# Research on Location Characteristics of UCF Layout Based on DNSCAN Algorithm

Authors: Zhao Lu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Since the reform and opening up, the prosperity of culture has always been the strong desire of the party and the country, and repeatedly put forward the goal of improving the public cultural service system (PCSS), requiring priority development of infrastructure construction related to the vital cultural interests of the people. Urban cultural facilities (UCF) are an important material basis in the cultural service system. The essential assurance for achieving the goal of developing a PCSS that covers the entire community is to improve the layout of cultural facilities (CF) and to allocate CF in a scientific and reasonable manner. This research examines the geographical layout characteristics of CF in Xiamen using POI data from libraries, art galleries, and museums crawled by Baidu API and spatial statistical tools such as ArcGIS. Taking the interest points of cultural promote serving residents as research objects, the advancement of spatial pattern of CF in Zhengzhou in 2007 and 2017 was quantitatively analyzed by using standard deviation ellipse and kernel density analysis. The paper compares and analyzes the location distribution characteristics of museums, libraries, cultural centers, art galleries and theaters from two aspects of macro spatial form and microgathering center. Residents’ behavioral characteristics are introduced to examine the influence on the spatial form of CF, and appropriate suggestions are made for the planning and development of CF in Zhengzhou, based on large-scale field survey data and geographical detectors. This article, on the analysis of the state and international public facilities location layout on the basis of optimization study, starting from the present circumstances of urban public sports facilities layout, puts forward the geographic information system (GIS) technology and local approximation (LA) model is introduced into urban public sports service facility location, using DNSCAN network analysis function of urban public sports facilities in site selection and layout optimization, Provide a new method for site selection of sports facilities. And the actual case analysis, in order to provide a reference for the future location layout of public service facilities. Zhengzhou cultural resources through the establishment of GIS database, investigation, cultural needs, put forward the planning should not only include public CF, CF planning should also include the cultural heritage, cultural creative industry, and put forward the development strategy of the construction of the overall urban culture network, realize the cultural space planning and career planning, the fusion of the culture industry planning.


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## Body

## 1. Introduction

CF refers to the space where cultural activities take place and the necessary equipment [1]. General speaking, the CF is an expression of cultural exchanges to provide or gathering space, its function is for people to participate in activities such as exhibitions, performances, art provides space, in order to satisfy people demand for knowledge, spiritual beauty and self-realization, thus promote the community of cultural and artistic appreciation ability enhancement and contribute to social harmony. In a narrow sense, CF can not only enrich the lives of urban residents and improve their quality of life, but also play an indispensable role in building a city brand and improving its core competitiveness in the development dilemma of “one city with one city.”At present, scholars at home and abroad have conducted a large number of studies based on UCF. After the Second World War, faced with the huge demand of urban construction, western countries carried out researches on urban public facilities. The researches on CF mainly focused on the construction and management policies of UCF [2], multipurpose development of CF, etc. Western CF for multipurpose comprehensive layout has a lot of successful cases, such as the Dallas arts district, the museum of modern art in New York, etc., through the different USES integrated CF and CF and other services, in the form of performance for purposes of building complex, to promote the prosperity of cultural construction and urban infrastructure has many benefits. At present, domestic research is mainly focused on three points: first, research on the spatial distribution of CF or cultural industries (CI) in specific cities [3]; Second, the utilization efficiency of UCF or the relationship between supply and demand; thirdly, the research on the planning and development strategy of CF. However, in these studies of facility distribution, utilization efficiency and facility planning, individual behavioral characteristics are seldom taken as the influencing factor or the entry point of planning decision, or only taken as the analysis basis, lacking the connection and comparison with the real spatial distribution.In addition, although there are many studies on the spatial pattern of CF at present, electronic maps, traditional statistical data or survey data are mostly used in data acquisition. In terms of research areas, most of them focus on First-tier cities in China such as Shanghai, Shenzhen, Beijing and Guangzhou, and few studies on big cities with profound potential in central China. Zhengzhou is the capital of Henan Province and a national famous historical and cultural city, and was selected as the “National Central City” in December 2016 [4]. With the rise of central China and the implementation of the national strategy of central Plains Economic Zone, marked by the development and construction of Zhengdong New Area, the urban space of Zhengzhou is expanding rapidly. Rapid urban expansion leads to the shortage of infrastructure in central urban areas, low reasonable utilization rate, and significant development differences between new and old urban areas [5]. How to promote the residents of Zhengzhou to enrich their cultural life and improve the quality of their spiritual life guided by the rational allocation of CF, and thus improve the influence of Zhengzhou as a cultural and historical city, has become a problem worthy of in-depth research and meaningful [6]. In recent years, with the development of the era of big data, geographic data sources have been increasingly enriched, and location-based Point of Interest (POI) has become an important breakthrough point for refined urban spatial analysis, which can intuitively and effectively reflect the distribution of various urban facility elements [7].Moreover, it has certain advantages over remote sensing data in terms of update speed and acquisition cost [8], and has the characteristics of high accuracy and wide coverage. Therefore, this paper takes the downtown area of Zhengzhou as the research area, selects POI data of five types of CF in 2007 and 2017, and compares the distribution changes of CF from 2007 to 2017 with spatial analysis tools to study their location distribution characteristics. Meanwhile, combined with large-scale field survey data, Residents pay more attention to behavioral factors on the formation and CF space, in the hope of Zhengzhou city in the center of the selected countries under the background of better implement the national center for science and education, culture, innovation, improve the international influence and regional competitiveness, and CF configuration and optimization of the future city space layout provides more scientific and reasonable theoretical reference and practical basis [9].With the mature development of the revolution of computer and information technology and the rise of the fourth intelligent industrial revolution, the era of big data is also coming. The disadvantages of mass data that were not easy to obtain and analyze in the past have been improved, providing people with the possibility of quantitative analysis of subtle problems [10]. It also provides people with a more rational quantitative perspective to analyze all aspects of urban research for urban design and planning. In recent years, with regard to the research and application of POI data, domestic scholars have also studied urban spatial structure, spatial layout and other urban problems through POI and other big data from different perspectives. For example, Zhao Wei, Cheng Yiyi et al. studied the local catering and imported catering outlets in the old city center of Chengdu, and put forward corresponding suggestions on the planning ideas and focuses of urban catering industry spatial scale agglomeration and spatial layout, classification and spatial support, diversified integration and sharing layout [11]. Xue Bing, Xiao Xiao et al. extracted the distribution pattern of retail commercial centers in Shenyang by kernel density estimation and compared the differential characteristics of different retail formats.It provides some scientific cognition for the planning and layout of urban commercial space [12]. From the perspective of sustainable development of pension facilities in Beijing, scholars such as Shao Lei and Zhang Jing collected and analyzed the data of 794 pension facilities in Beijing and studied their spatial distribution characteristics to provide reference suggestions for the demand and construction of pension facilities in central urban areas. According to the literature review, POI data are mostly applied to the study of urban commercial facilities and urban functional areas, while there are few studies on UCF. However, with the improvement of urban and rural residents’ consumption level, the proportion of cultural consumption expenditure is increasing. Under the guidance of citizens’ huge spiritual and cultural needs, the construction of CF is mushroomed, which cannot be ignored. Xiamen is the main center city of cross-strait economic zone [13]. It not only plays a major role in cross-strait economy and finance, but also gradually becomes a modern international port sightseeing city. However, the construction of CF has not caught up with the rapid expansion of the city; the number and layout of CF have many defects. This paper takes urban cultural sites in Xiamen as the research object, obtains Baidu POI data through Python, and cleans and sorts the data. ArcGIS spatial analysis is used as a research tool to study the overall spatial layout characteristics of CF in Xiamen, and briefly discusses its influencing factors. In order to better understand the status quo of the spatial distribution of CF, but also to provide reference for the future development and planning of cultural industry in Xiamen [14].This paper proposes an antipower stealing analysis model based on DBSCAN clustering algorithm and establishes multidimensional feature factor correlation model. Through practical application in low-voltage platform area, the effectiveness of the method is verified, which can effectively locate power stealing users, improve work efficiency and protect the interests of power supply companies.The paper arrangements are as follows: Section 2 defined the Characteristics of CF planning; the CF planning objects examine and elaborate the multidimensional features. Section 3 explores the UM-DBSCAN algorithm for uncertain data clustering. Section 4 explains the various experiment analysis for uncertain data. Section 5 accomplishes the article.


## 2. Characteristics of CF Planning

In this section, discusses the properties of CF planning objects, culture is the important characteristics of integration. The planning process will be examined clearly. In the planning process, the government’s guarantee function for urban public CF, the overall spatial layout plan and the recent construction layout plan are clearly discussed.


### 2.1. Planning Objects

Due to the diversity and rich extension of culture, there has never been a unified definition of culture. Therefore, compared with other public facilities such as basic education, medical care, sports and old-age care, CF have rich connotation, broad boundary, difficult foundation and high integration with other urban functions [15]. In a broad sense, culture can be divided into two aspects: material environment and human environment. Based on the material environment and discussed from the perspective of urban planning, culture mainly involves cultural heritage, CF and cultural creative industries, covering cultural undertakings and CI. Cultural heritage refers to cultural relics, buildings and sites that have survived from history. Cultural heritage includes a variety of contents and types, including classified cultural relic protection units, unclassified immovable cultural relics, excellent modern and modern architecture, industrial heritage, cultural landscape protection areas, and intangible cultural heritage. At present, there is no clear definition and unified classification standard for CF, which can be divided into public welfare CF and commercial CF. Public CF mainly include public libraries, museums, cultural centers, art galleries, memorial halls, science and technology museums, workers’ cultural palace, youth palace, etc. Commercial CF mainly includes theaters, concert halls, clubs, cinemas, amusement parks, book cities and so on. Cultural and creative industry refers to the intrinsically connected industry clusters that provide cultural experience for the public by taking creation, creation and innovation as the fundamental means, taking cultural content and creative achievements as the core value, and taking the realization or consumption of intellectual property rights as the transaction characteristics. At present, there is no unified classification standard for cultural and creative industries. Beijing issued the Classification Standard for Cultural and creative Industries in Beijing in 2006, which is divided into 9 categories, 27 middle categories, and 88 subcategories.


### 2.2. Planning Process

Culture is the essential characteristics of integration, the development of culture is not independent, the trend of the development of the culture within the fusion, and the cultural trend of convergence with other industries are increasingly apparent, such as culture and science and technology, business, finance, manufacturing, tourism, education, medical and other industrial integration development, increase the content of related industry culture, extension of the cultural industry chain, improve the well-being of society. Integrated development is not only the need of accelerating cultural development, but also the urgent requirement of economic and social development for cultural construction. Based on cultural characteristics with the essence of urban integration, the plan will lead to a culture of the building into the overall urban development framework to look at, planning content includes not only the public CF, including the cultural heritage, cultural creative industry, and puts forward the overall development strategy, highlighting the cultural space planning and career planning, the fusion of the culture industry planning. In the planning plan, the government’s guarantee function for urban public CF, the overall spatial layout plan and the recent construction layout plan are clearly defined (Figure1).Figure 1
Planning framework.The planning study based on GIS platform, relying on zero company for investigation, cultural resources, and citizens demand survey will investigate unmovable cultural relics, industrial heritage, modern architecture, excellent public CF, cultural creative enterprises and cultural groups and cultural square, a total of 37891 data for receiving programming platform for the spatial data, attribute information includes all of the data The construction, operation and management of cultural content (Table1). A GIS database of Cultural resources in Chaoyang District has been established. Relying on the database, we can make a comprehensive analysis of the content, level, scale, usage and relationship with cities of various cultural resources in space.Table 1
Main information content of GIS database of cultural resources.
NumberAttribute informationThe basic contentTuning into contentImmovable cultural relic118Street township name address land area operationProtection level, category of cultural relics, age, ownership, name of the unit to which they belong, number of single cultural relics, current use, cause of damage, others, remarksPublic CF968Type of institution, level of organization, independent occupation, use time, shared facilities, floor area, implementation mode, noncultural functions, quantity of books in public library, number of seats for reading in public libraryCultural and creative industry34559Type of industry, nature of unit, main business, registration time, registered capital, cultural and creative cluster, independent occupation, annual turnover, number of employees, business areaCultural groups2019Business content, number of membersCulture square205Activity status, management statusHistorical buildings and historical areas, CF, cultural creative industry space, greening system and public space are all spatial elements to improve the regional cultural environment. At present, the development of urban culture is not aimed at a specific cultural content, but the overall consideration of various elements, the construction of an overall urban cultural network, through culture to enhance the suitability of cities and regions, improve the quality of local residents’ living environment, and play a positive role in attracting tourism, investment and talent. For example, the Protection of strategic green space is proposed in London’s Cultural Metropolis, Mayor’s Cultural Strategy Draft, 2010. All kinds of material elements are organically connected through urban green space and water system to endue natural elements with cultural connotations and build an overall cultural development strategy.


## 2.1. Planning Objects

Due to the diversity and rich extension of culture, there has never been a unified definition of culture. Therefore, compared with other public facilities such as basic education, medical care, sports and old-age care, CF have rich connotation, broad boundary, difficult foundation and high integration with other urban functions [15]. In a broad sense, culture can be divided into two aspects: material environment and human environment. Based on the material environment and discussed from the perspective of urban planning, culture mainly involves cultural heritage, CF and cultural creative industries, covering cultural undertakings and CI. Cultural heritage refers to cultural relics, buildings and sites that have survived from history. Cultural heritage includes a variety of contents and types, including classified cultural relic protection units, unclassified immovable cultural relics, excellent modern and modern architecture, industrial heritage, cultural landscape protection areas, and intangible cultural heritage. At present, there is no clear definition and unified classification standard for CF, which can be divided into public welfare CF and commercial CF. Public CF mainly include public libraries, museums, cultural centers, art galleries, memorial halls, science and technology museums, workers’ cultural palace, youth palace, etc. Commercial CF mainly includes theaters, concert halls, clubs, cinemas, amusement parks, book cities and so on. Cultural and creative industry refers to the intrinsically connected industry clusters that provide cultural experience for the public by taking creation, creation and innovation as the fundamental means, taking cultural content and creative achievements as the core value, and taking the realization or consumption of intellectual property rights as the transaction characteristics. At present, there is no unified classification standard for cultural and creative industries. Beijing issued the Classification Standard for Cultural and creative Industries in Beijing in 2006, which is divided into 9 categories, 27 middle categories, and 88 subcategories.


## 2.2. Planning Process

Culture is the essential characteristics of integration, the development of culture is not independent, the trend of the development of the culture within the fusion, and the cultural trend of convergence with other industries are increasingly apparent, such as culture and science and technology, business, finance, manufacturing, tourism, education, medical and other industrial integration development, increase the content of related industry culture, extension of the cultural industry chain, improve the well-being of society. Integrated development is not only the need of accelerating cultural development, but also the urgent requirement of economic and social development for cultural construction. Based on cultural characteristics with the essence of urban integration, the plan will lead to a culture of the building into the overall urban development framework to look at, planning content includes not only the public CF, including the cultural heritage, cultural creative industry, and puts forward the overall development strategy, highlighting the cultural space planning and career planning, the fusion of the culture industry planning. In the planning plan, the government’s guarantee function for urban public CF, the overall spatial layout plan and the recent construction layout plan are clearly defined (Figure1).Figure 1
Planning framework.The planning study based on GIS platform, relying on zero company for investigation, cultural resources, and citizens demand survey will investigate unmovable cultural relics, industrial heritage, modern architecture, excellent public CF, cultural creative enterprises and cultural groups and cultural square, a total of 37891 data for receiving programming platform for the spatial data, attribute information includes all of the data The construction, operation and management of cultural content (Table1). A GIS database of Cultural resources in Chaoyang District has been established. Relying on the database, we can make a comprehensive analysis of the content, level, scale, usage and relationship with cities of various cultural resources in space.Table 1
Main information content of GIS database of cultural resources.
NumberAttribute informationThe basic contentTuning into contentImmovable cultural relic118Street township name address land area operationProtection level, category of cultural relics, age, ownership, name of the unit to which they belong, number of single cultural relics, current use, cause of damage, others, remarksPublic CF968Type of institution, level of organization, independent occupation, use time, shared facilities, floor area, implementation mode, noncultural functions, quantity of books in public library, number of seats for reading in public libraryCultural and creative industry34559Type of industry, nature of unit, main business, registration time, registered capital, cultural and creative cluster, independent occupation, annual turnover, number of employees, business areaCultural groups2019Business content, number of membersCulture square205Activity status, management statusHistorical buildings and historical areas, CF, cultural creative industry space, greening system and public space are all spatial elements to improve the regional cultural environment. At present, the development of urban culture is not aimed at a specific cultural content, but the overall consideration of various elements, the construction of an overall urban cultural network, through culture to enhance the suitability of cities and regions, improve the quality of local residents’ living environment, and play a positive role in attracting tourism, investment and talent. For example, the Protection of strategic green space is proposed in London’s Cultural Metropolis, Mayor’s Cultural Strategy Draft, 2010. All kinds of material elements are organically connected through urban green space and water system to endue natural elements with cultural connotations and build an overall cultural development strategy.


## 3. UM-DBSCAN Algorithm for Uncertain Data Clustering

U-PAM algorithm uses interval number and standard deviation to reasonably describe the uncertainty of uncertain measurement data, and then completes the effective clustering of uncertain data. The advantage of U-PAM algorithm is that it solves the traditional UK-means sensitive problem of estimation points, and it can cluster the uncertain data effectively when the probability density of uncertain data is unknown. However, this algorithm is based on the traditional partition clustering algorithm, which has its own determination, that is, cannot find clustering of arbitrary shapes; to solve this problem, this section proposes the density-based UM-DBSCAN algorithm, which can find clusters of casual shapes because it is a density-based clustering algorithm.In order to better represent uncertain data objects, the concept description of interval number is(1)AL=mA−αA,AR=mA+αA,where mA is the midpoint of interval number A, α A is the radius of interval number A, so the interval number can also be expressed as mA−αA,mA+αA.Interval number distance: for a given interval number,X=XL,XR,Y=YL,YR, the distance between them is(2)dX,Y=X−Y=XL−YL2+XR−YR2.As can be seen from the above definition, interval number refers to the number represented by an interval, so that interval number can be used to represent the uncertainty of data in the form of interval, which can then be applied to the clustering algorithm of uncertain data. By type (2) know when expressed in interval number to two uncertain data objects, the distance between the uncertain data object is available to represent the distance between interval Numbers, so on uncertain data object clustering, can use the distance between interval number to represent the uncertainty of data objects similarity, the greater the distance between interval numbers, the smaller the similarity, The smaller the distance between the interval numbers, the greater the similarity. Interval number can also be said a multidimensional data model, when the data model is one-dimensional, interval model a shaft on a line, when the data model for the two-dimensional, interval number model for the two-dimensional planar rectangular box, when the data model for three-dimensional model for interval number as the cube model, when the data object is multidimensional, the data model for a super geometry.The idea of DBSCAN algorithm is as follows: firstly, an object Oi is randomly selected and Eps of Oi neighborhood is calculated. Secondly, if Oi is the core object and is not divided into any other cluster, objects whose Oi density can be reached from Oi are found out in turn until a cluster containing Oi is formed. If Oi is not a core object, the object is treated as noise processing. Finally, if all the research objects are processed, the algorithm ends andk updated clusters are finally output.DBSCAN algorithm can find clusters of arbitrary shape and is not sensitive to noise. However, the data the algorithm deals with is a deterministic data set. When the input data is uncertain, the algorithm cannot achieve effective clustering. Therefore, on the basis of DBSCAN algorithm, UM-DBSCAN algorithm is proposed in this paper by combining interval number and statistical knowledge. This algorithm mainly deals with uncertain measurement data sets, and can still effectively cluster the data sets even when the distribution function or probability density of the data sets is unknown.The basic idea of UM-DBSCAN clustering algorithm is to use interval number and standard deviation to represent uncertain data, which is then transformed into clustering of the determined interval number. Firstly,N uncertain measurement data are represented by interval numbers. Secondly, an object Oi is randomly selected and Eps of Oi is calculated. If Oi is the core object and is not divided into any other cluster, the objects with Oi density can be found in turn until a cluster containing Oi is formed. If Oi is not the core object, the object is regarded as noise processing. Finally, if all the research objects are processed, the algorithm ends and k updated clusters are finally output. In order to better describe the UM-DBSCAN algorithm, this section first gives Definitions 1 and 2.Definition 1.
LetO1,O2,O3…On is nm-dimensional uncertain measurement data, and φOi¯ represents the error vector of the ith uncertain measurement data, so the probability of the ith uncertain measurement data Oi falling into the interval Oi−kφOi¯,Oi+kφOi¯ is(3)Pk=1=68.3%,Pk=2=95.4%,Pk=3=99.7%.
Thus it can be seen thatk value can be used to control the accuracy of the interval number of uncertain measurement data, generally k=2.Definition 2.
SupposeX and Y are two uncertain measurement data objects, X represents a,b,Y represents c,d, and DX,Y is the distance between them, then(4)dX,Y=a−c2+b−d2.
According to Definitions1 and 2, um-DBSCAN algorithm is proposed in this section. This algorithm completes data clustering when the function distribution or probability density of uncertain data is unknown. The algorithm is described Algorithm 1 as follows:Input:N uncertain Measurements O1,O2,O3,…On, Eps: parameter radius, MinPts: neighborhood density valueOutput: clustering based on density;begin:(1)
UseQ1,Q2,Q3…Qn stands for O1,O2,O3…On,(2)
unvisited ← all of objects;/(3)
do{(4)
select Qifrom unvisited,0<i<k(5)
visited←Qi(6)
comput count(Qi, Eps)(7)
if count(Qi,Eps)>MinPts(8)
C←Qi,(9)
M←c(Qi, Eps);(10)
for each ofM do{(11)
if unvisited ← mi(12)
visited ← mi(13)
comput count(Qi, Eps)(14)
if count(Qi, Eps)>MinPts(15)
M←mi(16)
If mi is not a member of any cluster(17)
C ←mi(18)
end for(19)
output C(20)
else noise←Qi;(21)
while(unvisited = = null)End
In the UM-PAM algorithm, in order to effectively process massive uncertain measurement data, we first randomly sample the uncertain measurement data objects. Center of the sampling data randomly selectedk, other objects of the sampled data in accordance with the assigned to k center distance criterion, the k initial clusters, then in the center of clusters with the representative objects to replace, computational cost function, if the cost function is less than zero, use the center instead of center, the loop all the time, until the cluster do not change;
Assume the uncertain measurement dataO1,O2,O3…On and n have large values. If the data is sampled randomly and the sample size S meets the following formula, the sampled samples can well represent the characteristics of the whole population:(5)s=f×n+nni×log1δ+nnilog1δ2+2×f×n×log1δ,where f is the proportion of the specified data extracted, 0≤F≤1,n is the data scale, and Ni is the scale of cluster Ci.
The spatial density analysis of geographic information calculates the data aggregation status of the whole region according to the input data set of point elements, thus generating a continuous density surface. Kernel Density Estimation (KDE) is a spatial density analysis method based on data density function clustering algorithm. During the analysis process, events adjacent to the center point of the quadrat are given a higher weight xi, while events farther away from the center pointX are given a lower weight. Its equation is defined as follows:(6)∫hx=1nhd∑i=1nKx−xih.
In the formula, the symmetric unimodal probability density function is usually taken;H is bandwidth and is a free parameter that defines the size of smoothing quantity. D is the dimension of data; N is the number of points I in the bandwidth range. In this paper, the kernel density estimation method is used to analyze the clustering centers of various CF.
Geographic detector is a tool to detect and utilize spatial differentiation. Compared with general statistical analysis methods, its advantage lies in that it can show the similarity of spatial distribution of independent variables and dependent variables that have important influence on dependent variables, including differentiation and factor detection, interaction detection, risk area detection and ecological detection. This paper mainly uses factor detection to study the explanatory degree of each influencing factor of spatial differentiation of CF in Zhengzhou city. In factor detection,q value is used to measure the extent to which factor X explains the spatial differentiation of Y, and the formula is(7)q=1−∑h=1LNhσh2Nσ2=1−SSWSST,where L is the stratification of factor X or dependent variable Y,h=1,2…L;N and σ2 are sample size and variance, respectively.
SupposeX=xk∈RN,k=1,2,…,l is a sample set of a nonempty input space that is mapped by some nonlinear mapping O to some eigenspace H to get Θx1,Θx2,…,Θxl. If K:X×X⟶R satisfies(8)Kxi,xj=ΘxiΘxj,∀xi,xj∈X.
Then we callK the kernel. Any function that satisfies the Mercer condition can be used as a kernel. In unsupervised learning models, kernel functions are generally selected empirically. In general, Gaussian kernel functions are considered first (see formula (8)), because the feature space corresponding to Gaussian kernel functions is infinite dimensional, and finite samples are definitely linearly separable in this feature space.(9)Kxi,xj=exp−βxi−xj2.
After input space sampleX is mapped by θ to feature space H, Euclidean distance of feature space can be expressed as(10)DHxi,xj=xi−xj2=ΘxiΘxj−2ΘxiΘxj+ΘxiΘxj.
Formula (11) is obtained by substituting formula (8) into formula (10):(11)DHxi,xj=Kxi,xi−2Kxi,xj+Kxj,xj.
According to formula (9), the distance between point xi and point Xj in the feature space can be conveniently calculated. Therefore, formula (10) is used as the measurement function of sample distance in DBSCAN clustering algorithm.


## 4. Experimental Demonstration and Analysis

In order to understand the characteristics of spatial distribution form of various CF, this paper adopts SDE method to analyze. From the comparison of spatial distribution patterns of all kinds of CF between 2007 and 2017, the distribution centers of all kinds of CF are almost the same as that of 2007, except that the center of distribution of library moved 1.4 km from east to north. In addition, the direction of distribution of all kinds of CF, set in 2007° has the very big difference, art galleries, theaters and other facilities shaft development status, and comparison of various CF in 2017 distribution direction, distribution of degree between difference is smaller, that over the last 10 a, Zhengzhou tends to equilibrium between various CF. Figure2 shows the spatial distribution patterns of various CF in 2007 and 2017.Figure 2
Standard deviation ellipse of various CF in 2007 and 2017.In 2007, 147 CF in Zhengzhou urban area increased to 485 in 2017, with the number increasing by more than two times. In terms of geographical distribution, the number of CF still exhibits the “inside and outside are densely packed” characteristic. The number of CF decreases from downtown to surrounding level, showing a trend of flowering everywhere (Figure3).Figure 3
Overall distribution and standardization ellipse analysis of CF in 2007 and 2017.From the perspective of the current spatial distribution of CF : Theaters, libraries, art galleries and museums of less-critical geometric distribution center and downtown center, cultural center distribution center of gravity compared with urban geometry center by west 1.6 km, which suggests that cultural center in the popular scientific and cultural knowledge, to carry out mass cultural activities for the characteristics of the traditional culture facilities distribution is concentrated in the traditional residents living area, And in the eastern planning construction development of the new district distribution is a little sparse. The direction of the long and short axes and the length of the standard deviation ellipse of each culture reflect the direction of the primary and secondary trends and the degree of dispersion respectively, which obviously shows the following characteristics: (1) In the degree of dispersion, the spatial distribution of CF (such as museums, libraries, cultural centers, etc.) is relatively discrete, while the spatial distribution of CF (such as art museums, cinemas and theaters) is relatively concentrated. This is because compared with other CF, cultural and exhibition facilities are almost all funded by the government, so the first consideration in planning construction is to maximize the cultural needs of citizens. (2) The length of the long axis and the short axis of the standard deviation ellipse are similar, and the shape is nearly round, which indicates that the spatial distribution of cinemas and theaters is relatively balanced in all directions, which is related to the vigorous development of film and theater industry in recent years. As can be seen from Figure4, the number of cinemas and theaters in Downtown Zhengzhou has increased by 5 times in the past 10 years. (3) The main spatial distribution trend of museums, cultural centers and art galleries is along the northwest to southeast direction. The main reason for the emergence of this axial state is the influence of road traffic conditions on urban spatial planning.Figure 4
Kernel density analysis results of various CF in 2007 and 2017.In order to further understand the clustering situation of various CF from the micro perspective, this paper conducts kernel density analysis on five types of CF (Figure4). In kernel density analysis, the choice of bandwidth is the key. The larger the bandwidth value is, the smoother the density surface will be, but the agglomeration hotspot area may be covered. The smaller the bandwidth value is, the more obvious the local characteristics of density surface are, but the overall correlation may be masked. Okabe et al. found in their study that under a certain number of study areas and event points, there was a bandwidth interval to keep the agglomeration center stable, and it was reasonable to select the bandwidth in this interval. This paper focuses on the clustering characteristics of all kinds of CF in the current situation and makes a comparison with 2007. Therefore, the principle of bandwidth selection is to highlight the clustering characteristics of all kinds of CF in 2017. The reasonable bandwidth range is 2.0–2.5 km by comprehensive estimation. After several tests, the unified bandwidth value is finally 2.2 km.Geographical detectors were used to analyze the explanatory power of the impact factors of CF as a whole and five types of CF, respectively, and the results are shown in Figure5.(1)
The CF in Zhengzhou increased rapidly from 2007 to 2017. From the perspective of spatial pattern, the CF have always been characterized by “dense inside and sparse outside,” and the distribution of CF in some streets in the northeast and southeast of the city is quite rare. In spatial form, it shows the momentum of eastward development, which is closely related to the planning and construction of Zhengdong New Area. In addition, residents’ choice of CF has gradually shifted from traditional cultural forms to aesthetic arts and leisure culture.(2)
From the perspective of spatial patterns of various CF, the distribution direction and center of CF were very different in 2007, but different types of CF were relatively balanced in 2017; the distribution of CF of art appreciation and analysis category is more concentrated than that of cultural museums. The main trend of spatial distribution of museums, cultural museums and art galleries shows that transportation layout and urban spatial planning have great influence on the planning and layout of CF. From the analysis of the cluster centers, all kinds of CF have little change compared with that before 10 years, and form a spatial pattern of massive cluster, axial extension and multicenter development. Their spatial distribution is related to their own characteristics and the actual development of the city.(3)
From the analysis of influencing factors, in addition to the external environment of population, transportation, economy, city planning and other factors that have been studied in the literature, the influence of the layout of CF cannot be ignored. Among them, residents’ disposable time, consumption habits and cultural level have a great impact on the distribution of CF, and different factors have a great difference in the impact of different types of CF.Figure 5
Influencing factors of CF distribution.


## 5. Conclusion

From 2007 to 2017, the CF in Zhengzhou increased rapidly. From the perspective of spatial pattern, the CF have been characterized by “dense inside and sparse outside,” and the distribution of CF in some streets in the northeast and southeast of the city is absolutely rare. In spatial form, it shows the momentum of eastward development, which is closely related to the planning and construction of Zhengdong New Area. In addition, residents’ choice of CF has gradually shifted from traditional cultural forms to aesthetic arts and leisure culture. From the point of view of the spatial form of the distribution of all kinds of CF, the distribution direction and the center of gravity of all kinds of CF were very different in 2007, and different kinds of CF were relatively balanced in 2017. The distribution of CF of art appreciation and analysis category is more concentrated than that of cultural museums. The main trend of spatial distribution of museums, cultural museums and art galleries shows that transportation layout and urban spatial planning have great influence on the planning and layout of CF. From the analysis of the cluster centers, all kinds of CF have little change compared with that before 10 years, and form a spatial pattern of massive cluster, axial extension and multicenter development. Their spatial distribution is related to their own characteristics and the actual development of the city. From the analysis of influencing factors, in addition to the external environment such as population, traffic, economy and city planning, residents’ group factor cannot be ignored. Among them, residents’ disposable time, consumption habits and cultural level have a great impact on the distribution of CF, and different factors have a great difference in the impact of different types of CF.



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*Source: 2222232-2022-03-22.xml*