Abstract
Innovative activities are a key driver of economic and social development, with urban blocks serving as essential hubs for innovation. However, how urban block morphology shapes innovation vitality remains challenging. This study uses spatial analysis and SHAP-based explainable machine learning to analyze how block morphology characteristics affect urban innovation vitality, taking Hangzhou, a typical city of digital innovation, as a sample. The findings show that: 1. Land use diversity, floor area ratio, and street network density are the most influential factors; 2. Block morphology exhibits nonlinear effects. For example, when street network density exceeds 200 m per square kilometer, its impact on innovation vitality is positive, but it diminishes beyond 400 m per square kilometer; 3. Synergistic effects are prevalent, such as when street network density exceeds 200 m per square kilometer and floor area ratio is between 0 and 7, enhancing innovation vitality. The results reveal the nonlinear effects and interaction mechanisms at the block scale. And also discusses potential planning strategies for different regions based on varying influencing factors. The study provides an effective approach to balancing precision and interpretability in spatial analysis and offers empirical support for the application of complexity science in urban studies.
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Introduction
With the rapid development of globalization and information technology, the role of cities has evolved from a single engine of economic growth to a complex platform that integrates innovation-driven development, environmental sustainability, and social inclusion1. As the core space for knowledge production and dissemination, cities not only bear technological progress but also shape new global economic competition patterns through cultural innovation and social network reconstruction. In this context, Urban Innovation Vitality, the ability of a city to continuously drive innovative activities and realize value conversion by integrating knowledge, technology, and institutional resources, is considered a core indicator of urban competitiveness2. Against the backdrop of accelerated globalization and digitalization, a city’s innovation capacity has expanded beyond technological innovation to include social and cultural innovations, which together enhance the city’s competitiveness in the global economic system3,4. Therefore, understanding the multidimensional nature of urban innovation vitality and exploring pathways for its enhancement is crucial not only for improving overall urban development but also for achieving high-quality urbanization, optimizing resource allocation, and realizing sustainable development goals.
Systematic research on innovation activities can be traced back to Schumpeter’s theory of “creative destruction,” which emphasizes the fundamental role of technological innovation and institutional change in economic development5. He defined innovation as designing new products or applying new technologies, new processes, and new management methods to practical work to generate positive economic and social value6. Subsequent scholars expanded the spatial dimension of innovation research. Freeman’s national innovation systems theory revealed the interactive mechanism between institutional environments and knowledge flow7, while Cooke’s regional innovation systems theory emphasized the critical impact of localized networks on innovation performance8. As a carrier of national or regional innovation activities, cities are hubs for high-quality talent and technological resources. Enhancing urban innovation vitality is essential for promoting high-quality economic development and improving the overall innovation level of a country9. Urban innovation vitality is a widely applied concept describing the intensity of innovation activities10. Angelidou proposed that urban innovation vitality promotes the development of knowledge-based and innovation-driven economies, with space form optimization under the smart city framework significantly improving the efficiency of knowledge economy output11. In a comparative study on the urban innovation vitality of different cities, Zhou pointed out that urban innovation vitality refers to a city’s potential and ability in the development of innovation activities, proposing a two-dimensional evaluation model of “innovation potential-conversion capacity,” highlighting the importance of micro-level spatial design12. Chen argued that innovation vitality is a core element of advanced productive forces and a fundamental driving force of economic development13. Although existing research on the definition of innovation vitality varies (such as patent numbers, enterprise R&D intensity, or residents’ participation)14,15,16, the core consensus is that innovation vitality reflects the degree of participation in innovation activities in a region, embodying the innovation agents’ activity and creativity17. From the perspective of spatial production, innovation vitality, in essence, is an emergent result of the interaction between spatial elements and innovation agents18. This understanding provides a theoretical basis for constructing the “morphology-vitality” linkage framework in this study.
As the spatial carrier of innovation activities, urban morphology determines people’s activity patterns, communication paths, and social interaction methods, profoundly influencing knowledge spillover and social collaboration efficiency. Classic studies such as Saxenian’s analysis of Silicon Valley showed that open street layouts and mixed-use designs could foster informal exchanges19, leading to technological breakthroughs. Bill Hillier’s spatial morphology theory pointed out that cities are composed of basic spatial elements that form different open and enclosed spaces and various traffic corridors20. He emphasized that individual spatial elements cannot fully influence socio-economic activities, and the complex relationships between holistic spatial elements are the factors that influence and determine socio-economic phenomena21. Based on Hillier’s space syntax analysis, it is further pointed out that the “compositional properties” of space (such as integration and connectivity) indirectly shape innovation network structures by regulating population density and interaction frequency22,23,24. Therefore, the moderate mixture of urban morphological features helps integrate spaces, promotes knowledge spillover, and provides opportunities for innovation activities25. For example, Brisbane’s Public space design, convenient public transport connections, and shared spaces promote creative and technological exchange and collaboration26. Tokyo’s urban morphology demonstrates the positive impact of high density, mixed-use areas, and well-connected transport networks on innovation27. Shenzhen, through high density, high mobility, and functionally mixed urban layouts, has promoted interactions between tech talent and entrepreneurs, accelerating the development of businesses and technologies28. These practices collectively suggest that morphological features at the block scale (such as building density, function mix, and spatial permeability) may impact the innovation process through nonlinear mechanisms. However, existing research tends to focus on macro-scale urban forms (such as multi-center structures or green corridor networks) and lacks systematic dissection of the morphological effects and interaction mechanisms at the micro-level street block scale.
However, current research has three main limitations: First, there is an imbalance in the scale of analysis. Most literature focuses on the morphological impact at the city or regional level, emphasizing how optimizing the overall city form and functional layout can enhance innovation vitality and the interaction and collaboration of large-scale urban blocks or city clusters. The role of the street block as the basic unit for innovation activities is underexplored, and discussions on micro-level space forms and layouts within cities are relatively rare, resulting in planning strategies lacking practical implementation. Second, the methodology is singular. Traditional regression models struggle to capture the nonlinear effects of morphological factors (such as threshold and saturation phenomena), while machine learning methods, despite their strong fitting capabilities, are limited in their explanatory depth due to their “black-box” nature29. Third, there is insufficient explanation of mechanisms. Existing studies often simplify the morphology-vitality relationship into linear causality or only focus on the nonlinear impact of a single factor on innovation vitality, failing to reveal the complex network of multi-factor synergy/antagonism, such as the interaction effects between floor area ratio and street network density. These shortcomings make existing theories challenging to guide detailed design practices.
Quantitative analysis of urban morphology has evolved from statistical analysis to machine learning30. Machine learning methods, with their powerful fitting and prediction abilities, have been widely used in analyzing nonlinear features31. However, machine learning faces the challenge of balancing precision and interpretability32. Therefore, in tasks that require a deeper understanding of causal mechanisms, traditional machine learning models may struggle to provide clear or actionable insights33. Explainable AI (XAI) has shown promising results in analyzing the relationships and influencing factors between urban morphology, environments, and energy systems34. Notably, post-hoc explainable models like LIME and SHAP have demonstrated their value35. These methods not only allow for customized machine learning approaches for specific urban issues but also provide nonlinear explanations of features, multi-feature collaboration effects, and local sample analysis36, with significant potential in understanding complex interactive relationships within urban systems.
Therefore, this study takes Hangzhou City in China as an example, leveraging big data on urban morphology and urban patents, and applies SHAP-based explainable machine learning methods to analyze the impact of spatial morphology on urban innovation vitality, capturing its nonlinear characteristics and interactions, and providing more precise quantitative support for urban planning and policy making. The main contributions of this study include: 1. Quantifying and revealing the nonlinear effects and interactions of spatial morphology on innovation vitality, enriching the theoretical details of urban morphology. 2. Applying explainable machine learning models to balance the issues of precision and transparency that traditional analyses struggle with. 3. Conducting block-scale impact analysis to support the refinement of urban planning design strategies.
Methods
Analytical framework
This study uses big data and interpretable machine learning methods for analysis, which are divided into three steps, as show in (Fig. 1). First, data preparation is conducted by obtaining patent data from Baidu maps API (https://lbsyun.baidu.com/). Then, Baidu Maps’ batch geocoding function is used to acquire the geographic coordinates of patent applicants, establishing a geographic database of patents. Next, the kernel density of patents is calculated as the dependent variable for this study. Simultaneously, architectural data is collected from Baidu Maps, and green space and road network data are sourced from OpenStreetMap, creating a geographic database for block morphology. Twelve indicators, such as building scale, block compactness, morphological diversity, spatial intensity, functional structure, connectivity, and ecological structure, are calculated using a kilometer grid statistical method, and these serve as independent variables.
Analytical framework for the study. Left panel: Data acquisition process. Right panel data for Hangzhou were obtained from www.Baiten.cn, with geographic coordinates derived via batch geocoding on Baidu Maps. Urban block morphology data were sourced from OpenStreetMap. Bottom panels: Model training and comparing process using the random forest algorithm, with patent data and block morphology features inputted for analysis. Taking gradient boost and OLS as comparison. Bottom panel: SHAP-based explainability analysis. SHAP values were used to assess the importance of block morphology, variables nonlinear influencing and their interactions in urban innovation vitality. Then take hotspot analysis for the blocks and offering Planning strategy according to the differences in factor Importance of blocks in different hotspots.
Next, we conduct model training and comparison, comparing Random Forest with Gradient Boosting Trees. The optimal parameter combination is determined through grid search, and the model’s accuracy and generalization ability are evaluated based on fivefold cross-validation, MSE, and adjusted R2, with the best model selected. The multiple regression model is then compared with the optimal model to assess whether there are significant nonlinear characteristics in the impact of block morphology on urban innovation vitality.
Finally, an explainability analysis is performed using SHAP. The mean SHAP value is calculated based on the optimal model to generate a Force Plot, assessing the importance of each block morphology indicator. The Top 6 Important Factors are selected to calculate SHAP-values and generate a Dependence Scatter Plot to evaluate their nonlinear effects. Then, the Top 8 Important Factors and their most related factors are selected to calculate SHAP-interaction-values to assess interaction effects. Hotspot and cold spot analysis is applied to classify areas of urban innovation vitality, followed by a differential analysis of Factor Importance within these classified areas, and specific spatial planning strategies are proposed.
Study area
This study selects the urban area of Hangzhou as the research scope, as shown in (Fig. 2). The city not only possesses digital innovation endowment but also features a composite characteristic within the Chinese urban system, offering universal insights for cities at different stages of development and functional types. Hangzhou is a typical city in the Yangtze River Delta region for the deep integration of digital economy and real economy. As the headquarters of global tech giants such as Alibaba and Hikvision, and with emerging tech companies like DeepSeek and Untree in recent years, the value-added proportion of its digital core industry to GDP has reached 27.6% (2022). This characteristic makes it an ideal sample for studying urban innovation vitality37. Covering an area of 7,850 square kilometers with a population of 12.52 million, Hangzhou provides a complete spectrum of mixed urban forms. The main urban area of Hangzhou includes diverse morphological types such as historical neighborhoods, industrial-urban integration districts, traditional industrial zones, and ecological innovation experimental zones, which help reveal the impact of block morphology on urban innovation vitality.
Study area Hangzhou city. The geographic extent of the study area in Hangzhou, with urban and construction areas shown in gray, mountainous regions in green, and water bodies in blue. The map was created by the author using ArcMap 10.5 based on DEM data. The terrain data used is sourced from the open-source DEM (Digital Elevation Model) provided by the Geospatial Data Cloud of the Chinese Academy of Sciences (https://www.gscloud.cn/sources/index?pid=1&rootid=1), and the water body data comes from OSM. The software used for processing is ArcMap 10.5 (https://desktop.arcgis.com/zh-cn/desktop/index.html).
Data description
Architecture, roads and green spaces
The architectural data, sourced from Baidu Maps (updated in March 2023), covers all completed buildings in the main urban area of Hangzhou (a total of 311,368 buildings), as show in (Fig. 3). The buildings include residential, commercial, office, industrial, public service, and public facilities of all types. The data attributes include the building height, floor area, floor area perimeter, and the primary function of the land where the building is located. The Baidu Maps BD09 coordinate system was converted to the CGCS2000 national geodetic coordinate system. Abnormal building records with a height > 500m (accounting for 0.01%) were removed, and missing building height values (0.03%) were imputed using the average building height within the same grid. The completeness of the building data was verified through remote sensing imagery and building data profile matching and validation.
Research data: Buildings, roads and green spaces. Top Panel: The distribution of building data within the study area. A zoomed-in box highlights the detailed building layout of a specific area. The table below the box provides a sample of the data attributes related to the buildings. Bottom panel (Left): The road network data, displaying the expressways, main roads, and urban branch road. Bottom panel (Right): The urban green spaces. The map was created by the author using ArcMap 10.5 based on Baidu Building and OSM data. The Baidu Building data is sourced from the Baidu Map API (https://lbsyun.baidu.com/), and the data for rivers, roads, and green spaces are from OSM. The software used for processing is ArcMap 10.5.
Roads and green spaces
The road network and urban green space data for the Hangzhou urban area were sourced from OpenStreetMap (OSM, January 2023 version), which includes highways, main roads, secondary roads, and branch roads in a four-level road network, as well as open spaces such as parks, squares, and street greenery. The OSM WGS84 coordinate system was converted to the CGCS2000 national geodetic coordinate system. The road data were checked and corrected for topology using ArcMap 10.5, and green space area was calibrated using the NDVI index (Landsat 8 imagery) with an error rate of < 5%. Compared to publicly available data from the Hangzhou Urban Planning Bureau, the completeness of the OSM road network was 95.3%, and the green space data completeness was 87.6% (the missing parts were mainly unregistered small community green spaces).
Authorized patents
Patent data has been widely recognized as an effective representation of innovation vitality from the perspective of innovation output38. For example, Jiang used patent data to assess the level of urban innovation39, while Shi analyzed the contribution of talent to urban innovation using patent data40. Therefore, in this study, authorized patent data, which are the most technically demanding and innovative, were used as representative data for the explanatory variable of innovation vitality.
The study used authorized patent data from January 1 to December 30, 2022, sourced from www.Baiten.cn. Geographic coordinates were retrieved through geocoding using the “patent applicant address” attribute on Baidu Maps, followed by coordinate correction and conversion to the CGCS2000 national geodetic coordinate system. Duplicate records of the same patent number and patents with applicant addresses located at non-innovative entities, such as post office boxes or government courtyards (accounting for 2.1%), were excluded. The final dataset contained a total of 145,333 authorized patents within the study area. Compared to the public data from the National Intellectual Property Office, the discrepancy rate was < 3% (the total authorized patents in Hangzhou in 2022 were 149,812).
Variables
This study divides the block morphological indicators into two main dimensions: Morphological Features and Structure Features. The theoretical foundation is based on the analysis of physical space characteristics in urban morphology and the spatial mechanisms of innovation activities in innovation geography. The selection of indicators follows 3 principles:
Theory-driven, Indicators closely related to innovation vitality are selected based on classic literature (e.g., Jacobs’ street diversity theory)41. Data availability, Ensure that the indicators can be quantified using open geographic big data (e.g., building, POI, and street network data). Potential interpretability, Prioritize indicators that have been validated by existing empirical studies (e.g., floor area ratio, functional mix).
Morphological features
Urban morphology focuses on the composition and evolution of urban physical space, emphasizing the direct shaping effect of the physical environment on human behavior42. It illustrates how morphology determines function, i.e., how physical characteristics of blocks (such as building scale, density, and morphological diversity) influence interaction frequency and patterns among innovation agents by adjusting spatial accessibility, visual permeability, and activity density43. The relevant indicators are as show in (Table 1).
Building scale
The average building area, building volume, and building height within a grid are calculated. Medium-scale buildings are most conducive to knowledge spillover44. Larger building scales may restrict public space permeability, impacting collaborative innovation45.
Block compactness
The ratio of total building area to grid area is compared to measure the compactness of the block. High density promotes informal exchange by reducing walking distances46, but excessive compactness can lead to environmental pressure47.
Block morphological diversity
The standard deviation of building heights and the complexity of building forms (the ratio of average floor area to average perimeter) are calculated. Complex forms (low CBF) provide diverse semi-public spaces and support cross-boundary cooperation42.
Block spatial intensity
The ratio of total floor area to grid area (FAR) is calculated. A moderate FAR balances density and comfort, which is a typical feature of innovation clusters47.
Structure features
Innovation geography focuses on the spatial distribution and driving mechanisms of innovation activities. Research has shown that space promotes knowledge spillover effects, and innovation relies on face-to-face communication of tacit knowledge. Spatial structure (such as functional mix and street network connectivity) promotes cross-sector collaboration by reducing the distance of knowledge transfer48. In constructing innovation ecosystems, innovation vitality is supported by both “hard infrastructure” (such as research institutions) and “soft environments” (such as cultural inclusivity), with both being integrated through spatial structure45. The relevant indicators in this study are as show in (Table 1).
Block functional structure
The shannon diversity index of different types of POIs within the grid is calculated to assess the functional structure of the block. Mixed functions reduce costs and enhance innovation efficiency42.
Block connectivity
The ratio of total street length to grid area is calculated. Increased connectivity significantly promotes the formation of innovation networks44.
Block ecological structure
The ratio of green space area to grid area is used to measure this feature. Moderate green space enhances creativity by reducing stress49, while excessive greenery may dilute spatial vitality.
In the subsequent Pearson correlation analysis of the variables, the results revealed three groups of indicators that exhibited high correlations (over 0.7), as show in (Fig. 4). One group consisted of average built-up area (ABA) and Average Building Volume (ABV), which share a correlation coefficient of 0.9. Both indicators describe the feature of Building Scale, and due to their high correlation, we decided to exclude ABV which had a lower correlation with patent kernel density.
Pearson correlation of indicators on block morphology. The pearson correlation coefficients between various indicators of urban block morphology. Each square represents the correlation between two specific block morphology feature. The numbers displayed within each square indicate the Pearson correlation coefficients, ranging from −1 to 1, where values closer to 1 represent a strong positive correlation, values closer to −1 represent a strong negative correlation, and values near 0 suggest no significant correlation. The color scale further emphasizes the strength of these correlations, with darker shades representing stronger positive correlations and lighter shades indicating weaker or negative correlations.
The other group comprised floor area ratio (FAR) and building density (BD), with a correlation coefficient of 0.87. These indicators represent two distinct features, block spatial intensity and block compactness, respectively. Given their representation of different aspects of block morphology and the significance of both features in our analysis, we opted to retain both indicators in our study.
This study focuses on analyzing the impact of block-scale urban innovation vitality, using the kilometer grid, commonly employed at the micro scale in urban studies44, as the sampling unit. This approach effectively balances the following needs: detail preservation, capturing internal morphological heterogeneity within blocks, and avoiding spatial feature homogenization caused by larger scales. Spatial continuity, preventing small-scale fragmentation of the block’s functional integrity. Scale matching, as the spatial spillover effect of urban innovation activities typically radiates over 800-1200m47, and the kilometer grid can effectively cover this interaction range. Additionally, the spacing between major roads in Hangzhou is generally 800-1500m, making the kilometer grid nearly equivalent to the block scale.
Modeling approach
This study uses Random Forests to model the nonlinear effects of block morphology on urban innovation vitality. Random Forest is a supervised learning algorithm based on an ensemble learning framework, widely used for classification and regression problems. It improves model accuracy and robustness by constructing multiple decision trees and averaging their predictions50. Each decision tree in the model is trained on a random subset of the training data, and during the division at each node, only a random subset of features is selected. This reduces the variance of the model and prevents overfitting. Random forest can handle large datasets and provides good predictive performance. By integrating multiple trees, it also reduces sensitivity to data noise and outliers. In this study, we control accuracy and generalization ability by adjusting the parameter combinations of {‘max_depth’, ‘min_samples_leaf’, ‘min_samples_split’, ‘n_estimators’}.
To interpret the random forest model, we apply the SHAP package (Python 3.9), which computes both Shapley values and Shapley interaction values. SHAP (shapley additive explanations) is a framework used to explain machine learning model outputs, based on the concept of Shapley values from game theory. Originally used to allocate the share of benefits among collaborators, Shapley values in SHAP quantify the contribution of each feature to the model output by calculating its marginal contribution51. The core idea of SHAP is to precisely calculate the marginal contribution of each feature by considering all possible feature combinations, thus providing the specific impact of each feature on the final prediction. SHAP not only provides global feature importance evaluation but also offers the specific impact of features for each data point (locally), making the model more interpretable. Compared to other model interpretation methods, SHAP provides a consistent approach, allowing for reasonable distribution of each feature’s contribution as the model changes, and is applicable to various machine learning algorithms, including random forest, support vector machines, and neural networks52. By leveraging SHAP, we are able to uncover the model’s behavior, providing a global summary of the relative importance of block morphology and offering local insights into its nonlinear and interaction effects.
Code availability
The code used to perform the SHAP-based nonlinear analysis in this study is publicly available at https://github.com/EatXx/SHAP-for-nonlinear-analysis.
Results
Innovation vitality in Hangzhou city
The spatial distribution of urban innovation vitality reveals that areas with higher vitality are predominantly located in the eastern part of Hangzhou, forming two significant concentric clusters on both sides of the Qiantang River (especially in the urban areas east of West Lake), which represents the central area of the city, as show in (Fig. 5). Beyond the central zone, several secondary vibrant regions emerge, illustrating a polycentric structure of urban innovation spaces. Further investigation into spatial heterogeneity indicates the existence of spatial agglomeration in urban innovation vitality, with a Moran’s Index value of 0.37. This suggests a non-random pattern of innovation vitality across the city, highlighting areas of concentrated innovation activities and potential zones for targeted urban development and policy interventions to foster innovation ecosystems.
Spatial distribution of urban innovation vitality. The spatial distribution of urban innovation vitality, based on kernel density of patent data. The grid cells color-coded to represent varying levels of vitality, ranging from low to high. Warmer colors indicate areas with higher patent activity and innovation vitality, while cooler colors reflect lower vitality. The inset box displays the distribution of patents.
Relative importance of block morphology
Random Forest (best parameter by gride search: {‘max_depth’: None, ‘min_samples_leaf’: 1, ‘min_samples_split’: 2, ‘n_estimators’: 200}) exhibits lower MSE on both the training and test sets, as show in (Fig. 6), shows more stable performance across cross-validation folds, while Gradient Boosting exhibits larger variability in its MSE across different folds, suggesting random forest has lower sensitivity to data variation and better generalization. Random Forest achieves higher adjusted R2 values on both the training and test sets, meaning it explains a greater portion of the variance in both the training and test datasets. The Random Forest also shows relatively consistent performance across both the training and test sets, shows a better robustness. Besides, the adjusted R2 of the multivariate linear regression model, prepared as a benchmark, was 0.18, indicates the presence of nonlinear effects of block morphology on innovation vitality, underscoring the necessity for further analysis to elucidate these complex influences.
The cross-validation, MSE and adjusted R2 between random forest and gradient boosting. Left panel (cross-validation MSE comparison): The comparison of the mean squared error (MSE) from cross-validation between two models, random forest (represented by the blue line) and gradient boosting (represented by the red line), across different folds (Fold 1 to Fold 5). Middle panel (Comparison of MSE for random forest and gradient boosting): A bar chart comparing the MSE values for Random Forest (in the left) and gradient boosting (in the right) models, showing the performance for each model (training sets in blue and test sets in red). Right panel (comparison of adjusted R2 for random forest and gradient boosting): A bar chart comparing the adjusted R2 values between the two models, Random Forest (in the left) and Gradient Boosting (in the right), for training sets in blue and test sets in red.
Global importance is determined by averaging the absolute shapley values for each variable. Land use diversity (LUD) emerged as the most crucial explanatory variable, as show in (Fig. 7), highlighting the significant role of block functional structure in urban innovation vitality. This was closely followed by floor area ratio (FAR) and street network density (SND), indicating that the efficiency of spatial utilization and connectivity of blocks significantly influence the promotion of urban innovation vitality. Following these, as indicators representing block morphology diversity, variance in building height (VBH) and complexity of building form (CBF), demonstrate the positive impact of morphological diversity on fostering innovation activities.
Importance of block morphology indicators. The importance of various block morphology factors on urban innovation vitality, calculated based on the average absolute SHAP values. The rank of different block morphology indicators according to their impact on urban innovation vitality. The height of each bar reflects the relative importance of each factor.
The contribution of the building density (BD) indicator, representing Block Compactness, was significantly weaker than that of FAR. This divergence from the general drivers of urban vitality, which are more pronouncedly affected by planar compactness, underscores a distinct dynamic in the context of innovation vitality. The influence of land use diversity (LUD) was less than that of predominant land use (PLU), indicating that the promotive effect of a block’s dominant function outweighs that of functional diversity.
Within the building scale, the role of average building height (ABH) was less impactful than ABA, suggesting that the public’s perception of architectural scale in the planar dimension is stronger than in the vertical dimension, thus leading to differences in contributions to urban innovation vitality.
Overall, the intermingling of morphological features and structure features in the importance ranking underscores that both internal morphological differences and overall structure are crucial for urban innovation vitality at the block scale, necessitating a combined approach for maximal effect.
Nonlinear effects of block morphology
This study employs local dependence plots to uncover the patterns of influence exerted by block morphology variables on urban innovation vitality. The top six indicators ranked by importance from the previous section were selected to calculate SHAP values for generating local dependence plots. In these plots, the position on the x-axis represents variable values, while the position on the y-axis signifies the local effect (SHAP value). Overall, the plots reveal that the local effects of block morphology variables on urban innovation vitality vary at different rates when falling into diverse ranges of values, indicating the nonlinear patterns as previously hypothesized.
Predominant land use exhibits a threshold-type nonlinear effect, as show in (Fig. 8), where local effects initially increase and then plateau. Further categorical analysis reveals that blocks with primary attributes related to corporations, science and education, or healthcare contribute more to innovative outputs. FAR is positively correlated with innovation vitality, particularly noticeable are two distinct trend lines within the 0–10 FAR range. One possible explanation is the spatial variability of FAR’s impact, with a higher rate of local effects in central urban areas or technology parks. SND’s influence approximates an S-shaped curve, where an increase in street network density beyond 200 m/km2 enhances innovation vitality by intensifying spatial interactions among innovation entities. However, beyond 400 m/km2, this promotive effect becomes less significant. Moderate density road networks promote innovation vitality by enhancing spatial accessibility and facilitating informal communication and knowledge spillover among innovation entities. For instance, the Wukang Road-Anfu Road block in Shanghai, through optimized street network density (SND ≈ 300 m/km2), created a "walkable-friendly" environment, attracting creative enterprises, which verifies the importance of moderate connectivity47. Excessively high street network density may lead to spatial fragmentation, increasing traffic conflicts and resource allocation issues. For example, some technology parks in Nanshan District, Shenzhen, weakened the clustering effect of core innovation units due to excessive densification of branch roads (SND ≈ 450 m/km2)53. Furthermore, when the road area proportion is too high, it may crowd out public space and green areas, reducing environmental comfort and inhibiting innovation cognitive efficiency.
Local effects of top 6 block morphology variables on urban innovation vitality. The SHAP values for the top six influential factors affecting urban innovation vitality. For each factor, the position on the x-axis represents the variable values, while the position on the y-axis signifies the local effect (SHAP value). Each small plot illustrates how changes in the respective block morphology indicators impact innovation vitality.
Complexity of building form mildly promotes innovation vitality within the 0–10 range but ceases to do so beyond this interval. Variance in Building Height (VBH) requires reaching a certain threshold to be effective, where diversity in building height enhances innovation vitality when the standard deviation of block building heights exceeds 20. Average ABA also demonstrates a threshold-type nonlinear effect, where an increase in area within the 0–2000m2 range rapidly fosters innovation vitality, slowing down between 2000–3000m2, and disappearing beyond 3000m2. Smaller base areas (ABA ≤ 2000m2) promote innovation by improving block permeability and shortening walking paths. Additionally, some variables exhibit small cluster samples deviating from the overall trend, such as FAR, SND, and ABA, which have samples with significantly higher rates of local effects. One potential explanation is spatial heterogeneity or other forms of heterogeneity, such as the pronounced promotive effects in specific institutions or educational districts in city centers.
Interaction effects among block morphology
The impact of block morphology is comprised of local effects and local interaction effects with other variables. To delve deeper, we visualized the local interaction effects among block morphology variables. For each variable, we calculated its interaction effects with other variables by averaging the absolute Shapley interaction values for each pair of variables, and then identified the variable with which it has the strongest interaction effect. Each subplot corresponds to a pair of variables, illustrating how the local effect of one variable on vibrancy amplifies or diminishes with changes in another variable. Specifically, each point in the plots corresponds to a kilometer grid sample. The x-axis displays one variable, and the color on the right y-axis indicates the range of changes in the other variable with which it has the strongest interaction effect. The position on the left y-axis represents the local interaction effects between the pair of variables.
The interaction between predominant land use and variance in building height is the most intense, as show in (Fig. 9), indicating that diverse building forms/volumes on specific land uses can stimulate urban innovation vitality. The strongest interaction between floor area ratio and street network density, with the interacting Street Network Density ranging from 0 to 250 m per square kilometer, suggests that a synchronized increase in land use intensity and connectivity within a reasonable range can stimulate synergistic effects. The variable that interacts most strongly with Street network density is floor area ratio, with a significant synergistic effect (SHAP interaction value above 0) when street network density exceeds 200 m per square kilometer and Floor Area Ratio is between 0 to 7. Blocks can form a “3D innovation network” by coupling vertical mixed functions (e.g., commercial at the bottom + R&D above) and horizontal connectivity (moderate SND). However, high FAR development relies on high land value support (e.g., central areas), while increasing SND involves road construction and maintenance costs. Their synergy needs to match the regional economic carrying capacity. For example, the “high FAR + high SND” model was successful in Lujiazui, Shanghai, but attempts to replicate this combination in suburban areas led to project stagnation due to cost overruns54. Complexity of Building Form’s strongest interacting variable is also Floor Area Ratio, indicating that an increase in land use intensity promotes urban innovation when planar dimensional changes in block morphology are enhanced. The interaction between Variance in Building Height and Average Building Height is the strongest, suggesting that the combination of vertical complexity and scale can produce synergistic effects, which should be considered synchronously in vertical design. The strongest interaction between average built-up area and variance in building height is most pronounced within a area of 0-2000m2, with the synergistic effect declining beyond 2000m2 and tending to disappear beyond 6000m2. Moderate VBH can enhance block visual richness, stimulate non-directional thinking, and, through changes in wind channels and sunlight distribution, affect outdoor activity comfort. However, excessive VBH may cause spatial chaos, hindering innovation collaboration efficiency. The interaction between land use diversity (LUD) and SND has a threshold effect, where LUD greater than 1.5 and SND greater than 50 m per square kilometer promote innovation. Enhancing mixed land use and street network density can effectively promote collaboration and spatial utilization efficiency of different functions at the block scale, helping to form innovation industrial chains and improve innovation vitality.
local interaction effects of top 8 block morphology variables on urban innovation vitality. The SHAP interaction values for the top eight influential factors and their most relevant factors. The series of scatter plots illustrate the interaction effects between pairs of demographic characteristics on urban innovation vitality. Each plot shows how the SHAP value (on the left y-axis) for one feature (on the right y-axis) changes in relation to another feature (on the x-axis). Blue Dots: indicating a lower impact on the predictive outcome when both features are considered together. Red Dots: suggesting a higher impact on the predictive outcome when considering the interaction of both features.
Synergistic interactions are prevalent among variables, indicating that in block planning and urban design, guiding block morphology to foster innovation vitality requires more than just considering the nonlinear impacts of individual variables. It is also essential to account for the synergistic effects of interacting variables.
Discussion
Evaluating the local effects of block morphology variables on urban innovation vitality can provide insightful references for enhancing the development of urban innovation spaces. A critical approach to achieving this goal involves identifying similar patterns of local effects across blocks with varying levels of urban innovation vitality and formulating targeted strategies. Such an approach could lead to more precise and nuanced interventions in block morphology. We utilized Getis-Ord Gi* to identify areas with similar levels of innovation vitality intensity and grouped them for subsequent analysis using random forest regression. Based on this, the variable importance evaluation of SHAP is used to identify the key influencing factors in each region, and, based on the previous interaction effects, planning strategies and possible design directions are proposed for the differentiated influencing factors. The results delineated three types of areas: blocks in urban centers areas, blocks besides urban centers areas and blocks besides urban centers areas, as show in (Fig. 10). These blocks comprising 298 km grid samples, which account for 3.41% of all grids.
Hotspot areas and the spatial heterogeneity of variable impacts. Top panel: The results of hotspot analysis, the color gradient represents the significance of spatial hotspots in relation to urban innovation vitality. Areas shaded in blue denote cold spots, with red indicating hotspot in 99% confidence. Areas shaded in yellow represent hotspots in 95% confidence, with green grides indicating hotspots in 90% confidence. The light white blue regions indicate areas that are not significant. Bottom panel: The SHAP value importance rankings for block morphology’s impact on innovation vitality in three distinct hotspot grid categories. The height of each bar reflects the relative importance of each factor.
Strategies for blocks in urban centers areas
Dominating the hotspot regions, high hotspot areas constitute 63.76% of these regions and are spatially located in the core areas of the city’s main and major sub-centers. The top three variables in terms of importance in these areas are Complexity of Building Form, variance in building height, and predominant land use. This significantly differs from the global variable importance, suggesting that due to higher land rent in central areas, there is limited affordability for certain land types, leading to higher land use intensity. Therefore, the urban design in these areas should place more emphasis on the diversity of block morphology, taking into account the synergistic effects of variables. The FAR can be appropriately increased, such as controlling the FAR in the core area between 3.5–6.5, and alleviating high-density pressure through an elevated skywalk system (with a spacing of ≤ 200 m). At the same time, promote diversity in form and height in vertical design, such as incorporating vertical mixed-use designs, adjusting the ratio of high-rise buildings (10 floors and above) to mid-rise buildings (7–9 floors), and setting up shared innovation spaces in rooftops and podiums. The next three important variables are average built-up area, green space ratio, and land use diversity, this suggests that maintaining an appropriate building scale and adopting buildings with a footprint area of less than 2000 square meters to ensure block permeability may be more conducive to innovation vitality. Simultaneously, three-dimensional greening can compensate for insufficient ground-level greenery, enhancing vertical greening coverage and the proportion of rooftop gardens. Increasing building volume should also be combined with height diversity. For example, the case of Shenzhen Bay Eco-city can be referenced, where techniques such as setbacks and cantilevers are used to increase facade diversity53. Attention should also be given to block structure, emphasizing diversity of functions and the integration of green spaces in block planning.
Strategies for blocks besides urban centers areas
Typically located on the periphery of high hotspot areas and accounting for 19.46% of hotspot regions, these areas have similar top three importance variables: Average Built-up Area, Variance in Building Height, and Predominant Land Use. Similar to high hotspot areas, urban design should focus on enhancing form diversity while increasing spatial utilization and appropriately scaling up building dimensions, for instance, referring to the “small block regulation” in Chengdu High-tech Zone, “parcel consolidation” is used to reduce fragmented land55, guiding compact development, enhancing the alignment rate of street-facing buildings, and strengthening the continuity of the street interface. The next set of important variables includes Complexity of Building Form, Street Network Density, and Building Density, indicating that these areas lack the construction intensity and infrastructure completeness of high hotspot areas. Hence, the branch road network can be appropriately densified, controlling the road right-of-way width while ensuring bidirectional two-lane roads and pedestrian lanes. Increasing intersection density and reducing walking distance between block units can gradually enhance the connectivity and compactness of the blocks through urban design and blockplanning.
Strategies for blocks in subcenter areas
Mostly situated in the city’s peripheral sub-centers and making up 16.78% of hotspot regions, the top three variables of importance here are predominant land use, street network density, and average built-up area. On the one hand, lower rents in these areas offer a broader choice of land types, necessitating a focus on the layout of land for research, education, commercial finance, etc., in planning innovation-oriented blocks. On the other hand, infrastructure and spatial utilization further decline in these areas, making it crucial to increase the marginal utility of enhancing street network density and building volume in planning, for example, strengthen road cross-section design by adopting a “3-5-3” model (3 m pedestrian lanes +5 m mixed traffic lanes +3 m innovation display lanes), integrating movable facilities such as container labs or roadshow cabins. The next three elements: Floor Area Ratio, Average Building Height, and Green Space Ratio, reiterate that increasing land use intensity and form diversity in urban design promotes innovation vitality. Simultaneously, enhancing the ecological structure of blocks and optimizing the environmental quality is also essential for innovation output. Therefore, the blue-green network of the block can be appropriately enhanced. For example, the blue-green network could create an ecological framework with “500 m greenery and 1 km water visibility,” reserving 10–15% of flexible land in waterfront areas for temporary exhibitions. Climate-responsive design should be emphasized, such as increasing the permeability of paving materials, improving building shading coefficients, and reducing the urban heat island effect.
Other blocks
Urban innovation constitutes only a facet of the multifunctionality of urban areas. Consequently, blocks in non-hotspot regions (represented as ‘not significant’ grids in the figure) predominantly serve other residential and productive functions, rather than bearing the responsibility for urban innovation output. In urban design and block planning, there generally isn’t a need for additional guidance aimed specifically at enhancing innovation vitality in these areas.
Conclusion
Innovation activities are a key driving force for the economic and social development of humanity, and urban blocks serve as the primary venues where innovation occurs. Their morphology influences the vitality of urban innovation. However, quantifying the nonlinear effects of block morphology on innovation activities remains a challenge. This study, based on urban morphology and innovation geography, reveals the nonlinear effects and interaction mechanisms at the block scale, discussing possible planning and design strategies in different regions under the background of differentiated influencing factors. This aligns with the current trend of spatial design shifting from purely morphology-oriented to utility-morphology-oriented, providing empirical support for the application of complexity science in urban research. Meanwhile, by using SHAP-based interpretable machine learning, this study overcomes the “black-box” dilemma, achieving a balance between high-precision prediction and mechanism interpretation, offering a new tool for analyzing spatial non-stationary relationships.
The study shows that land use diversity is the most important contributing factor, which aligns with research emphasizing that functional mixing promotes knowledge spillover48. Following closely are FAR and SND, which indicate the significant impact of spatial utilization efficiency and connectivity of blocks. VBH and CBF highlight the facilitative role of block morphology diversity. The contribution of BD is significantly lower than that of FAR, which contrasts with the general understanding of urban vitality drivers, where planar factors typically have a greater impact than vertical dimensions47. A possible explanation is that innovation is a geographically low-probability event, and innovation vitality relies more on the efficiency and intensity of space utilization. Overall, at the block scale, a combination of internal morphological differences and overall structure is necessary to achieve the maximum effect.
Local dependence plots reveal the nonlinear effects of block vitality variables on urban innovation vitality. Variables generally exhibit threshold inflection points, where the rate of increase or decrease in local effects changes before and after the inflection point, which corroborates existing morphological studies44. However, compared to previous literature, this study further quantifies the threshold effects of the indicators, providing scientific boundaries for refined planning. For example, when the FAR exceeds 10, the growth rate of local effects starts to slow down, indicating that spatial production efficiency may have already been largely met. Inflection points can be divided into two categories: upper and lower points. The upper point indicates that further increases in block morphology variables will no longer enhance urban innovation vitality. For example, increasing ABA beyond 3000 square meters no longer effectively promotes vitality. The lower point represents the threshold required to begin enhancing innovation vitality. For instance, when VBH greater than 20 is required to accelerate vitality growth. These nonlinear effects provide policymakers with detailed insights into the effective range within which urban innovation vitality can be promoted through planning/design interventions.
SHAP interaction values show that the local effects of block morphology variables can be amplified or diminished by changes in other variables. In particular, the interaction effects of variables from different dimensions are consistent with the findings regarding the impact of urban block morphology on urban vitality. For example, the interaction between SND and FAR is most significant when SND exceeds 200 m per square kilometer and FAR ranges from 0 to 7. Therefore, if the planning goal is to enhance vitality, it is recommended to increase block connectivity and spatial utilization. Similarly, the strongest interaction between VBH and ABH produces synergistic effects. This resonates with the recent “dissolution model” theory, where Yang proposed that “heterogeneous mixing” design can stimulate innovation56, but did not specify the morphological parameter thresholds. This study quantifies the effective range of morphological diversity, providing empirical support for the “dissolution model.” Besides, combining mid/high-rise buildings with low-rise buildings is an effective way to integrate architectural forms, which is likely to trigger more economic activities, thereby stimulating innovation vitality57. The interaction effects suggest that promoting urban innovation vitality requires considering the conditions of other block morphology dimensions/variables to achieve synergistic effects while avoiding negative interactions.
Although this study provides new insights into the relationship between block morphology and innovation vitality, there are still some limitations. Firstly, patents are a commonly used indicator for measuring innovation output, but they do not fully represent all types of innovation activities. They fail to capture non-technological innovations (e.g., business models, cultural creativity), tacit knowledge outputs (e.g., craftsmanship, localized experience), and a large amount of academic innovation (such as published papers), and there are spatial attribution errors, as multinational companies often register patents at their headquarters. Secondly, SHAP methods have limitations in spatial interpretation. Geospatial data typically exhibit spatial dependence, but SHAP’s feature contribution calculation assumes sample independence, ignoring the interference of spatial autocorrelation on interpretability. And although SHAP can quantify the contribution of variables to individual samples through local explanations, the contribution of certain sample groups in interaction and nonlinear effects still needs to be accurately quantified by combining other statistical analysis methods. Moreover, this study explored statistical interpretation of SHAP local explanations but did not use them for spatial interpretation. Additionally, regarding data timeliness and spatial granularity, this study is based on static 2022 data and fails to capture the dynamic evolution of urban morphology. The kilometer grid units may also weaken the morphological heterogeneity of micro-level blocks. Finally, in terms of case generalizability, this study only discusses one city, Hangzhou, and the conclusions may have limitations in cross-regional applicability.
Therefore, future research could integrate data on enterprise R&D cooperation, university-industry knowledge flow, and other relationships to supplement the measurement of innovation vitality from multiple subjects. Combining spatial explicit methods like Geographically Weighted Regression (GWR) to capture spatial non-stationarity and features, and using local Moran’s I to conduct spatial analysis of SHAP local explanations could also be beneficial. Additionally, a multi-scale spatiotemporal dynamic analysis framework could be constructed using historical patent data, integrating time-series remote sensing data and street view imagery. Comparisons could be made across different cities, such as Shanghai, Guangzhou, and Singapore. Future studies could further explore the connection between interaction mechanisms and design strategies, examining planning and design strategies for innovation incentives in different types and scales of spaces.
Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
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Acknowledgements
The author would like to thank Professor Xinyue Ye from Texas A&M University for his valuable assistance in this research. And we would like to thank ChatGPT for its assistance in translating and refining the language of this manuscript.
Funding
This work was supported by The Joint Funds of The Zhejiang Provincial Natural Science Foundation of China under Grant LHZY24A010001.
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Yichen Ruan wrote the main manuscript text and prepared figures. Nina Liu did the research and data collection. Xiaoyi Zhang developed the manuscript. Yichen Ruan did data analysis. Nina Liu and Jiwu Wang checked the main manuscript text. Nina Liu did the survey. All authors reviewed the manuscript.
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Ruan, Y., Zhang, X., Wang, J. et al. Understanding the role of urban block morphology in innovation vitality through explainable machine learning. Sci Rep 15, 21337 (2025). https://doi.org/10.1038/s41598-025-06587-5
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DOI: https://doi.org/10.1038/s41598-025-06587-5
