Agglomeration Characteristics and Influencing Factors of Urban Innovation Spaces Based on the Distribution Data of High-Tech Enterprises in Harbin

: In the knowledge economy, innovation is playing an increasingly important role in urban sustainable development. Thus, how to strengthen the construction of innovation spaces has become a significant issue. Based on data from high-tech enterprises in the central urban area of Harbin, this study analyzes the distribution, agglomeration characteristics, and influencing factors of urban innovation spaces. The influencing factor index system was constructed based on four aspects: innovation support, service facilities, the social environment, and the natural environment. After analyzing these influencing factors through comparing the results obtained with an ordinary least squares (OLS) model and a geographical weighted regression (GWR) model, the GWR model was determined to have a better fitting effect and was thus used for further analysis. The findings are as follows: (1) Five closely related clusters of innovation spaces are identified. Innovation space has a significant agglomerating distribution pattern. (2) Overall, factors supporting innovation and transportation station factors have a positive effect on the agglomeration of innovation spaces, while natural environment factors have a negative effect on small innovation areas. (3) By region, the aggregation of innovation spaces in downtown areas is slightly negatively affected by service facilities, whereas those in the Harbin New District are mainly supported by policies and those in the Pingfang District are positively affected by the quantity of the labor force. Finally, based on the research results, some suggestions are put forward to promote the development of urban innovation spaces. This paper has certain guiding significance for optimizing and improving the construction and development of urban innovation spaces.


Introduction
In the knowledge economy, innovation has become the core force promoting economic development.The theory of innovation was first proposed by Schumpeter in 1912 in The Theory of Economic Development [1].In 1955, Perroux [2] first linked innovation theory to space and proposed the "growth pole" theory.In 1992, Cooke [3] proposed the concept of a "regional innovation system" for the first time, defining the spatial scope of research activities at the regional level.In the 21st century, the role of knowledge innovation in economic development has increased dramatically, and cities have become important platforms for the clustering of global innovation activities.In 2000, Charles Landry [4] proposed the concept of the "innovative city," linking innovation with city-scale space.Later, scholars conducted research on urban innovation spaces from various perspectives, such as conceptual connotations, structural layout, evaluation metrics, and planning strategies.
As the main regions for the export of new technologies and ideas, urban innovation spaces are important carriers of innovation activities, and their importance has become increasingly prominent [5,6].Urban innovation space refers to a networked urban spatial important impacts on site selection.Based on these factors, the best locations for innovation spaces are determined, and some suggestions are put forward to promote the development of small-and medium-sized enterprises [27].Li, L. et al. took the patent data from Shanghai from 2000 to 2015 and found that innovation showed a strong tendency to concentrate at the micro-scale, and gradually developed into a polycentric model.Enterprises played a leading role in innovation activities.Individuals and universities also played a role in the growth of urban innovation.Moreover, the overall innovation output of a city was found to be significantly affected by public budget expenditure and green space in [28].
In summary, based on interview data, patent data, high-tech enterprise data, POI data, and other types of data, scholars use structured interview surveys, OLS models, spatial statistical models, and other spatial models to carry out research on the influencing factors of urban innovation spaces.However, in terms of influencing factors, most existing studies focus on the macro level, such as cultural atmosphere, land price, local economic input, ecological environment, and so on.In contrast, micro-level studies employing spatial analysis models assessing factors supporting innovation space development such as universities, scientific research institutions, and maker spaces, as well as various types of service facilities such as transportation stations, educational institutions, and leisure and entertainment facilities, are rare.In addition to macro-level influencing factors, this study includes micro-level factors supporting the development of innovation spaces and service facility factors.A system of factors influencing innovation space is constructed based on four aspects: factors supporting innovation, service facility factors, social environment factors, and natural environmental factors (Figure 1).
of offices from parking lots, site area, land price, and distance from the market have important impacts on site selection.Based on these factors, the best locations for innovation spaces are determined, and some suggestions are put forward to promote the development of small-and medium-sized enterprises [27].Li, L. et al. took the patent data from Shanghai from 2000 to 2015 and found that innovation showed a strong tendency to concentrate at the micro-scale, and gradually developed into a polycentric model.Enterprises played a leading role in innovation activities.Individuals and universities also played a role in the growth of urban innovation.Moreover, the overall innovation output of a city was found to be significantly affected by public budget expenditure and green space in [28].
In summary, based on interview data, patent data, high-tech enterprise data, POI data, and other types of data, scholars use structured interview surveys, OLS models, spatial statistical models, and other spatial models to carry out research on the influencing factors of urban innovation spaces.However, in terms of influencing factors, most existing studies focus on the macro level, such as cultural atmosphere, land price, local economic input, ecological environment, and so on.In contrast, micro-level studies employing spatial analysis models assessing factors supporting innovation space development such as universities, scientific research institutions, and maker spaces, as well as various types of service facilities such as transportation stations, educational institutions, and leisure and entertainment facilities, are rare.In addition to macro-level influencing factors, this study includes micro-level factors supporting the development of innovation spaces and service facility factors.A system of factors influencing innovation space is constructed based on four aspects: factors supporting innovation, service facility factors, social environment factors, and natural environmental factors (Figure 1).

Data Sources
The scope of this study covers Harbin, including Nangang District, Xiangfang District, Daoli District, Daowai District, Pingfang District, Songbei District, Hulan District, and others (Figure 2).The data from high-tech enterprises in Harbin were selected as the representation indices of the distribution of innovation spaces and were obtained through the official government website [31].The dataset includes 1751 enterprises certified in

Data Sources
The scope of this study covers Harbin, including Nangang District, Xiangfang District, Daoli District, Daowai District, Pingfang District, Songbei District, Hulan District, and others (Figure 2).The data from high-tech enterprises in Harbin were selected as the representation indices of the distribution of innovation spaces and were obtained through the official government website [31].The dataset includes 1751 enterprises certified in 2019-2021.Enterprise information includes the enterprise name, the district where the enterprise is located, latitudinal and longitudinal coordinates, and each enterprise's core technology.The map data and part of the influencing factor data were based on the road, green space, and water system data in the OpenStreetMap (OSM) dataset [32] and the China GDP Spatial Distribution Km Grid Dataset [33].The POI data of the influencing factors were crawled through the Gaode Map API, and the time span was set up to 2022.Six types of data related to the study, including food and beverage, shopping and consumption, leisure and entertainment, science, education and culture, tourist attractions, and transportation facilities, were selected from 14 categories, with a total of 86,808 items.After data collection was completed, coordinate correction, screening, and de-duplication were carried out.Finally, the ArcGIS pro3.0.2 software platform was used to carry out geographical matching, integrate all kinds of spatial data, and build the geographic information database of hightech enterprises.
2019-2021.Enterprise information includes the enterprise name, the district w terprise is located, latitudinal and longitudinal coordinates, and each enter technology.The map data and part of the influencing factor data were based o green space, and water system data in the OpenStreetMap (OSM) dataset [ China GDP Spatial Distribution Km Grid Dataset [33].The POI data of the factors were crawled through the Gaode Map API, and the time span was set Six types of data related to the study, including food and beverage, shoppin sumption, leisure and entertainment, science, education and culture, tourist and transportation facilities, were selected from 14 categories, with a total of 8 After data collection was completed, coordinate correction, screening, and dewere carried out.Finally, the ArcGIS pro3.0.2 software platform was used t geographical matching, integrate all kinds of spatial data, and build the geogr mation database of high-tech enterprises.In order to analyze the factors affecting the development pattern of innovation spaces from the macro and micro scales, this study created a fishnet with a size of 1 km × 1 km in Harbin and divided it into 901 grids.Each square of the grid was taken as a basic unit of analysis, and the grid region where high-tech enterprises are located was taken as an innovation space unit.The density of high-tech enterprises in an innovation space unit was used as the explanatory variable of the regression analysis in this study.Compared with the total number of innovation spaces, the grid density of high-tech enterprises can more accurately reflect the spatial distribution characteristics of innovation space.Referring to existing studies [15][16][17][18][19] and considering the availability of data, this study selected 14 influencing factors for analysis (Table 1).The kernel density estimation method, as a representative non-parametric statistical method, has been widely used in research exploring spatial agglomeration.The kernel density function can be used to estimate the density around an innovation space according to the density of innovation spaces in the unit region, intuitively showing the aggregation characteristics and degree of the innovation space.The kernel density is calculated as follows: fn where k is the weight function of the kernel, h is the bandwidth (that is, the width of the spatial extension of the surface taking the innovation space position as the origin), n is the number of innovation spaces, and x − x i is the distance from valuation point x to sample x i .

Spatial Autocorrelation Analysis
Spatial autocorrelation analysis takes sectional spatial data as the analysis object, characterizes the distribution of spatial elements, and identifies their agglomeration laws.Firstly, the adjacency relation of spatial objects is defined, that is, the spatial weight matrix.Generally, the greater the distance between two geographical units, the smaller the spatial weight.Spatial autocorrelation analysis is divided into two categories: global spatial autocorrelation analysis and local spatial autocorrelation analysis.The former adopts global Moran's I analysis, and the formula is as follows: where n is the number of space units; w ij is the space weight matrix; and x i , x j , and x are the number of innovation spaces in space units I and j and on average, respectively.The value of Moran's I index is between [-1, 1], where a value less than 0 indicates a negative correlation; that is, the spatial distribution of innovation presents discrete characteristics.A Moran's I greater than 0 indicates a positive correlation, that is, agglomeration characteristics.Finally, a value equal to 0 indicates that there is no spatial autocorrelation between innovation spaces.Based on the global spatial autocorrelation analysis, the local Moran's index is used to obtain the specific location of the spatial aggregation.The formula is as follows: Local spatial autocorrelation describes the correlation between the observed values of a specific spatial area and its neighboring areas and divides the spatial models into five types: high-high, low-low, high-low, low-high, and non-significant.The low-high pattern indicates a low incidence in the area but a high incidence in the surrounding region, and so on.

Ordinary Least Squares (OLS)
The ordinary least squares (OLS) method is the most basic and commonly used regression method.It establishes numerical models or fitting means to conduct correlation analysis on two or more variables and determine the relationship between them.In order to study the influence of different factors on the distribution of innovation spaces, this study first conducted spatial regression analysis based on OLS.The formula is as follows: where y is the dependent variable, that is, the distribution of innovation space; x k is the independent variable, that is, the influencing factor of the distribution; β 0 is the equation constant; β k is the coefficient value of x k ; and ε is the random error.

Geographical Weighted Regression Analysis (GWR)
Geographical weighted regression analysis (GWR) was proposed by Fotheringham et al. [34].This method uses spatial data to solve the local regression equation of each spatial unit within the study range based on the global regression model.GWR analysis allows the distribution of innovation space on the urban scale to be explored and identifies related influencing factors.In this study, based on the OLS analysis, GWR was carried out, and the goodness of fit of the two models was compared.Compared with the OLS model, the GWR model can more effectively reveal the spatial variation in the influence coefficients in the study area and better describes the spatial heterogeneity.The equation is expressed as follows: where y i is the dependent variable, x ik is the independent variable, (u i ,v i ) is the central geographic coordinate of the i sample, β 0 (u i ,v i ) is the intercept value at i, β k (u i ,v i ) is the coefficient value of the independent variable x ik , and ε i is the random error term.

Characteristics of Overall Distribution Pattern
The spatial scale is a key variable in kernel density analysis.Using the ArcGIS pro3.0.2 software, after repeated comparisons, it was found that the optimal effect was achieved when the pixel size was set to 100 m and the search radius was set to 2 km.According to the results of the kernel density analysis (Figure 3), it was found that there are five high-density innovation spaces, that is, five clusters of high-tech enterprises, in Harbin: According to data from enterprises in the high-density area (Table 2), the enterprises can be divided into three levels: the number of enterprises in the The distribution structure of innovation spaces is extracted and summarized (Figure 4).

Spatial Autocorrelation Analysis
The ArcGIS pro3.0.2 software was used to analyze the global spatial autocorrelation of innovation spaces.The conceptualization of spatial relationship in this study adopts CONTIGUITY EDGES CORNERS, and the standardization is ROW.The results showed that the global Moran's I index was 0.337518, the z value was 14.549456, the p value was 0, and the confidence level was 99%, which showed a strong positive spatial correlation.This finding shows that the innovation space in Harbin is highly concentrated.This can be explained by the advantage of geographical proximity in innovation, as it can reduce the communication costs of high-tech enterprises, promote interactive learning, facilitate the sharing of knowledge and technology, and improve innovation performance and output [35,36].
In order to further explore the micro-level agglomeration of innovation spaces, local spatial autocorrelation analysis was performed on innovation space data to generate a LISA agglomeration diagram (Figure 5).The results show that there are three distribution patterns: high-high agglomeration, low-high agglomeration, and non-significant agglomeration.Among them, high-high agglomeration is distributed in five areas, and the location of high-high agglomeration is basically consistent with the high-density areas in the nuclear density analysis (Figure 3), which further verifies the geographical location of the agglomeration of innovation space.The low-high concentration is distributed in the north of the Science and Technology Innovation City area; we speculate that this is because of the relatively concentrated distribution of high-tech enterprises there, resulting in a significant difference in density inside and outside the agglomeration area.
nuclear density analysis (Figure 3), which further verifies the geographical loc agglomeration of innovation space.The low-high concentration is distributed of the Science and Technology Innovation City area; we speculate that this is the relatively concentrated distribution of high-tech enterprises there, resulti nificant difference in density inside and outside the agglomeration area.

Analysis of Influencing Factors
The GWR4.0 software was used to eliminate independent variables with variance expansion coefficients greater than 7.5 to reduce the influence of collinearity among variables.The eliminating factors included the density of restaurants and the density of supermarkets and convenience stores, two types of dining and shopping facility variables.

OLS Analysis
The OLS model was constructed in the GWR4.0 software, and the analysis results were obtained (Table 3).
In terms of factors supporting innovation, the density of incubators has a significant positive impact on the agglomeration of innovation spaces.Incubator and maker spaces for science and technology enterprises provide spaces, facilities, capital, and other aspects of support to high-tech enterprises in their early stages of growth, reduce the risk and cost of innovation, promote the intervention and support of financial capital, accelerate the transformation of scientific and technological achievements, and play an important role in the development of high-tech enterprises.In terms of service facilities, the network density of transportation facilities shows a secondary significant positive effect, and the transportation station density shows a significant positive effect.On one hand, transportation infrastructure facilitates the flow of people and the transmission of innovative elements such as information and technology, helping to improve innovation efficiency.On the other hand, it is conducive to the transfer of tacit knowledge.In today's information age, the wide application of the Internet has gradually reduced the cost of information exchange, but face-to-face communication, which has irreplaceable value for the formation and dissemination of tacit knowledge, can still be realized with the help of transportation infrastructure.Tacit knowledge, which exists in people's minds and is difficult to convey in words, is highly individualized and formalized.The aggregation of tacit knowledge affects the innovation efficiency of high-tech enterprises, improving individual innovation ability and helping to train innovative talents [37,38].
In our study, the influence of social environment factors and natural environment factors is not significant, which is different from the previous research results [28,30].One possible explanation for this difference is that the effects of these two types of influencing factors on the innovation space are indeed small; the other possibility is that the effects of these two types of influencing factors have large spatial differences and have not formed a unified influence direction, which needs to be further verified by means of spatial statistical modeling.

GWR Analysis
Based on the OLS estimation results, the GWR model estimation results were further analyzed.A Gaussian model was used, and golden-section search was used as the bandwidth selection method.Comparing the two models, the results show that the residual sum of squares, AICc, −2 Log-likelihood, and adjusted R 2 of the GWR model are better than those of the OLS model (Table 4), indicating that the local regression model has a greater improvement than the global regression model and has a stronger explanatory power for the distribution of innovation spaces.

The efficacy of the influencing factors
In terms of the proportion of significant coefficients, according to the statistical results of the GWR analysis coefficient (Table 5), variables including the density of universities and scientific research institutions, the density of incubators, and the density of transportation stations account for a relatively high proportion (>35%), indicating that these three variables have a significant impact on the distribution of innovation spaces from a global perspective.In contrast, the significant coefficients of green space density and distance from water are relatively low (<5%), indicating that these two factors have little influence on the distribution.The other types of variables have an average degree of significance (coefficient ratio between 10% and 25%).*: "+" represents the proportion of significant positive coefficient to significant coefficient, and "−" represents the proportion of significant negative coefficient to significant coefficient.
From the maximum and minimum values of the GWR coefficients, the coefficients of incubator density, road network density, and transportation station density are all positive, indicating that these three variables have a positive impact on the aggregation of innovation spaces.The coefficients of green space density and distance from water are both negative; thus, there is negative influence.The other variables are both positive and negative, indicating that the influence on innovation space changes with the spatial location of sample points in the whole study area, and further research is needed on this spatial effect.
Concerning the average and median values of the coefficients in the POI dot data, the absolute value of incubator density is significantly higher than other variables.It is therefore preliminarily inferred that incubator density has a strong influence on the aggregation of innovation spaces.Other data, such as road network density, population density, and GDP value, cannot be directly compared with each other due to differences in their data types and units.

Spatial distribution of influencing factors
Combined with the efficacy and the proportion of the significance coefficient of each influencing factor, the two variables with low significance coefficients (<3%), namely, green space density and distance from water, were removed, and the value of p < 0.05 in the grid was visually analyzed (Figure 6).According to the classification of influencing factors presented above (Table 1), these factors were divided into four categories and analyzed separately on a more micro-level scale: factors supporting innovation, service facility factors, social environment factors, and natural environment factors.
Combined with the efficacy and the proportion of the significance coefficient of each influencing factor, the two variables with low significance coefficients (<3%), namely, green space density and distance from water, were removed, and the value of p < 0.05 in the grid was visually analyzed (Figure 6).According to the classification of influencing factors presented above (Table 1), these factors were divided into four categories and analyzed separately on a more micro-level scale: factors supporting innovation, service facility factors, social environment factors, and natural environment factors.

• Factors supporting innovation
The factors of universities and scientific research institutions have spatial heterogeneity and significantly promote the agglomeration of innovation spaces in the downtown area south of the Songhua River.The downtown area has a long history of development, with many universities and scientific research institutions such as the Harbin Institute of Technology, the Harbin Engineering University, the Northeast Forestry University, and the Northeast Agriculture University.With its sufficient knowledge resources, the area can provide knowledge and technology support for high-tech enterprises, promoting their agglomeration in this area.In Harbin New District north of the Songhua River, the negative influence is reflected.In combination with the actual situation, the number of universities and scientific research institutions in this area is relatively small; however, Songbei District, which belongs to the area north of the Songhua River, has more preferential policies for innovative enterprises and has set up a Science and Technology Innovation City with more high-tech enterprises.This phenomenon can also be seen from the kernel density analysis above (Figure 3).The difference between the two data contributed to the negative influence of this result.
In most areas of the research scope, the incubator density has a significant positive effect, which reflects the extensive and important value of science and technology enterprise incubators for the development of high-tech enterprises.

•
Service Facility Factors The influence of road network density on the agglomeration of innovation spaces is small, mainly concentrated in the Science and Technology Innovation City area and part of the intersection of Xiangfang District and Daowai District.On one hand, innovative industries are similar to producer services; however, different from traditional processing and manufacturing industries that require greater road transportation conditions, innovation industries are relatively less sensitive to road transportation conditions [39].On the other hand, road network density can only represent transportation efficiency to a certain extent, and some areas with low road network density but high road quality with wide roads and large areas also have higher transportation efficiency.
The density of transportation stations has a positive effect on Harbin New District and large areas south of the Songhua River.Densely distributed bus stations, subway stations, and other transportation stations can better represent the development of a transportation system compared with the road network density, providing strong support for the agglomeration of high-tech enterprises.
Primary and secondary schools have a negative impact on the downtown area.This may be because primary and secondary schools are mostly distributed in the vicinity of residential areas, which are a certain distance from the distribution of high-tech enterprises, resulting in differences in spatial location.In the same grid, the different trends in the number of the two types of schools lead to a negative effect.
Cultural facilities have a positive impact on Harbin New District and some areas of Xiangfang District.Sufficient cultural facilities and diverse cultural activities provide people with a place for learning and cultural exchange, promote the dissemination of knowledge and the collision of ideas, which is conducive to the generation of innovative activities.In addition, cultural facilities help to create an open cultural atmosphere and high-quality living environment, attract innovative people, and thus attract high-tech enterprises to settle in.
Parks and squares have a negative inhibitory effect on the eastern part of the downtown area south of the Songhua River.On one hand, parks and squares generally have large areas, and the distribution of their locations is mostly a certain distance from the core area of the city.On the other hand, due to the limitations in the data, only data on the number of parks and squares are available, and data on their areas are lacking and therefore do not fully reflect the service level of park facilities in the grid.
Leisure facilities such as cinemas and theaters have a negative impact on Harbin New District and the eastern part of the downtown area.As mentioned above, most of the high-tech enterprises in Harbin New District are distributed in the Science and Technology Innovation City area, with a high degree of centralization and a certain distance between leisure facilities and them.

• Social Environmental Factors
Population density has a significant positive effect on the aggregation of innovation spaces in southern Pingfang District.A high population density represents a sufficient labor force, and previous studies have shown that the labor force is an important factor affecting innovation output [40,41].In addition, high-tech enterprises in Pingfang District are mainly advanced manufacturing industries, which have higher requirements for labor resources.Unlike the conception of the traditional manufacturing industry as a peripheral observer of the technological innovation chain, the labor force in the advanced manufacturing industry is deeply involved in every stage of innovation, which greatly affects the success, failure, scale, and speed of the industrialization of innovative technology [42] and thus plays a key role in the development of high-tech enterprises.
GDP has a negative effect on the aggregation of innovation spaces in the Science and Technology Innovation City area and some areas south of the Songhua River, which reflects the complexity of the distribution of innovation spaces.In the early stage, high-tech enterprises tended to be distributed in areas with a higher level of economic development, making it is easy to access capital, talent, and other innovation support elements.With the further development of these areas, the spillover of knowledge and technology occurred, and the newly born enterprises were more distributed in the areas that were different from the previous ones with a relatively low level of economic development [30].This reflects the phenomenon of spatial mismatch between innovation space and economic development in the core area of Harbin.The government needs to improve the accuracy of financial support for high-tech enterprises in the future and play a greater radiating and driving role for high-tech enterprise cluster areas.

•
Natural Environmental Factors The distance from green space has a negative influence on the agglomeration of innovation space in some areas south of the Songhua River.This location belongs to the core area of the city, where green space has a mostly scattered distribution, the total green area is small, and the relatively large green spaces are generally far from the core area of the city.In addition, there is a lack of effective supporting facilities.Together, these factors have an inhibiting effect on the agglomeration of high-tech enterprises.

Summary of influencing factors
In general, the factors supporting innovation, comprising universities, research institutions, and incubators, have a positive impact on the aggregation of innovation spaces.Among the service facility factors, the density of the road network and transportation stations have a positive impact, but the spatial scope of the former is small.Moreover, primary and secondary schools, parks and squares, and other leisure facilities have a negative impact on Harbin New District, and cultural facilities have a positive impact.In terms of social environmental factors, population density has a positive effect on Pingfang District, while GDP has a negative effect in the Science and Technology Innovation City area and some areas south of the Songhua River.The influence of the natural environment on the aggregation of innovation space is negligible, and the variable of distance from green space has a negative influence in some areas south of the Songhua River.

Discussion
With continuous adjustments being made to China's economic growth model, innovation has become the core driving force for the sustainable social and economic development of cities. Urban innovation spaces have become important carriers of economic innovation.Through studying the agglomeration characteristics and influencing factors of urban innovation spaces, we can promote the agglomeration and layout optimization of innovation elements and enhance the development of innovation spaces, which is of great significance for the transformation and development of cities and the improvement of comprehensive strength.
Firstly, based on the analysis of the distribution characteristics of innovation spaces detailed in this study, five significant high-density innovation areas have formed in Harbin; these five areas show characteristics of agglomerated distribution and have certain driving and radiating effects on their surrounding areas.This finding agrees with the existing research content on the geographical agglomeration of innovation spaces [43][44][45].At the spatial level, the dynamic mechanism of urban innovation agglomeration includes a geographi-cal proximity effect, the optimal allocation of innovation resources, more convenient connections with the market, and a social and cultural environment of collaborative innovation.
Secondly, the analysis of factors influencing innovation spaces showed that factors supporting innovation, transportation facilities, and other service facilities play significant roles in promoting the agglomeration of innovation spaces.In addition, social and natural environment factors also play a certain role, and the effects of each influencing factor are different in their spatial distributions.Innovation is a relatively complex process, and the complete process of outputting innovation results generally includes basic theoretical research in universities and scientific research institutes, applied research and development within incubators, the industrialization of companies and enterprises, and the expansion of industrial parks.Factors supporting innovation play a key role in the agglomeration of innovation spaces.
Thirdly, service facilities, such as universities and research institutions, incubators and maker spaces, transportation facilities, and cultural facilities, play a significant role in promoting the agglomeration of innovation spaces.In the future, it will be crucial to continue to promote the efficient integration of multiple platforms such as physical and virtual innovation spaces, make reasonable allocation decisions about innovation resources and infrastructure, build spaces guaranteeing comprehensive and diversified innovation elements, promote the settlement of high-tech enterprises, form a growth pole of regional innovation, and drive innovative development in surrounding areas.
Finally, based on the spatial distribution results, it is inferred that the high-tech enterprises in Harbin New District are mainly affected by policy, which shows the significance of policy in supporting the agglomeration of innovation spaces.Policy support can provide certain incentives for high-tech enterprises to invest venture capital into innovation and patent technology incubation and to implement the market-oriented participation of multiple investment entities into the industrial application of these innovations.At the same time, the government should give appropriate capital support to high-tech innovation, establish an innovation service platform, reduce the cost of enterprise innovation, stimulate the output of innovation achievements, and improve the overall innovation level of the area.

Summary and Recommendations
Urban innovation spaces are a powerful driving force and efficient engine for urban development.Exploring their spatial distribution, influencing factors, and mechanism from the perspective of urban planning has great theoretical and practical significance for optimizing spatial layout, improving operational efficiency, and enhancing innovation performance.Through the analysis of the spatial distribution characteristics and influencing factors of 1751 high-tech enterprises in the central urban area of Harbin, the following conclusions were reached: 1.
The innovation space in Harbin is organized into five clusters.These clusters are closely connected with each other, and there is a development trend of outward expansion.The leading industry categories of each area are roughly similar.There are two distribution modes of innovation spaces: high-high agglomeration and high-low agglomeration.

2.
The development of innovation spaces in Harbin is not balanced, and the five clusters that have been formed play a leading role in the overall development of innovation spaces.Therefore, relevant interest groups such as urban planners and policy makers need to pay attention to these clusters and prioritize the allocation of resources into these areas with dense distributions of innovation spaces to improve resource utilization efficiency and output performance.

3.
Using the OLS model, it is initially identified that the incubator density and the transportation facilities in the service facilities of innovation support factors have significant positive promoting effects on the agglomeration of innovation space, while the social and natural environment factors have no significant effects.The agglomeration of urban innovation space is affected by various service facilities and the external environment.For example, the service level of a city will affect the settlement intention of innovative talents and thus indirectly affect the spatial distribution of innovation.4.
The GWR model was selected for further analysis thanks to its better fitting effect.In general, factors supporting innovation and transportation station factors had a positive effect on the agglomeration of innovation spaces, while natural environment factors had a weak effect.In terms of the spatial distribution of influencing factors, the spatial agglomeration of innovation in the downtown area is slightly or negatively affected by service facilities, the Harbin New District has greater policy support, innovation spaces are mostly distributed in the Science and Technology Innovation City area with a high degree of concentration, and Pingfang District is mainly positively affected by the size of the labor force.Urban planners and policy makers should aim to further improve the level of service facility construction of innovation spaces in the downtown area while establishing a diversified public transportation system and innovation support factors.In Harbin New District, the influence of innovation policies and comprehensive service carriers of innovation spaces should be strengthened.As for the innovation space in Pingfang District, which is dominated by manufacturing industrial parks, it is necessary to enhance the area's competitiveness in terms of labor force training and the introduction of innovative talents.By giving full play to local advantages and making up for shortcomings using other strategies, a diversified urban innovation space system can be built to promote innovation, leading to the sustainable economic and social development of cities.

Research Limitations and Future Works
There are some limitations to this study.Due to limitations in data acquisition, further analysis is required on the impact of innovation policies, regional rents, and enterprise output value on innovation spaces, necessitating further research in the future.
In addition, this research divides the target region into a homogeneous grid of 1 km × 1 km, which is convenient for micro-scale data analysis.However, an analysis of the heterogeneity characteristics of the agglomeration of urban innovation spaced and a comparative analysis of multi-scale geographical weighted regression will be required in follow-up research works.
Finally, the perspective of this paper is limited to the central urban area of Harbin, which limits the generalizability of the results.In the future, the research scope can be expanded to more cities with different urban spatial structures, levels of economic development, and built environments, and comparative studies on innovation space construction modes with Harbin can be conducted to deepen the understanding of the characteristics, influencing factors, and the mechanism of the agglomeration of urban innovation.

Figure 1 .
Figure 1.System of factors influencing innovation spaces.

Figure 1 .
Figure 1.System of factors influencing innovation spaces.

Figure 3 .
Figure 3. Kernel density distribution of innovation spaces (The number 1-5 represent density innovation spaces).
It can be seen that the five high-density areas are closely connected by trunk roads, such as the Third Ring Road and the Fourth Ring Road between the Science and Technology Innovation City and High-tech Industrial Development areas, and Haping Road between the No.1 campus area of the Harbin Institute of Technology and the Harbin Veterinary Research Institute area.The high-density areas all spread outward, and there is a trend of outward expansion on the whole.
ing and automation, the last two areas are new materials in the High-tech Industrial De velopment area and biology and medicine in the Harbin Veterinary Research Institut area.The leading industries of each area are roughly similar, and some areas have thei own characteristic industries.

Figure 4 .
Figure 4. Distribution structure diagram of innovation spaces.

Figure 4 .
Figure 4. Distribution structure diagram of innovation spaces.According to data from enterprises in the high-density area (Table2), the number of enterprises can be divided into three levels: the number of enterprises in the Science and Technology Innovation City area and the International Exhibition Center area exceeds 300; the number in the No. 1 campus area of the Harbin Institute of Technology and the Harbin Veterinary Research Institute area is nearly 150; and the number of enterprises in the High-tech Industrial Development area is relatively lower, with 70.The number of enterprises across the three levels of high-density areas basically form a 4:2:1 ratio.In terms of the top three professional fields in the number of enterprises, the first three areas are the same: electronic information, high-tech services, and advanced machinery manufacturing and automation.In addition to electronic information and advanced machinery manufacturing and automation, the last two areas are new materials in the High-tech Industrial Development area and biology and medicine in the Harbin Veterinary Research Institute area.The leading industries of each area are roughly similar, and some areas have their own characteristic industries.

Figure 5 .
Figure 5. LISA cluster map of innovation spaces.

Figure 5 .
Figure 5. LISA cluster map of innovation spaces.

Figure 6 .
Figure 6.Factors influencing the spatial distribution of innovation spaces in the GWR analysis results.

Table 1 .
Influencing factors and data sources of the agglomeration of innovation spaces.

Table 2 .
Statistics on spatial distribution of innovation.

Propor- tion of To- tal (%) Area of Region (km 2 ) Number of Enter- prises per km 2 Top Three Enterprises in the Pro- fessional Field
3.1.2.Spatial Autocorrelation AnalysisThe ArcGIS pro3.0.2 software was used to analyze the global spatial autocorrelatio of innovation spaces.The conceptualization of spatial relationship in this study adopt

Table 2 .
Statistics on spatial distribution of innovation.

Table 3 .
OLS coefficient statistics of innovation space.

Table 4 .
Fitting effect of OLS and GWR models.

Table 5 .
The statistics of GWR coefficient of innovation space.