Can cognitive inferences be made from aggregate traffic flow data? Itzhak Omer¹*, Bin Jiang² 1
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Department of Geography and Human Environment, Tel-Aviv University Division of Geomatics, Faculty of Engineering and Sustainable Development, University of Gävle Email:
[email protected];
[email protected]
Abstract Space syntax analysis or the topological analysis of street networks has illustrated that human traffic flow is highly correlated with some topological centrality measures, implying that human movement at an aggregate level is primarily shaped by the underlying topological structure of street networks. However, this high correlation does not imply that any individual’s movement can be predicted by any street network centrality measure. In other words, traffic flow at the aggregate level cannot be used to make inferences about an individual’s spatial cognition or conceptualization of space. Based on a set of agent-based simulations using three types of moving agents―topological, angular, and metric―we show that topological-angular centrality measures correlate better than does the metric centrality measure with the aggregate flows of agents who choose the shortest angular, topological or metric routes. We relate the superiority of the topological-angular network effects to the structural relations holding between street network to-movement and through-movement potentials. The study findings indicate that correlations between aggregate flow and street network centrality measures cannot be used to infer knowledge about individuals’ spatial cognition during urban movement.
Keywords: urban movement, cognitive distance, network analysis, space syntax, agent-based simulation
1. Introduction Space syntax studies have shown that aggregate flows in urban environments correlate with structural street network properties but far more with topological or angular than with metric properties (e.g., Hillier et al., 2007). Topological and angular street network centrality measures are therefore considered more relevant when modeling pedestrian and vehicular movement in these environments (e.g., Hillier, 2009). Later studies have nonetheless reported that topological centrality measures may not be suitable for predicting actual traffic flows because they neglect the dynamics of travel behavior and the geographical or physical dimensions of the urban street network (Kazerani and Winter, 2009), the spatial heterogeneity of human activities and the distance-decay law effect (e.g. Gao et al., 2013; Liu et al., 2012). That is, only street network centrality measures are unsuitable for predicting traffic flow because travel behavior is not based just on a selection of shortest paths. These debates, as found in the literature (e.g., Hillier and Iida, 2005; Penn, 2001), relate to a fundamental issue in urban movement research: How much are the correlations found between street network centrality measures and aggregate flows related to people’s spatial 1
cognition and perception of distance during urban movement? Hillier and Iida (2005) focused on correlations of pedestrian and vehicular flows with topological, angular and metric street network centrality properties in four of London's urban areas. Correlations with topological and angular centrality properties were found higher than were correlations with metric properties. Based on these findings, the authors concluded that people read urban networks in angular and topological rather than metric terms (pp. 487-488). This inference about cognitive knowledge being based on aggregate flows has been criticized (Jiang, 2009; Jiang and Jia, 2011). Using a set of topological measures, including Google’s PageRank (Page and Brin, 1998), Jiang (2009) found that PageRank, or its variant, capture human movement better than do any attentive measures. He further formulated the reason why space syntax or other types of topological analyses assumed to help predict traffic flows have not fully reflected human travel behavior. At a later stage, Jiang and Jia (2011) simulated the travel of two kinds of moving agents – random walkers and purposive walkers – in the same four London urban areas. They found that the movement patterns generated by purposive and by random walkers were almost identical. Hence, they argued, it is not the human element but the underlying street structure that determines such flows (Jiang and Jia, 2011). The reason posited for the correlations obtained between street network centrality measures and observed aggregate traffic flows is therefore open to question: Is it people’s spatial cognition of distance and shortest route or is it the underlying street structure? The literature thus indicates disagreement regarding the suitability of the correlations obtained between street network centrality measures and observed aggregate traffic flows with respect to two important aspects of urban movement: prediction of traffic flows and inferring how people perceive or cognitively represent distance during urban movement. In this study reported here, we found that the topological-angular movement potentials created by the street network structure may be higher than its metric movement potential and consequently more fully realized in the formation of urban movement patterns. It follows that the street network centrality measures do not necessarily express individual spatial decisions and distance perception during urban movement. Analysis of simulated movement data collected in two London areas and two Israeli cities shows that Closeness and Betweenness measures (representing to-movement and throughmovement potentials, respectively) differ in their ability to reflect the distance type (angular, topological or metric) employed by agents during urban movement. Topological and angular centrality measures, especially Closeness, correlate better than do metric measures with aggregate flows irrespective of the distance type used by simulated agents for calculating the shortest routes. This differential representation of individuals' travel behavior by street network centralities indicates that urban movement is mediated by a network effect oriented toward the angular and the topological movement potential more than toward the metric potential. This networkeffect bias explains why angular and topological centralities, primarily to-movement Closeness (Integration in space-syntax terms), are more suitable than are metric centralities as predictors of aggregate movement. However, for exactly the same reason, we ultimately argue that the relatively high correlations of angular and topological centralities with observed aggregate flows neither indicate nor prove how people perceive, calculate, or select their shortest-distance urban movements.
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In light of the simulated movement findings, we analyzed the correlations between observed aggregate flows and street network centrality measures as well as between observed and simulated aggregate flows in the two London areas. The results indicate that unlike the position taken by Hillier and Iida (2005), metric distance may be not less relevant than angular and topological distance for perception and/or conceptualization of distance in urban movement. In the following section we describe the analytical framework used in the analysis and measurement of urban movement together with the agent-based model constructed to simulate movement in the research areas. The correlations between different street network centrality measures with simulated and observed movements, as well as the correlations between the simulated and observed movements themselves, are presented in the third section. We discuss the findings in the fourth section, with conclusions given in the final section.
2. Analytical Framework 2.1 Space syntax: Background The space syntax methodological framework is based on topological-visual analyses of street networks. These analyses produce what has been termed an axial map, constructed from the smallest set of straight axial (visual) lines covering a city's street network (Hillier and Hanson, 1984; Hillier, 1996). The centrality of each axial line within the network is then computed by means of graph-based centrality measures (i.e., topological distances between axial lines) in order to represent the street network's movement potential. The premise behind the application is that such an analysis enables modeling the built environment in a way that reflects how it is perceived by people on the ground. Recent studies have nevertheless indicated that segment-based analysis of the street network performs better than does axialbased analysis when modeling urban movement (e.g. Hillier, 2009). Although still based on axial lines, the basic unit of segment analysis is the line segment located between junctions. Segment use facilitates the conduct of configurational analysis on a finer scale than does axial line use. Furthermore, segment analysis enables computation of topological distance (fewestturns distance), angular distance (least-angle distance) and metric distance (e.g. Hillier et al., 2007), the distance types of interest. In the current study we used segment-based analysis for the purpose of comparing our metric, angular and topological centrality measures with the findings obtained by Hillier and Iida (2005), whose research was likewise based on network analysis at the segment level. 2.2 Data and measurement Our empirical research focused on Barnsbury and South Kensington, two of the four London areas in which the Hillier and Iida (2005) research was conducted, and on Ashdod and Raanana, two medium-sized Israeli cities (Figure 1). The selection of urban areas was meant to enable examination consistency in interactions between street network structure, aggregate flow and individuals’ spatial behavior over diverse urban environments (size and form), e.g., a tree-like street pattern (Ashdod) and a nearly-grid pattern (Raanana).
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Figure 1. Street networks of the study areas at the segment level. The observed points (‘gates’) in London areas are presented by blue points. Number of segments in each study areas: Kensington – 10,825; Barnsbury – 7,272; Raanana – 1,187; Ashdod – 3,871.
The axial maps and observed traffic flow data of the two London areas are publicly available (downloadable at http://eprints.ucl.ac.uk/1398/) and have been used in earlier studies (e.g., Hillier et al., 1993; Jiang and Jia, 2011). The axial maps were transformed into segment maps to enable segment-based analysis of movement. Street networks in the center of these areas were sampled for availability of observed vehicular data by means of the ‘gate count’ method (see Figure 1). The data on Ashdod's and Raanana's street networks were obtained from the firm MAPA. We should note that we used the Ashdod and the Raanana data only for analysis of simulated movement, with no consideration of observed traffic flow data. Segment-based analysis treats individual street segments as nodes (vertices) and street segment intersections as edges of a connectivity graph. The graph forms the basis for computing centrality measures (Hillier and Iida, 2005, pp. 481-483; Jiang and Claramunt, 2004). A graph G (V,E) is defined as a pair of finite sets of vertices (or nodes) V = {v1, v2…. vn} together with a finite set of edges E = {Vi, Vj}. We used two types of segment-based topological, angular and metric space syntax centrality measures – Integration and Choice – corresponding to the graph theory-based measures Closeness and Betweenness, respectively. Closeness indicates how close a street segment is to other street segments by computing the shortest distances between every street segment node to every other street segment node, a feature that reflects a given street segment's accessibility within the network (i.e., the tomovement potential). Formally, the closeness measure is defined by: 4
(1)
where n is the total number of streets (nodes) within a street network; d is the shortest (topological, angular or metric) distance from a given street segment (Vi) to every other street segment (node Vk) in the segment map. Betweenness indicates the extent to which a street segment is located between pairs of street segments; as such, it directly reflects the intermediate location of the specific segment (i.e., the through-movement potential) in the entire street segment network. Accordingly, we define the Betweenness centrality as follows: (2)
where Pjk denotes the number of shortest paths from j to k, and Pjik the number of shortest paths from j to k that pass through street i; hence, CB is the proportion of shortest paths from j to k that pass through i. To be consistent with the Hillier and Iida (2005) study, each centrality attribute was computed at several metric radii – 250, 500, 750, 1000, 1250, 1500, 1750, 2000, 2500, 3000, 4000, 5000 m – and over the entire urban area, i.e., Radius n (Rn). That is, sub-networks in a defined radius from a given street segment are taken into consideration when computing Closeness and Betweenness measures. The transformation from axial maps to segment maps and the computation of the space syntax measures were conducted with Depthmap software (version 10.14, UCL). 2.3 Agent-based simulation The agent-based simulation, specially constructed for the present research, was devised to investigate the relationship between agents’ spatial behavior during urban movement and the resulting aggregate flows. The term ‘spatial behavior’ refers here to the distance type – topological, angular and metric – agents might used when calculating the shortest routes throughout the street networks. Construction of the simulation was inspired largely by the work of Jiang and Jia (2011), who suggested a model having two kinds of moving agents – random walkers and purposive walkers – for simulating movement in street networks. However, because this model is based on axial maps and considers only topological distance, adaptations were required to enable referencing angular and metric distances at the segment level. The simulation model we employed was designed with the NetLogo (ver.5.0.5) environment (Wilensky 1999). Segment maps of the study areas – London's Barnsbury and South Kensington areas as well as the Israeli cities Ashdod and Raanana – were transformed into NetLogo environments by means of ArcGIS software ver. 10.0 (the *.shp file can be loaded directly by NetLogo). The segment maps were then used to simulate movement. (for the Barnsbury area model interface see Figure 2). Three types of agents were defined: the metric, the topological and the angular, each of whom chooses the shortest path – metric, topological, or angular, respectively – between origin-destination pairs of segments (see Appendix A for the algorithm). The shortest path was computed by means of the Dijkstra algorithm (Dijkstra 1959) within the NetLogo framework; the shortest topological distance was obtained by computing the number of turns or direction changes between origin and destination, while angular (geometric) distance was obtained by computing cumulative angular change. That is, 5
unlike topological distance, which considers only the number of turns, angular distance is calculated by considering the angle of the turns made between origin and distention.
Figure 2. Main interface segment of the Agent-Based Model. The interface is illustrated by the movement of metric (red), topological (green) and angular (blue) agents in the Barnsbury area against the aggregate flow pattern (in magenta) of all agent types formed during the simulations.
Our model's setup is as follows: Origin-destination pairs are created randomly, with equal probabilities assigned to all segments in the entire area; agents are programmed to choose the shortest path according their type. Once they reach their first destination, they randomly choose their second destination and so on. In each simulation iteration (tick), the aggregate flow is measured by the ‘gate count’ )i.e., the number of agents( and by the ‘footprint count’ )i.e., the number of footprints comprising the movement trajectories in a given time period(. For each run of the 40k simulation iterations programmed, we assigned 10 agents to each of the 3 agent types (a total of 30 agents). During the simulation, the distribution of aggregate flows at the segment level is obtained with the cumulative counts of agents and footprints for each of the three agent types. In addition, correlations between the centrality attributes and the aggregate flow of each of the three types of moving agents are computed.
3. Results 3.1 Correlation between simulated movement flows and street network structure The correlation between the simulated aggregate flows of each agent type (agents who select the shortest topological, angular, or metric route) and the geographic distributions of the Betweenness and Closeness centralities for Barnsbury and Ashdod are illustrated in Figure 3.a and Figure 3.b, respectively. With respect to aggregate flows, we see that in both areas, 6
the similarity between topological and angular aggregate flows is greater than is the similarity between topological/angular aggregate flows and metric aggregate flows. In addition, although the movement paths of all types of agents tend to pass through the main long lines, the metric agents’ shortest routes are distributed among a relatively greater variety of line lengths and tend to be located in each area's geographical center.
a. Barnsbury
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b. Ashdod
Figure 3. The spatial distributions of aggregate flows of different agent types and space syntax attribute values at the entire area/city scale (Rn) in (a) Barnsbury and (b) Ashdod. The grouping of the aggregate flow values and of the Betweenness values (which are not normally distributed) was constructed with head/tail breaks (an algorithm that continuously breaks a heavy-tailed distribution into head and tail categories; for details see: Jiang, 2013). The grouping of the Closeness values was constructed by using Jenks’s natural breaks.
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Differences between aggregate flows are clearly reflected in the geographic distributions of through-movement Betweenness centralities. That is, the higher values in the metric centrality distribution, like in the metric agents’ aggregate flows, tend to be concentrated in the geographical center and distributed among a greater variety of line lengths than in the topological and angular centrality distributions. This means that overall, the throughmovement potential of the Betweenness centralities nicely represent the actual movement paths of agents belonging to the same distance type. In contrast, comparisons of the aggregate flows with the to-movement Closeness centrality show great differences between the potential and actual movement with respect to the metric centrality. In both Barnsbury and Ashdod, the distribution of metric Closeness values was characterized by a sharp decrease from the geometric center of the street network to the periphery, a decrease much greater than the actual aggregate flow values of metric agents (agents who select the shortest metric routes), values that are distributed relatively more equally throughout the city. In general, topological and angular measures reflect aggregate metric flow much better than metric measures reflect topological or angular aggregate flows. In other words, short metric routes pass through topological and angular central locations more frequently than short topological and angular routes pass through metric central locations (see Table 1). In order to examine the relation between different movement potentials and simulated aggregate flows of different distance types in statistical terms, the correlations of the Closeness and Betweenness centralities with the simulated aggregate flows of each of the three types of moving agents were computed (see Table 1). For consistency with the Hillier and Iida (2005) study, the highest correlations of each measure, across scales (different metric radii), are presented. The results show that the Betweenness centrality measure of any given distance type quite accurately reflects agent behavior of the same type during shortest path selection. For all the study areas, correlations of the topological, angular and metric Betweenness measures with the respective topological, angular and metric aggregate flows are very high: Barnsbury (0.974 < r> 0.989), Kensington (0.875 < r> 0.972), Ashdod (0.982 < r> 0.985) and Raanana (0.962 < r> 0.987). The correlations are imperfect due to the simulation's random creation of origin-destination pairs. As also seen on Table 1, the aggregate flows of one distance type are reflected in the Betweenness measures of the other distance types. In all the study areas, the expression of aggregate flow by Betweenness measures tends to be asymmetric. The extent to which metric aggregate flows are expressed by topological and angular Betweenness measures is greater than the extent to which topological and angular aggregate flows are reflected by the metric Betweenness measure. In Barnsbury, for example, the correlation of metric aggregate flow with the angular Betweenness measure is 0.84 even though the correlation of the angular aggregate flow with the metric Betweenness measure is only 0.69. The same can be said with respect to the metric-topological distance type: While the correlation of the metric aggregate flow with topological Betweenness is 0.70, the opposite correlation is only 0.58. Thus, while all Betweenness measures quite accurately reflect the behavior of agents of the same distance types, the angular and topological Betweenness measures capture the behavior of the different types of agents better than does the metric Betweenness measure.
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Table 1. Pearson correlation coefficients (r) between space syntax attributes and simulated movement flows of different agent types by study area. The numbers in round parentheses indicate the radius, in meters, where the highest correlation was found.
Urban area
Barnsbury
Closeness – Accessibility Measures
Betweenness – Choice Measures
Agent type
Metric
Angular
Topological
Metric
Angular
Topological
Metric
**-0.303 (R3000) **-0.131 (Rn)
**0.551 (R3000) **0.633 (Rn)
**-0.37 (R4000) -0.362 **(R500)
**0.989 (R2500) **0.685 (R2500)
**0.84 (R1750) **0.981 (Rn)
**0.704 (R1500) **0.841 (R2500)
**-0.131 (Rn) **-0.287 (Rn) **0.345 (R3500) **-0.139 (Rn) *-0.238 (R5000) *-0.135 (R5000) *-0.12 (R5000) **-0.402 (R3000) **-0.231 (Rn) **-0.174 (R3000)
**0.523 (Rn) **0.523 (R2000) **0.523 (Rn) **0.414 (Rn) *0.509 (Rn) *0.545 (Rn) *0.452 (Rn) **0.647 (R1500) **0.712 (R4000) **0.630 (Rn)
**-0.368 (R3000) **-0.365 (Rn) -0.348 **(R750) **-0.316 (R1000) *-0.375 (R6000) *-0.383 (R5000) *-0.321 (R5000) **-0.408 (Rn) **-0.489 (Rn) **-0.461 (Rn)
**0.582 (R3000) **0.875 (Rn) **0.625 (R3000) **0.512 (R3000) **0.982 (Rn) **0.595 (Rn) *0.504 (Rn) **0.962 (Rn) **0.617 (R3000) **0.525 (R4000)
**0.825 (R3000) **0.82 (R2000) **0.955 (R5000) **0.8 (Rn) **0.675 (R3000) **0.985 (Rn) **0.933 (Rn) **0.813 (R2000) **0.983 (Rn) **0.948 (Rn)
**0.974 (Rn) **0.738 (R2000) **0.894 (R2500) **0.972 (Rn) *0.599 (R2500) **0.945 (Rn) **0.983 (Rn) **0.736 (R2000) **0.960 (R4000) **0.987 (Rn)
Angular Topological Metric
Kensington Angular Topological Metric
Ashdod Angular Topological Metric
Raanana Angular Topological
High negative values for metric and topological Closeness indicate high accessibility/Integration. Metric = least length; Angular = least angle; Topological = fewest turns. * p
