown that, in human s conceptualization of movement patterns, the ending relation of a movement pattern is of critical importance (Regier & Zheng, 2007). Hence, the movement patterns we are focusing on are distinguished on the basis of the topological relations that two spatial extended regions end in.

8 2 We derived nine topologically distinguished ending relations from the two most prominent topological calculi in spatial information science, the Egenhofer s 9-intersection model (Egenhofer & Herring, 1994) and the region connection calculus (RCC) (Randell, Cui, & Cohn, 1992). We focus on two spatially extended entities that are disconnected (DC) at the start. Depending on where the movement ends, nine ending relations are distinguished based on their conceptual paths through the conceptual neighborhood graph (Figure 1). i i Figure 1. Conceptual neighborhood graph. The nine topologically distinguished ending relations are elaborated below using two examples a hurricane scenario (translation movement) and a lake scenario (scaling movement):

9 3 DC1 CNG path: DC; The hurricane stops before it touches the peninsula. The lake stops extending before it touches the house. EC1 CNG path: DC EC; The hurricane stops when it just touches the peninsula. The lake stops extending when it just touches the house. PO1 CNG path: DC EC PO; The hurricane stops when half of its area is overlap with the peninsula. The lake stops extending when it engulfs half of the house. TPP1 CNG path: DC EC PO TPP; The hurricane stops when it is just overlap with the peninsula, but still connected to the ocean. The lake stops extending when the house is just fully submerged by the lake. NTPP CNG path: DC EC PO TPP NTPP; The hurricane stops when the hurricane is completely overlap with the peninsula. The lake stops extending when the house is completely submerged by the house (the edge of the house is not attached to the edge of the lake).

10 4 TPP2 CNG path: DC EC PO TPP NTPP TPP; Same as TPP1, but the hurricane connects to the other coast of the peninsula. The lake first extends until the house is fully engulfed, and then starts to shrink until it reaches the level of TPP again. PO2 CNG path: DC EC PO TPP NTPP TPP PO; Same as PO1, but the hurricane stops when half of its area is overlap with the other side of the peninsula. The lake first extends until the house is fully engulfed, and then starts to shrink until it reaches the level of PO again. EC2 CNG path: DC EC PO TPP NTPP TPP PO EC; Same as EC1, but the hurricane stops when it external connects to the other side of the peninsula. The lake first extends until the house is fully engulfed, and then starts to shrink until it reaches the level of EC again. DC2 CNG path: DC EC PO TPP NTPP TPP PO EC DC; Same as DC1, but the hurricane stops when it disconnects to the other side of the peninsula. The lake first extends until the house is fully engulfed, and then starts to shrink until it reaches the level of DC again.

11 5 Two questions are addressed through the experiments reported here: a) Does topology play a dominant role in conceptualizing different (geographic) movement patterns (i.e., translation and scaling)? b) How does domain semantics influence the salience of topological relations in conceptualizing geographic events? To shed light on these two questions, we designed animated stimuli of geographic events based on the nine topologically distinguished ending relations, and assessed the cognitive adequacy of topological calculi in translation movement and scaling movement through behavioral experiments.

12 6 Chapter 2 Experiments To shed light on how humans conceptualize translation and scaling movement patterns, we designed eight sets of animated icons that depict different geographic (and other) events in Adobe Flash 8. Within these events, four of them depict translation movement (such as a hurricane moving toward / across a peninsula) whereas the other four depict scaling movement (such as a lake extending and shrinking due to rain fall). For each scenario, there is a moving entity and a reference entity. Both entities are spatially extended. Details of eight scenarios are listed in the table below (Table 1 and Table 2): Table 1 Shows the design of icons in translation movement scenarios in the experiment. Scenario Sample Icon Moving Entity Reference Entity Hurricane (HUR) A hurricane A peninsula Ship (SHI) A ship A shallow water area Tornado (TOR) A tornado A city Geometry (GeoT) A gray circle area A gray triangle area

13 7 Table 2 Shows the design of icons in scaling movement scenarios in the experiment. Scenario Sample Icon Moving Entity Reference Entity Desert (DES) A recreation park (symbolized by a A desert area letter R which is enclosed by a boundary) Lake (LAK) A lake A house Oil spill (OIL) An oil spill A island Geometry (GeoS) A gray circle area A black diamond area Materials For each scenario, we created 72 animated icons for nine topologically distinguished ending relations (i.e., eight icons for each ending relation). All icons are 120*120 pixels in size. In the translation movement scenarios, the reference entity (e.g., peninsula, shallow water area, or city) is placed in the middle area of the icon (Figure 2, left). The starting point of the moving entity is randomly selected from a starting region, which is disconnected from the reference entity (Figure 2). Likewise, an ending point is also randomly selected from an ending region, which is on the other side of the reference entity. Thus, a path (straight from the starting

14 8 point to the ending point) is generated for the moving entity. It is noteworthy that the path is only used to determine the direction in which an entity moves. The moving entity does not necessarily need to reach the ending point of the path. When the animation starts, the moving entity moves along the path at a constant speed. Depending on where the moving entity stops relative to the reference entity, nine different topological ending relations are distinguished. Within the eight animated icons from the same topological equivalence class (e.g. DC1), the starting points and directions of moving entities are different from each other, but the topological ending relations between moving entity and reference entity are the same. Figure 2. Shown is the design layout of icons in hurricane scenario (translation movement) (the left icon) and lake scenario (scaling movement) (the right icon). In the scaling scenarios, the reference entity (recreation park, house, or island) is put in the central area of the icon. The coordinates of moving entity (e.g. desert, lake, or oil spill) are randomly selected from a starting region which is disconnected from the reference entity (Figure 2, right). When the animation starts, the moving entity expands at a constant speed. Depending on where the moving entity stops, nine topological ending relations are distinguished. Similar to the design in the translation movement scenarios, the starting points of eight animated icons in each

15 Scaling Translation 9 topological equivalent class are different from each other, but the topological ending relations between moving entity and reference entity are the same. To ensure the movements are perceptual clear in all animated icons, the duration of each movement is at least 2.0 seconds, followed by 1.5 seconds pause showing the ending relation between the moving entity and the reference entity before the animation restarts.. Participants We recruited 199 undergraduate students as participants at The Pennsylvania State University from introductory level geography courses. All participants were reimbursed with 10 USD for their participation. To ensure that participants were clearly aware of the domain semantics of the scenario they worked on, we checked the linguistic description provided by each participant, and replaced those participants who did not mention the scenario in their description (e.g. some participants referred the hurricane in the hurricane scenario as circle or white ball ). In addition, the data of two participants were accidentally overridden. Details for the final 20 participants in each scenario are listed below: Table 3. An overview of participant information over eight scenarios. Scenario # of participants # of female Average age Hurricane Ship Tornado Geometry Desert Lake Oil spill Geometry Total

16 10 Procedure All experiments were carried out as a group experiment in a GIS lab at Department of Geography, Penn State University. The GIS lab is equipped with 16 Dell desktops with 24-inch wide screen LCD monitors. To ensure that each participant can work on the experiment individually, view blocks were set up between participants such that they could not see each other s screens. All experiment tasks were performed in CatScan - a custom-made software tool (Klippel, Worboys, & Duckham, 2008) that allows animation presentation and data (grouping behavior and linguistic description) collection. In the experiments, the participants were randomly assigned to a desktop computer in the GIS lab, and then required to input their basic personal information (i.e., gender, age, field of study, etc.). After that, the participants were provided with a written introduction, which explained the scenario of the animated icons in that experiment and contained basic instructions for carrying out the experiment. To briefly train the participants how to perform grouping tasks in CatScan, a trial was provided in which the participants were asked to group a set of animal icons (dogs, cats, and camels) based on their own criteria. When the participants finished grouping all animal icons in the trial, they were able to proceed to the main experiment. In the grouping interface of the main experiment (Figure 3), all 72 animated icons were presented in the left panel of the interface. Animated icons on the left panel could be placed into groups on the right panel simply by clicking, dragging, and dropping the mouse. Groups could be created ( New Group button) or deleted ( Delete Group button). A third Compact Icons button was provided such that participants could compact all icons left in the left panel to the top. The Finish button was activated only after all icons were placed into group(s). All groups created by participants were automatically labeled with frames in distinct colors to assist participants finding a group they previously created at a later time. Averagely, the grouping task took 15 minutes. It is

17 11 critical to mention that the participants were clearly informed in the instruction that there was no right or wrong answer with respect to their grouping criteria or number of groups they created. After the participants finish the grouping task, they were shown the group(s) they previously created, each group at a time. For each group, they were asked to provide a short label (no more than five words) and a linguistic description to explain the criteria they used to create that group. Figure 3. Shown is the screenshots of the grouping interface of CatScan. The top one shows the initial screen that participants saw. The bottom one shows a mimic ongoing experiment in which a participant has created five groups.

18 12 Data Collection The following experiment data were automatically collected by CatScan during the experiment sessions: 1. The basic personal information of each participant (e.g. gender, age, field of study, etc.). 2. Which icons were placed into the same groups by participants. 3. The number of groups created by each participant. 4. The time (in seconds) each participant spent on performing the grouping task. 5. Linguistic description (short/long) of each group created by participants The grouping behavior of each participant was recorded in a 72 * 72 similarity matrix (72 is the number of icons we used in each scenario). All possible similarities between pairs of icons in a scenario are encoded in this symmetric matrix. Similarity between each pair of icons is binary encoded: A pair of icons coded as a 0 indicates that these two icons are not placed into the same group; a pair of icons coded as a 1 indicates that these two icons are placed into the same group. An overall similarity matrix (OSM) is obtained by summing over the similarity matrices of 20 participants in each scenario. Hence, the value of each cell in the OSM ranges from 0 (none of the 20 participants placed this pair of icons into the same group) to 20 (all 20 participants placed this pair of icons into the same group).

19 13 Chapter 3 Results Basic statistics The number of groups created by participants is shown in Figure 4 as box plots. The box plots reveal that the number of groups created in each single scenario is comparably similar over eight scenarios. Four outliers exist here: participant #11 in the hurricane scenario created 29 groups; participant #13 in the tornado scenario created 16 groups; participant #20 in the desert scenario created 18 groups; and participant #9 in the geometry (scaling) scenario created 17 groups. ANOVA (Appendix A) reveals that: a) There are no statistically significant differences in the number of groups created within four translation movement scenarios; b) Within four scaling movement scenarios, only the number of groups created in the geometry (scaling) scenario is statistically different from the number of groups created in the desert scenario (p < 0.05); c) Over all eight scenarios, only the geometry (scaling) scenario is statistically different from the desert scenario (p = 0.019) and ship scenario (p = 0.045) regarding to the number of groups created by participants.

20 14 Figure 4. Shows box plots of the number of groups created by participants in the eight scenarios. The Y- axis represents the number of groups created. Figure 5 shows the time that participants spent on performing the grouping task in each scenario, again in the form of a box plot. Based on the results shown by the box plots, the time participants spent on the grouping task is similar over four translation movement scenarios. Not surprisingly, ANOVA (Appendix B) also shows that there are no significant differences within translation movement scenarios. Within four scaling movement scenarios, the grouping time of the desert scenario is slightly shorter whereas the grouping time of the geometry (scaling) scenario is slightly longer when compared to the other two scenarios. ANOVA indicates that the only significant difference is between the grouping time of the desert scenario and the geometry (scaling) scenario (p < 0.05). We did not compare the time between translation movement

21 scenarios and scaling movement scenarios as in our experimental design, the durations of translation movements are generally shorter than the durations of scaling movements. 15 Figure 5. Shows the box plot of the amount of time that participants spent on the grouping task over eight scenarios. The Y-axis represents the amount of time (in seconds). Cluster analysis We used cluster analysis to examine the similarities among icons based on the overall similarity matrices. Comparison across different clustering methods has been suggested to cross-validate the interpretation (Clatworthy, et al., 2005). Thus, three different cluster methods are used here:

22 16 average linkage, complete linkage, and Ward s method. We mainly examined Ward s method dendrograms to identify patterns as it usually gives a near-optimal solution (Romesburg, 2004). The dendrograms generated from average linkage and complete linkage (Appendix C) were used to cross validate our interpretation. The first observation is, over all eight scenarios, icons with the same topologically equivalent CNG paths are forming distinct groups 1 (Figure 6 and Figure 7). This suggests that topology is a dominant criterion in participants grouping behavior. On the other hand, clusters of icons with different topological ending relations diverge from the main stream at different conceptual distances, which indicates that the nine topological ending relations are not equally salient. 1 Three exceptions occurred here. In hurricane scenario, a TPP1 icon falls into the cluster of PO1 icons and EC2 icons and DC2 icons form two mixed clusters. In the tornado scenario, PO2 icons are mixed with TPP2 icons.

23 17 Figure 6. The dendrograms of four translation movement scenarios that generated from cluster analysis in CLUSTAN TM.

24 18 Figure 7. The dendrograms of four scaling movement scenarios that generated from cluster analysis in CLUSTAN TM.

25 19 In translation movement scenarios, the dendrograms of the hurricane scenario and ship scenario show a very similar structure, which consist of three main clusters. The icons with no overlap or partial overlap relations (DC1/DC2, EC1/EC2, and PO1/PO2) form two main clusters, depending on whether moving entity (i.e., hurricane or ship) has crossed the reference entity (i.e., peninsula or shallow water area). The third main cluster is formed by icons whose ending relations are proper part relations (TPP1, TPP2, and NTPP). The only difference here is in the hurricane scenario where the PO2 icons are conceptually closer to the EC2 and DC2 icons, while in ship scenario, the PO2 icons are conceptually closer to the PO1, PO2, and NTPP icons. In the tornado scenario, icons with non-overlap ending relations (DC1, DC2, EC1, and EC2) are clearly separated from icons with overlap ending relations (PO1, PO2, TPP1, TPP2, and NTPP). The geometry (translation) scenario, in which domain semantics is absent, has a more distinct structure in its dendrogram. The DC1 and EC1 icons are clustered together and so too are the EC2 and DC2 icons. The partially overlapping icons (PO1 and PO2) form a distinct cluster, and proper part icons (TPP1, TPP2, and NTPP) form another cluster. In scaling movement scenarios, the grouping structures of desert, lake, and oil spill scenario are similar but show scenario specific differences. In all these three scenarios, the DC1, EC1, and PO1 icons are clustered together, and the EC2/DC2, PO2/TPP2, and NTPP/TPP1 icons are paired with each other. There are, however, some differences. In the desert scenario and lake scenario, the DC1 icons and EC1 icons are merged together first and then are tugged on to the PO1 icons, while in the oil spill scenario, the EC1 and PO1 icons are merged together first and then are tugged by the DC1 icons. This structure difference may result from the fuzziness of the effect of disaster as an oil spill reaching the coast of island (EC1) will cause damage while a desert reaching a recreation park (EC1) or a lake reaching a house (EC1) will not. Furthermore, the cluster of the PO2 and TPP2 icons are conceptually closer to the cluster of the DC2 and EC2

26 20 icons in desert scenario and oil spill scenario, while in the lake scenario, the cluster of the PO2 and TPP2 icons are closer to the cluster of the NTPP and TPP1 icons. Similar to what we have found in the translation movement scenarios, the dendrograms of the geometry (scaling) scenario shows a very different pattern than the other three real world scenarios. These interesting patterns in cluster analysis suggest three points: First, topology does play a dominant role in humans conceptualizing of movement patterns. Second, from a cognitive perspective, the similarities among nine topologically distinguished ending relations vary as a function of different movement types (i.e., translation and scaling), and different scenarios. Third, within each type of movement, the grouping behavior of participants is influenced by contextual (semantic) information. Multi-dimensional scaling To explore the similarities among icons from a different perspective, we performed a multidimensional scaling (MDS) analysis based on the overall similarity matrices (OSM) with the software CLUSTAN TM. We further visualized the MDS plots with a custom-made program in CatScan. Some interesting patterns emerge as we looked into the MDS plots (Figure 8 and Figure 9).

27 21 Figure 8. Shown are the MDS plots of four translation movement scenarios hurricane scenario (top left), ship scenario (top right), tornado scenario (bottom left), and geometry (translation) scenario (bottom right).

28 22 Figure 9. Shown are the MDS plots of four scaling movement scenarios desert scenario (top left), lake scenario (top right), oil spill scenario (bottom left), and geometry (scaling) scenario (bottom right). First, in the MDS plots of all eight scenarios, icons with the same topological ending relation basically form their own cluster, though there are some exceptions where icons whose topological ending relations are neighbors in the conceptual neighborhood graph overlap with each other. This finding supports the conclusion we draw from the cluster analysis topology does play a dominant role in humans conceptualizing of movement pattern.

29 23 Second, in the MDS plot of the hurricane scenario, all icons are distributed on a virtual arc in an order (counter-clockwise) that is identical to the order in the CNG. This pattern also exists in the MDS plots of the other two real world translation movement scenarios (i.e., the ship scenario and tornado scenario). Third, in the MDS plot of the lake scenario, three main clusters can be clearly identified. The first main cluster is formed by all the DC1 and EC1 icons, in which the house has never been submerged by the lake. We named this main cluster No Disaster. The second main cluster is exclusively formed by all the PO1 icons, in which the house is partially submerged by the lake at the end of the animation. We named this main cluster Medium Disaster. The third main cluster is formed by all other icons in the lake scenario. In these icons, the house has been completely submerged by the lake. We named this main cluster Complete Disaster. We also found the same pattern in the desert scenario. The MDS plot of oil spill, however, tells a slightly different story. All the EC1 icons, instead of falling in the No Disaster cluster, join the Medium Disaster cluster together with all the PO1 icons. This pattern matches the structure we saw in the cluster analysis, in which the EC1 icons are closer to the DC1 icons in the desert scenario and lake scenario but are closer to the PO1 icons in the oil spill scenario. From a domain semantics perspective, it is not surprising to see that participants considered an oil spill touching the coast of an island to be a Medium Disaster instead of No Disaster. In the case that an oil spill reaches the coast of an island, the beach will be contaminated by the black, disgusting oil. The three main clusters we identified confirm that domain semantics does have an influence on the grouping behavior of participants. This suggests that the conceptual distances between the nine topologically distinguished relations are influenced by domain semantics. Last, the MDS plots of the geometry scenarios (both for translation movement and scaling movement) show very distinct patterns. There are four main clusters in the MDS plot of

30 24 the geometry (translation) scenario. All the DC and EC icons are distributed on the upper part of the plot. Depending on whether the gray circle has crossed the gray triangle area (DC2 and EC2) or not (DC1 and EC1) in the animation, two main clusters are identified. All the icons whose ending relations are proper part (TPP1, TPP2, and NTPP) form a main cluster at the bottom left corner of the MDS plot, whereas all the icons whose ending relations are partial overlap (PO1 and PO2) form a main cluster at the right part of the MDS plot. In the MDS plot of geometry (scaling) scenario, icons with the same topological ending relation form a distinct cluster. The average conceptual distances among clusters of icons are greater than other real world scenarios. For both translation movement and scaling movement, the MDS plots of scenarios with contextual information (all six real world scenarios) are completely different from the MDS plots of scenarios without contextual information (geometry scenarios). Thus, this confirms that participants grouping behavior is influenced by contextual (semantics) information. Grouping raw frequencies To further analyze participants conceptualization of movement patterns, we performed an analysis of grouping raw frequencies using our custom-made visual analysis tool named KlipArt (Klippel, Hardisty, & Weaver, 2009). This tool allows us to dynamically explore each participant s grouping behavior in more detail (Figure 10), and to examine the linguistic description that participants provided for each group they created. For example, we can choose all the DC1 icons and examine how participants placed these eight icons into group(s). The linguistic description participants provided for each group is displayed in the software interface when icon(s) from that group is selected (not depicted in Figure 10). This function enables us to shed light on the rationale of participants grouping behavior.

31 25 Figure 10. Shown is a screenshot of the KlipArt tool (only the grouping behavior workspace). This figure shows 20 participants grouping behavior on eight DC1 icons (# ) in the lake scenario. Each yellow square represents a participant. A black arrow connecting a participant to a group of icon(s) indicates that this group of icon(s) was placed into the same group by that participant. For instance, participant #11 placed eight DC1 icons into two groups: One group consists of icon #005 and #007; the other group consists of icons # and #006. Moreover, participant #2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19 placed all eight DC1 icons into one group. To assess cognitive adequacy of topological calculi from a statistical perspective, we extracted the number of participants who placed all topological equivalent classes (e.g., all eight icons of DC1) using KlipArt. This enables us to perform Chi-square analysis on participants grouping behavior.

32 26 We first focus on whether there are statistically significant differences among the number of participants who placed all eight topological equivalence icons into the same group over nine topological defined ending relations within each scenario. The results from Chi-square analysis show that only tornado scenario yields a significant difference within nine topological equivalent classes (X = , df = 8, p < 0.05). Second, we focus on whether there are statistically significant differences among the numbers of participants who placed all eight topological equivalence icons into the same group for each topologically distinguished ending relation over eight scenarios. We performed a Chisquare analysis for all eight scenarios. The only ending relation that shows statistically significant differences over eight scenarios is PO2 (X = , df = 7, p < 0.05). This may indicate that the saliency of PO2 is influenced by domain semantics. We followed up with two Chi-square analyses for translation movement scenarios and scaling movement scenarios separately. No significant difference is found within translation movement scenarios or within scaling movement scenarios. By additionally comparing the two line charts we created based on the raw counts (Figure 11 and Figure 12), we can infer that the PO2 icons are more frequently grouped together by participants in scaling movement scenarios than translation movement scenarios.

33 27 Figure 11. Shown is the line chart of the number of participants who placed all eight topological equivalence icons into the same group for each topologically distinguished ending relation over four translation scenarios Figure 12. Shown is the line chart of the number of participants who placed all eight topological equivalence icons into the same group for each topologically distinguished ending relation over four scaling scenarios.

34 Scaling Translation 28 Linguistic Analysis Language is like a window to cognition. To shed more light on participants grouping behavior, we followed up with an analysis of linguistic description that participants provided. Here we focused on two aspects topology and domain semantics. Participants who described movement patterns using terms relating to topology or domain semantics were identified by examining the short/long description. Table 4. The number (and percentage) of participants who using terms relating to topology or domain semantics in each scenario. Scenario Topology Domain semantics Count % Count % Hurricane Ship Tornado Geometry N/A N/A Total Desert Lake Oil spill Geometry N/A N/A Total Total The results (Table 4) shows that the overwhelming portion of participants (91.9% on average over eight scenarios) used terms relating to topology such as inside, on the edge, overlap in their description for movement patterns. Participants more frequently used terms relating to domain semantics to describe scaling movement (27 out of 60 participants) than translation movement (16 out of 60 participants). For example, 13 out of 20 participants in the lake scenario used terms such as flooded, risk, damage, and threaten when described movement patterns. However, only 4 out of 20 participants in the hurricane scenario used terms

35 29 such as impact, destructing, affect, and cause damage in their description. This finding may suggests that domain semantics has more influence on conceptualizing scaling movement than translation movements.

36 30 Chapter 4 Conclusions Based on the findings discussed in the previous chapter, two main conclusions can be drawn. First, topology does play a dominant role in conceptualizing both translation and scaling movement patterns. As we have shown in the cluster analysis and multi-dimensional scaling, icons with the same topologically distinguished ending relation are conceptually closer than icons with other topologically distinguished ending relations. In addition, the linguistic descriptions from participants also reveal that topology is the main criterion in their grouping behavior. Second, from a cognitive perspective, the nine topologically distinguished ending relations are not equally salient across different scenarios. The similarities between these ending relations are influenced by domain semantics. In both translation and scaling movement scenarios, nine topological ending relations tend to be aggregated based on domain semantics. In contrast, the scenarios using geometric figures exhibit no such influence, albeit show that even geometrically certain topological relations are conceptually closer than others..

37 31 Bibliography Clatworthy, J., Buick, D., Hankins, M., Weinman, J., & Horne, R. (2005). The use and reporting of cluster analysis in health psychology: A review. British Journal of Health Psychology, 10(3), Egenhofer, M. J., & Herring, J. (1994). Categorizing binary topological relations between regions, lines, and points in geographic databases. The, 9, Egenhofer, M., & Mark, D. (1995). Naive geography. Spatial Information Theory A Theoretical Basis for GIS, Egenhofer, M., & Al-Taha, K. (1992). Reasoning about gradual changes of topological relationships. Theories and methods of spatio-temporal reasoning in geographic space, Freksa, C. (1992). Temporal reasoning based on semi-intervals. Artificial intelligence, 54(1-2), Klippel, A., Hardisty, F., & Weaver, C. (2009). Star plots: How shape characteristics influence classification tasks. Cartography and Geographic Information Science, 36(2), Klippel, A., Worboys, M., & Duckham, M. (2008). Identifying factors of geographic event conceptualisation. International Journal of Geographical Information Science, 22(2), Kurata, Y., & Egenhofer, M. (2009). Interpretation of behaviors from a viewpoint of topology. In B. Gottfried & H. Aghajan (Eds.), Behaviour monitoring and interpretation. Ambient intelligence and smart environments. Amsterdam: IOS Press. Randell, D. A., Cui, Z., & Cohn, A. G. (1992). A spatial logic based on regions and connection. KR, 92,

38 32 Regier, T., & Zheng, M. (2007). Attention to Endpoints: A Cross Linguistic Constraint on Spatial Meaning. Cognitive Science, 31(4), Romesburg, C. (2004). Cluster analysis for researchers: Lulu press.

39 33 Appendix A. ANOVA of the number of groups created over eight scenarios Univariate Analysis of Variance Between-Subjects Factors Value Label N Scenario 1.00 hurricane ship tornado geo_trans desert lake oil geo_scaling 20 Descriptive Statistics Dependent Variable:Groups Scenario Mean Std. Deviation N hurricane ship tornado geo_trans desert lake oil geo_scaling Total

40 34 Levene's Test of Equality of Error Variances a Dependent Variable:Groups F df1 df2 Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + Scenario Dependent Variable:Groups Tests of Between-Subjects Effects Source Type III Sum of Squares df Mean Square F Sig. Corrected Model a Intercept Scenario Error Total Corrected Total a. R Squared =.045 (Adjusted R Squared =.001)

41 35 Post Hoc Tests Dependent Variable:Groups Multiple Comparisons (I) Scenario (J) Scenario 95% Confidence Interval Mean Difference (I-J) Std. Error Sig. Lower Bound Upper Bound LSD hurricane ship tornado geo_trans desert lake oil geo_scaling ship hurricane tornado geo_trans desert lake oil geo_scaling * tornado hurricane ship geo_trans desert lake oil geo_scaling geo_trans hurricane ship

42 36 tornado desert lake oil geo_scaling desert hurricane ship tornado geo_trans lake oil geo_scaling * lake hurricane ship tornado geo_trans desert oil geo_scaling oil hurricane ship tornado geo_trans desert lake geo_scaling geo_scaling hurricane ship * tornado geo_trans desert * lake oil Bonferroni hurricane ship

43 37 tornado geo_trans desert lake oil geo_scaling ship hurricane tornado geo_trans desert lake oil geo_scaling tornado hurricane ship geo_trans desert lake oil geo_scaling geo_trans hurricane ship tornado desert lake oil geo_scaling desert hurricane ship tornado geo_trans lake oil geo_scaling

44 38 lake hurricane ship tornado geo_trans desert oil geo_scaling oil hurricane ship tornado geo_trans desert lake geo_scaling geo_scaling hurricane ship tornado geo_trans desert lake oil Based on observed means. The error term is Mean Square(Error) = *. The mean difference is significant at the.05 level.

45 Appendix B. ANOVA of the amount of time that participants spent on the grouping task over eight scenarios 39 Univariate Analysis of Variance Between-Subjects Factors Value Label N Scenario 1.00 hurricane ship tornado geo_trans desert lake oil geo_scaling 20 Descriptive Statistics Dependent Variable:Time Scenario Mean Std. Deviation N hurricane ship tornado geo_trans desert lake oil geo_scaling Total

46 40 Levene's Test of Equality of Error Variances a Dependent Variable:Time F df1 df2 Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + Scenario Dependent Variable:Time Tests of Between-Subjects Effects Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 3.084E Intercept 1.290E E Scenario Error 2.540E Total 1.575E8 160 Corrected Total 2.849E7 159 a. R Squared =.108 (Adjusted R Squared =.067)

47 41 Post Hoc Tests Dependent Variable:Time Multiple Comparisons 95% Confidence Interval Mean Difference Lower Upper (I) Scenario (J) Scenario (I-J) Std. Error Sig. Bound Bound LSD hurricane ship tornado geo_trans desert lake oil geo_scaling * ship hurricane tornado geo_trans desert lake * oil geo_scaling * tornado hurricane ship geo_trans desert lake oil geo_scaling geo_trans hurricane ship tornado desert

48 42 lake * oil geo_scaling * desert hurricane ship tornado geo_trans lake * oil geo_scaling * lake hurricane ship * tornado geo_trans * desert * oil geo_scaling oil hurricane ship tornado geo_trans desert lake geo_scaling geo_scaling hurricane * ship * tornado geo_trans * desert * lake oil Bonferroni hurricane ship tornado geo_trans

49 43 desert lake oil geo_scaling ship hurricane tornado geo_trans desert lake oil geo_scaling tornado hurricane ship geo_trans desert lake oil geo_scaling geo_trans hurricane ship tornado desert lake oil geo_scaling desert hurricane ship tornado geo_trans lake oil geo_scaling lake hurricane ship

50 44 tornado geo_trans desert oil geo_scaling oil hurricane ship tornado geo_trans desert lake geo_scaling geo_scaling hurricane ship tornado geo_trans desert lake oil Based on observed means. The error term is Mean Square(Error) = *. The mean difference is significant at the.05 level.

51 Appendix C. Dendrograms of average linkage and complete linkage 45

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