2026 Volume 34 Issue 2 Pages 20-27
This study explores how considering spatial variation in trip behavior affects the identification of Urban Activity Centers (UAC) using Person Trip data in Tokyo. Standard UAC identification models typically apply a single distance threshold for the definition of spatial neighborhood, assuming uniform spatial relationships between centers and their service areas. In contrast, this research incorporates local trip distance statistics into the weights matrix of a spatial autoregression model, capturing contextual differences across the city. The modified model identifies fewer peripheral UAC but reveals broader edge areas of major centers. Particular attention is given to clusters of public services, where local trip behavior strongly shapes spatial structure. These findings highlight both the technical feasibility and analytical value of considering local trip behavior in UAC models.
Urban Activity Centers (UAC) are areas of a city characterized by a concentration of urban activity positively distinct from their surroundings. UAC represent the core elements of the urban spatial structure, where human, traffic, and information flows converge and most urban interactions take place. Accurate identification and delineation of these areas reveals the spatial structure of cities and provides valuable insights for urban planners and developers (Anderson et al., 1996). The analysis of the spatial distribution and characteristics of UAC makes it possible to identify functional imbalances within a city, detect areas with insufficient accessibility to key services, and locate zones with a high potential for business development. Moreover, delineated UAC boundaries can serve as a basis for designing compact urban cores, supporting policies toward polycentric and sustainable urban forms (MLIT, 2015).
There are many methods to identify UAC, but most recent studies have employed spatial statistical models for this purpose (Yu et al., 2021). In this approach, centers are detected as positive residuals from models that predict the density of urban activity in each spatial unit based on the activity value in its surroundings. The key methodological challenge lies in how these surroundings (i.e., neighborhoods) are defined. In most studies, neighborhoods were defined arbitrarily, failing to reflect actual patterns of urban interaction. For instance, McMillen (2001) recommended using relatively large neighborhoods, covering up to half of the study area, whereas more recent studies considered only adjacent cells as neighbors (e.g., Guillain et al., 2006; Sun et al., 2015).
In a previous study, the use of typical trip distance for a given activity group, generalized across the study area, was proposed as a threshold for defining neighborhoods (Boratinskii & Osaragi, 2025). This approach is grounded in the interpretation of Urban Activity Centers as areas whose activity levels are defined relative to their surrounding service areas. In this context, the neighborhood represents the spatial extent against which local activity concentration is evaluated, corresponding to the area from which trips to a given center tend to originate. Within this framework, trip distance provides an intuitive and measurable spatial scale for defining center-periphery relationships, linking spatial-statistical definitions of centers with notions of centrality rooted in mobility flows (Veneri, 2013; Zhong et al., 2013).
Despite addressing the arbitrariness of neighborhood thresholds, the previously proposed method assumed uniformity in trip behavior across the city. In reality, catchment areas may vary substantially from place to place. Following the basic postulates of Central Place Theory (Christaller, 1966), major centers tend to attract visitors from broader areas, while smaller or more specialized centers mainly serve nearby residents. Although originally formulated for intercity systems, similar hierarchical patterns have been repeatedly observed within metropolitan regions (Giuliano and Small, 1991; Agarwal et al., 2012). Large business or commercial districts, typically offering diverse and high-order functions, draw users from extensive areas of the city, whereas peripheral or neighborhood-level clusters with daily use facilities are characterized by more localized interactions (Reilly, 1931; Huff, 1963).
This implies that service areas for the same activity type may differ significantly depending on the location, scale, and function of the facility or the center it is situated in. Consequently, service areas of central or higher-rank locations are spatially larger and should therefore be compared to larger neighborhoods during the UAC identification process. Neglecting such differences can lead to the under- or overrepresentation of certain centers, depending on how well the generalized trip distance fits their functional characteristics.
In this study, we address this limitation by introducing a new model that adapts to local trip distance. The proposed framework aims to reduce arbitrariness in defining spatial neighborhoods by grounding them in observed local mobility patterns, enabling the model to be applied consistently across different urban contexts. This ability to capture spatial variation in trip behavior within activity groups is particularly valuable in settings where detailed local knowledge is limited or where mobility patterns vary substantially across space.
For this study, we used data from the 6th Tokyo Metropolitan Area Person Trip Survey (2018) ― a large survey-based dataset providing detailed information on individual travel behavior. It was selected for the urban activity analysis because it contains data on both activities and trips associated with them, which is essential for the proposed model. The analysis focused on the 23 special wards of Tokyo.
２.１ Extraction of activitiesAmong other variables, the PT dataset includes information on trip purposes, which we used as an indicator of urban activity type. However, not all purposes listed in the PT data directly correspond to urban activities. As part of preliminary data cleaning, trips with the purposes “To home,”“Pick-up & drop-off,” and “Unknown” were excluded, as they are either unrelated to urban activity or lack a definable activity type. The remaining trips were grouped into three categories ― work, commercial, and public ― for a more representative spatial analysis of urban functions (Table 1). This classification was suggested by Boratinskii and Osaragi (2024a) primarily to capture spatial distribution patterns typical of each group, while also reflecting, to some extent, their temporal characteristics and the demographic profiles of the people engaged.
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/34_20_t1.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
Subsequently, activity locations were extracted for each group using the destination coordinates of the activity-related trips as proxies. Finally, each trip record was weighted by the survey’s magnification ratio to estimate the actual number of people engaged in the corresponding activity.
The weighted points were then aggregated into a regular grid of hexagonal cells with 175-meter sides (Figure 1). Throughout this paper, the term cell refers to an individual hexagonal unit, while grid refers to the entire collection of such cells into which the analyzed area is divided. The hexagonal geometry was adopted because it minimizes directional bias and allows for a more uniform treatment of neighboring cells. The size was selected based on multiple experiments with cells of different sizes. The selected size provided one of the most accurate representations of the spatial distribution of urban activities and centers in the study area.
２.２ Extraction of local trip distance
In the previous method, authors suggested setting the threshold for identifying neighboring cells in the UAC detection model based on the typical trip distance for each activity group. Specifically, they used the median trip distance aggregated over the entire study area (Boratinskii & Osaragi, 2025). In this study, we aim to incorporate local variation in trip behavior into the model. To achieve this, we calculated median trip distances for each activity group in each hexagonal cell ― hereafter referred to as local trip distance. These values were then used as cell-specific neighborhood thresholds, enabling the model to adapt to the spatial heterogeneity of trip behavior. It is important to note that, although the median was selected as the representative single value for the distribution of activities by trip distances, this choice constitutes a simplification of urban interactions, which in reality decline gradually with distance. Within this study, we treat it as a first step toward incorporating local trip behavior into the urban center detection process.
During the extraction of local trip distances, we encountered the issue of missing data. Some cells contained no trips for a given activity group, resulting in undefined local median values. For the subsequent modeling step, it was essential to ensure that each cell was assigned a valid neighborhood, allowing for obtaining a complete distribution of residuals. To achieve this, empty values were replaced with a fixed distance corresponding to the first-order neighborhood (i.e., adjacent hexagons), thereby ensuring full spatial coverage and enabling consistent activity estimation.
As expected, a general center-periphery gradient is observed in the distribution of local trip distances, particularly for work and public activities (Figure 1). Cells in central areas tend to have longer median trip distances, while those in peripheral areas typically exhibit shorter distances. For commercial activities, this trend is less pronounced. For all three groups, the distribution is not entirely smooth: multiple peripheral cells show unexpectedly high median distances, forming “hotspots.” These may correspond to cells with unique functions or facilities (e.g., university campuses, shopping malls), the specific local interactions of which are also crucial to incorporate into the UAC identification.
２.３ UAC Identification modelThe UAC identification model used in this study is based on spatial autoregression (SAR), following the previously mentioned work (Boratinskii and Osaragi, 2025). In this approach, the spatial model estimates expected activity levels based solely on spatial interaction with surrounding cells, as defined by the spatial weights matrix. Subsequently, spatial units where the observed activity values significantly exceed the expected ones are identified as UAC. In other words, the SAR model is used here as a spatial filtering tool to highlight deviations from the expected spatial distribution of activities, which is consistent with the definition of UAC adopted in this study and explains the absence of additional explanatory variables.
The overall flow of the updated algorithm, together with the reference model used for comparison, is summarized in Table 2. In both cases, we employ a spatial lag SAR model, where model parameters are estimated using maximum likelihood. The modeling step was implemented using the spautolm function in R. The key difference between the two versions lies in the construction of the spatial weights matrix W, which specifies which cells are considered neighbors. While the reference model assumes uniform trip behavior and therefore assigns identical neighborhoods to all cells, the proposed model incorporates local trip distances, defining neighborhood relations individually for each cell. In practical terms, cells located within the median distance of activity-related trips with destinations in a given cell receive a positive weight, whereas those located beyond this distance receive zero weight.
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/34_20_t2.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
The modeling steps outlined in Table 2 were performed separately for each of the three activity groups (a) to capture their distinct spatial distribution patterns. Additionally, to ensure that the model accounts for activity distribution outside the study area as well when estimating activity values, the hexagonal grid shown in Figure 2 was extended in all directions. For the estimation of commercial and public activities, the extension was 5 km, and for work activities ― 10 km. These distances were selected to cover the majority of trips for the corresponding activities while keeping the computational load within reasonable limits.
The estimated autoregression parameter (ρ) was statistically significant for all activity groups in both the reference and the proposed models (Table 3), confirming the presence of spatial dependence. Its magnitude varied across activity groups, with the highest value observed for work activities and the lowest for public activities. This corresponds with the observed degree of spatial clustering of these activities (Figure 1). There is also a decrease in ρ from the reference to the proposed model. It reflects the shift from a uniform neighborhood definition to locally adaptive spatial interactions based on trip behavior, rather than a weakening of spatial dependence itself.
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/34_20_t3.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
Figure 2 presents the distribution of fitted values and residuals for the newly proposed model for three activity groups. These maps provide an overview of the modeled activity values and the resulting deviations from the corresponding neighborhoods that form the basis for UAC identification.
UAC were identified as 600 cells with highest residuals within the 23 special wards of Tokyo. Such standardization of the number of detected centers is required to ensure consistent comparison between models. The number was selected as a rounded value close to the counts of cells identified using the defined significance threshold for two models and three activity groups (Table 4). It corresponds to approximately 6.8％ of the total number of cells in the study area (600 out of 8,761 cells). This proportion is comparable to that used in the reference study, where 532 cells (6.1％ of the same grid) were selected (Boratinskii and Osaragi, 2025). The authors noted that the threshold employed there was relatively strict, which makes a slight increase in the number of extracted cells justifiable in the present study. Furthermore, robustness checks and comparison with the results of the referenced study indicate that varying the threshold within a reasonable range (500-750 cells) does not alter the qualitative spatial patterns of the identified UAC.
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/34_20_t4.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
Having outlined the method for identifying UAC, we now turn to the results. Figure 3 presents the 600 cells with the highest residuals for the new model and the difference maps comparing new and reference models. The latter shows the cells identified by both models, as well as those identified by each one of them. Additionally, the Intersection Rate （IR） indicating the proportion of cells identified as UAC by both models out of 600 is shown on the difference maps. This metric is used for the quantitative evaluation of the spatial overlap of UAC extracted by the reference and proposed models.
From these visualizations and IR values, it can be observed that the differences between the two models are relatively minor, with the divergence rate not exceeding 12％. However, the observed differences exhibit distinct spatial patterns that vary by activity group. Mainly, they lie in the way UAC cells form spatial clusters. To support the visual analysis of maps in evaluating the differences in clustering patterns across activity groups and models, we computed two connectivity-based indicators: (i) the mean size of the connected component (cluster) to which a UAC cell belongs, and (ii) the share of UAC cells that form single-cell components (Table 5). Connected components were defined based on spatial adjacency of hexagonal cells.
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/34_20_t5.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
Furthermore, we provide activity coverage figures representing the proportion of the targeted activity (e.g., Work activities in the case of Work UAC) occurring within the identified UAC cells relative to all activities of the corresponding group in the study area. However, it is important to note that maximizing activity coverage is not the primary objective of UAC identification, which is instead focused on delineating areas that are distinct from their surroundings in terms of activity concentration.
Figure 3 reveals that, by both models, Work UAC are defined as large clusters located in the city center, generally reflecting the spatial distribution of the corresponding activity group. Most differences between the two models’ results are observed within the Yamanote Line, which can be considered the city center of Tokyo. Specifically, the new model omits some cells located inside large UAC while identifying more cells along their edges. For instance, the area around Tokyo Station, often referred to as Tokyo’s CBD, is detected as a coherent single cluster by the reference model, whereas the results of the new model contain several non-UAC cells within this area. The detailed analysis revealed that cells within large UAC that are not identified by the new model typically fall into two categories: (1) those with originally short median trip distances, and (2) those where missing values (NA) were replaced with the minimum neighborhood distance. In both cases, such cells are compared with highly active surrounding areas, resulting in negative residuals and, consequently, their exclusion from the identified UAC. Thus, while this exclusion may appear to disturb the internal continuity of large centers, it provides insights into their internal spatial structure. Regarding activity coverage, the proposed model exhibits a decrease of 2 percentage points compared to the reference model. This decrease reflects the shift from a global to a locally defined neighborhood for evaluating activity concentration: cells that are important within their local service areas are identified, rather than those with uniformly high values across the entire study area.
Commercial UAC tend to exhibit smaller clusters that are more evenly distributed around railway stations. Yet, there are also relatively large UAC along the Yamanote Line, corresponding to centers providing a wide range of services (e.g., Shibuya, Shinjuku). The new model detects additional cells around major city centers that were not classified as UAC in the previous version, while several peripheral cells previously identified as UAC are excluded. These differences are clearly reflected in a significantly larger mean cluster size in the new model’s results (Table 5). The wider peripheries of central UAC detected by the new model primarily result from the fact that it evaluates these cells against broader neighborhoods, due to longer local median trip distances in these central areas compared with the global median. As a result, such cells are assessed in the context of wider, typically less active surroundings, which increases their likelihood of being classified as UAC. Reconsidering the neighborhood definition resulted in a slight increase in the coverage of commercial activities (Table 5); however, as a side effect, the representation of peripheral UAC became more limited.
For public activities, UAC are typically detected as single cells or small clusters (Figure 3, Table 5). This reflects the allocation logic of public facilities, which, unlike commercial ones, often do not follow market-driven location patterns but are instead distributed to provide relatively even coverage across the urban area. Although this general tendency is also observed in the results of the new model, notable differences emerge in the spatial distribution of UAC cells. The new model reveals several relatively large clusters of UAC in the city center which were not visible in the reference model’s results. Although the increase in the mean cluster size is relatively modest due to the high proportion of single-cell components (Table 5), this change is clearly reflected in the size of the largest clusters, which increased from 10, 9, and 7 cells to 18, 15, and 13 cells, respectively. The new model reinforced and expanded clusters that were previously only weakly outlined or fragmented.
Thus, as suggested in the Introduction, accounting for wider service areas of large centers with unique or higher-order functions results in a broader representation of activity concentrations.
３.２ Analysis of newly identified public UACAs follows from the previous subsection, the spatial distribution analysis of Public UAC identified by the new and reference models revealed noticeable differences. Given the underrepresentation of public activities in previous studies and the importance of considering them for a more comprehensive understanding of urban structure (Boratinskii and Osaragi, 2024b), we conducted an additional analysis focusing on this group. Specifically, we examined several examples of Public UAC cells forming coherent clusters from the perspective of their content and functions. These clusters are highlighted by different colors in Figure 4.
Most of the selected UAC correspond to university campuses accompanied by surrounding facilities such as university hospitals and adjacent schools (Table 6). The two exceptions are Ikebukuro and Takadanobaba, which are not primarily formed around university campuses but instead function as multifunctional centers with a high concentration of activities from all three groups. Interestingly, other major centers such as Shinjuku and Shibuya are not as distinct in terms of public activities compared with their surroundings.
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/34_20_t6.jpg%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
This brief analysis suggests that large educational or healthcare institutions can generate substantial activity in their vicinity. By extracting and analyzing the three functional groups of UAC separately, it becomes evident that the concentration of activities in some locations is generated directly by public facilities, rather than by surrounding commercial or office functions. This observation further highlights the importance of inclusion of public activities in the urban center studies.
However, the functional profiles of areas where public activities concentrate seem to vary depending on their spatial and urban context. Among the identified clusters, Iidabashi, Ochanomizu, Takadanobaba, and Ikebukuro at least partially overlap with centers of commercial and work activities. In contrast, Aoyama, Todaimae, and Komaba are identified as predominantly public-oriented centers, with no direct spatial overlap with other activity groups.
One interesting question arising from this analysis is what factors determine whether a university campus or another large facility ― classified here as “Public” ― develops into a mixed-use center or remains a public-only activity cluster. In this section, we suggest several possible explanations based on local knowledge; however, a more systematic, quantitative investigation of these factors might provide more holistic findings.
1. Overall activity level and centrality. Location in the city center generally increases the likelihood of mixed-use development. However, examples such as Aoyama and Todaimae demonstrate that even central locations may be predominantly public UAC with little or no overlap with commercial or business functions.
2．Density and verticality of the built environment. In dense, multi-story urban environments, educational institutions often coexist with other facilities (e.g., hospitals, offices, department stores) within the same buildings or blocks. The vertical concentration of functions leads to different activity types being captured within the same cells of the two-dimensional grid, reinforcing the emergence of multifunctional UAC. However, whether this co-location implies strong functional interaction may vary from area to area.
3．Proximity to major multifunctional centers. The presence of a nearby but non-overlapping major center may increase the likelihood of public UAC emerging as distinct, mono-functional clusters. For instance, Aoyama is located at the edge of the larger Shibuya multifunctional center, which may absorb surrounding commercial and work activities. Such clusters ― often positioned at the margins of large commercial or business UAC ― may benefit from their proximity while remaining functionally separate, without developing their own retail corridors, as these are already provided by the adjacent major center.
4．Facility planning and spatial design. In some cases, facilities such as university campuses or hospitals are intentionally designed as self-contained environments, or “towns within towns,” to ensure security, privacy, or a specific atmosphere. These are often surrounded by green zones that separate them from other urban functions. On the other hand, even such campuses may include small-scale commercial facilities such as convenience stores or cafes, which could be identified as commercial UAC under a low significance threshold or a short neighborhood radius. Incorporating local trip distances and qualitative contextual analysis is expected to address this issue and yield more reliable results.
5. Physical and natural barriers. Major roads, parks, or other objects of the urban environment separating campuses from adjacent neighborhoods can limit their functional integration with surrounding areas, thus contributing to the formation of spatially isolated public centers.
This study proposed a modification of the UAC identification model by incorporating local median trip distances into the formulation of the spatial weights matrix within a spatial autoregression framework. While the overall differences from the reference model were modest, the new approach altered the spatial patterns of the detected UAC. Specifically, it tended to produce broader and more cohesive central clusters, while slightly reducing the inclusion of peripheral cells.
The most notable finding emerged in the “public activities” group, where the new model revealed several relatively big clusters centered around major university campuses and associated healthcare and educational facilities. These patterns suggest that large public institutions can independently sustain high activity levels, although their functional integration with commercial or employment areas varies depending on location, built form, and spatial context.
The findings demonstrate the technical feasibility of integrating localized mobility patterns into spatial interaction models, thereby enhancing their precision and contributing to a more nuanced understanding of urban activity dynamics. While the proposed model does not produce large quantitative differences in the spatial distribution of identified UAC compared to the reference model, the results demonstrate that a more flexible, local-behavior-informed specification can function stably and consistently. By adapting spatial neighborhood definitions to local trip patterns, the model is able to reflect differences between activity types and urban areas without relying on arbitrary or globally fixed thresholds. This suggests that the proposed framework provides a robust and transferable basis for UAC identification under heterogeneous urban conditions. Applying the method to other cities with different spatial structures and mobility patterns represents an important next step for further validation.
Finally, this study relied on a single aggregated metric (the median trip distance) for setting the neighborhood threshold, while future research could explore the use of location-specific distance decay functions to provide a more continuous representation of actual urban interactions in the spatial weights matrix.
