A method for measuring spatial aggregation of point data within a certain area

Abstract

The present invention discloses a method for measuring the spatial aggregation of point data within a certain area, and belongs to the field of spatial metrology and geography technology. The method comprises: for the area to be measured, converting the population or facility data to be measured within the area into the location distribution information of the point data; calculating the sum of the actual distances between all the point data within the area to be measured according to the location distribution information of the point data; setting an assumed state that all the point data are uniformly distributed within the area to be measured, and calculating the sum of the distances between all the point data under the assumed state; calculating the spatial aggregation of the population or facility data within the area, and performing graded classification, wherein the smaller the spatial aggregation value, the higher the degree of aggregation. The measurement method of the present invention is based on spatial distance, places more emphasis on spatiality, has a wide range of applications, is highly interpretable, and has high accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of spatial metrology and geography technology, and in particular relates to a method for measuring the spatial aggregation of point data within a certain area. Background Art

[0002] In urban geography, economic geography, and urban and rural planning, determining the spatial distribution of population, facilities, and other factors within a region (or city, or a specific urban area), and interpreting its spatial distribution characteristics and existing problems, is essential for formulating appropriate regional and urban development policies and planning measures. Accurately understanding spatial agglomeration is a crucial area of ​​research. The importance of studying spatial agglomeration is emphasized in relevant Chinese publications (e.g., Urban Geography, Economic Geography, Foundations of Quantitative Geography, and Principles of Urban Planning), and numerous relevant research findings have been published both domestically and internationally.

[0003] Given the importance of spatial aggregation, the measurement of spatial aggregation has become the foundation of research and practice in this field. Several measurement methods have been proposed and applied, including urbanization rate, Lorentz curve, centralization index, kernel density analysis, nearest neighbor index, neighbor count method, spatial autocorrelation method, etc. These methods measure spatial aggregation from different perspectives and provide a certain quantitative analysis basis for the analysis of spatial aggregation characteristics. However, each method has certain deficiencies and defects, such as:

[0004] (1) Urbanization rate: describes the proportion of the population in a region or country that is concentrated in urban areas. This index is only applied to the population level and cannot be applied to the facility level. It basically ignores spatial distance, that is, it only uses the population proportion of the population concentration area without considering the distance between different population settlements. There are many differences in the concepts of "township" and "urban population" in different regions (countries), which makes the definition and measurement of urbanization rate quite incomparable.

[0005] (2) The Lorentz curve and the concentration index: The former is a cumulative frequency curve that determines the degree of aggregation of a certain element by comparing the degree of concavity and convexity of the curve; the latter quantifies the concentration by calculating the area enclosed by the cumulative frequency curve and the diagonal line. Both methods use frequency (or proportion) as the basic data for measurement and basically ignore spatial distance. In practical applications, they are often based on regions and are therefore greatly influenced by the regional division method.

[0006] (3) Kernel density analysis: Using GIS, the density of the target element in its surrounding neighborhood is calculated to form a visual map. However, it can only be expressed graphically and cannot be quantitatively measured; the map results vary greatly due to the influence of the set parameters (search radius).

[0007] (4) Nearest neighbor index: The degree of clustering of points is measured by the ratio of the average value of the nearest neighbor distance between points to the average distance between points under a random distribution. This method only considers the distance between a point and its nearest neighbor, while ignoring the positional relationship with other points, making the calculation results prone to large errors. For example, if all points in space are grouped together with the same shortest distance d, no matter how these groups are arranged (as long as the distance between groups is greater than d), the nearest neighbor distance of all points is d, so the nearest neighbor index becomes a fixed value and cannot measure the differences in different spatial distributions.

[0008] (5) Neighborhood number measurement method: The value is obtained by calculating the number of neighboring points within a specified distance and then dividing it by the number of neighboring points in a randomly distributed state. On the one hand, there is a limitation that the specified distance is based on subjective judgment, and the result will vary depending on the specified distance. On the other hand, there is a similar limitation to the aforementioned nearest neighbor index, that is, only the points within its immediate neighborhood are considered, while the distribution of other points and their positional relationships are ignored.

[0009] (6) Moran's Index: Also known as spatial autocorrelation analysis, it is often used to measure whether the distribution of spatial objects has autocorrelation. Strong autocorrelation indicates that spatial phenomena have clustering. For the determination of the degree of clustering, this method is more often used to compare the same object at different times. Comparisons between different objects are largely incomparable due to sample differences. In addition, the calculation process is relatively complex and requires the construction of a spatial weight matrix, which is affected by the operator's subjective judgment. Summary of the Invention

[0010] The purpose of the present invention is to overcome the existing deficiencies and provide a method for measuring the spatial aggregation of point data within a certain area. The technical solution is as follows:

[0011] A method for measuring the spatial aggregation of point data within a certain area includes the following steps:

[0012] S1: For the area to be measured, the population or facility data to be measured within the area is converted into location distribution information of point data;

[0013] S2: Calculate the sum D of the actual distances between all point data within the area to be measured based on the location distribution information of the point data;

[0014] S3: Assume that all point data are uniformly distributed within the area to be measured, and calculate the sum D′ of the distances between all point data under the assumed state;

[0015] S4: Calculate the spatial concentration of population or facility data within the area:

[0016]

[0017] Among them, A represents the spatial aggregation degree;

[0018] S5: The spatial aggregation calculated in step S4 is classified into different levels. The smaller the spatial aggregation value, the higher the degree of aggregation.

[0019] Furthermore, in step S1, the conversion of the population or facility data to be measured within the regional range into the location distribution information of the point data includes a population data method for converting the population data to be measured into the location distribution information of the point data, and a facility data method for converting the facility data to be measured into the location distribution information of the point data;

[0020] The population data conversion method is:

[0021] The area to be measured is divided into several sub-areas according to the administrative area, and the population to be measured in each sub-area is obtained; the population in all different sub-areas is converted proportionally and rounded up to obtain the converted population in each sub-area P i , convert the population data to be measured into the population center position P of the corresponding sub-region i Point data, P in each sub-area i The data positions of the points overlap;

[0022] The location distribution information converted from the population data to be measured into point data is expressed as S Q ={q1,q2,…,q i ,…,q m},q i =(c i ,P i ), Among them, q i Indicates the point data information corresponding to the i-th sub-region, m represents the number of sub-regions, c i represents the population center coordinates of the ith sub-region, P i represents the converted population corresponding to the ith sub-region, that is, the number of point data in the ith sub-region; n represents the total amount of point data in the area to be measured;

[0023] The facility data conversion method is:

[0024] Obtain the actual location information of the facility to be measured, regard each facility to be measured as a point data in the area to be measured, and directly convert the data of the facility to be measured into the location distribution information of the point data in the area, which is expressed as S F ={f1,f2,…,f i ,…,f n}, where f irepresents the actual location coordinates of the i-th facility, and n represents the number of facilities in the area, that is, the number of point data in the area to be measured.

[0025] Furthermore, in step S3, it is assumed that all point data are uniformly distributed within the area to be measured. Under the assumed state, the coordinate positions of all point data are updated in the following manner:

[0026] The area to be measured is divided into n identical regular hexagons, and the coordinate positions of the n point data are updated to the center coordinates of the n regular hexagons.

[0027] Furthermore, when the number of point data in the area to be measured is greater than 100 and the shape of the area to be measured is square or circular, the sum of the distances D′ in step S3 is expressed as:

[0028]

[0029]

[0030] in, It represents the average distance between all point data in a uniformly distributed state, Q represents the number of distance pairs between all two points in the area to be measured, L represents the side length of the square, and r represents the radius of the circle.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] (1) Different from the methods such as the Lorentz curve and the centralization index, the present invention uses spatial distance as the measurement basis, ensuring that the measurement results have stronger spatiality.

[0033] (2) Unlike the nearest neighbor index which only considers the nearest neighboring points, the present invention considers all points and performs distance measurement for all points, making the measurement results more accurate. In the face of the area range of a specific shape, a simple approximate calculation method is further proposed, which significantly reduces the amount of calculation and improves the scope of application and practicality of the present invention.

[0034] (3) The present invention proposes to use the assumed uniform distribution state of points as comparison data, so that even multiple areas of different sizes and shapes can be compared with each other, and has strong versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of a method for measuring the spatial aggregation of point data within a certain area proposed by the present invention.

[0036] Figure 2 This is a schematic diagram showing the actual distribution of point data in a certain area after conversion from population data according to an embodiment of the present invention.

[0037] Figure 3 This is a schematic diagram of an assumed uniform distribution state of point data in a certain area after being converted from population data according to an embodiment of the present invention.

[0038] Figure 4 This is a schematic diagram of the actual distribution of point data converted from urban public service facility data around four subway stations in a city, shown in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in the various embodiments of the present invention can be combined accordingly without conflicting with each other.

[0040] The present invention takes the assumed uniform distribution of points as comparison data and proposes a method for measuring the spatial aggregation of point data in a certain area. Figure 1 As shown, it mainly includes the following steps:

[0041] Step 1: For the area to be measured, convert the population or facility data to be measured within the area into location distribution information of point data;

[0042] In this step, the specific research objects in actual applications are converted into location distribution information of point data. The research objects can be the population to be measured or specific facilities, where the type of facilities is determined based on actual needs. For example, the specific facilities can be one or more combinations of medical facilities, cultural and entertainment facilities, transportation facilities, educational facilities, and sports facilities.

[0043] For example, when measuring the spatial concentration of regional population, the population data conversion method is used to convert the population data to be measured into the location distribution information of point data, and the converted point data can overlap; when measuring one or more facilities, the facility data conversion method is used to convert the facility data to be measured into the location distribution information of point data.

[0044] Step 2: Calculate the sum D of the actual distances between all point data within the area to be measured based on the location distribution information of the point data;

[0045] In this step, it is assumed that within the range of a measurement area, its area is S, and n different point data are distributed (the point positions can overlap). Then the calculation formula for the sum of the actual distances D between all the point data is:

[0046]

[0047] Where D is the sum of the spatial distances between all two points, n is the total number of points, and d ij is the actual distance from the i-th point to the j-th point, i≠j;

[0048] Regional spatial analysis is mainly based on two-dimensional spatial analysis. In two-dimensional coordinates, the spatial distance d ij Expressed as:

[0049]

[0050] Among them, x i and y i is the coordinate of point i; x j and y j is the coordinate of point j.

[0051] Step 3: Assume that all point data are uniformly distributed within the area to be measured, and calculate the sum D′ of the distances between all point data under the assumed state;

[0052] In this step, since the regular hexagon is the most stable polygonal structure, and in a figure composed of multiple regular hexagons, the center of a regular hexagon is equidistant from the centers of other adjacent hexagons, n regular hexagons of equal size can be used to cover the entire area to be measured. The centers of each regular hexagon are evenly distributed data points, then:

[0053] The area of ​​a regular hexagon is:

[0054]

[0055] The side length of a regular hexagon is:

[0056]

[0057] Where S is the area to be measured, and n is the total number of data points;

[0058] The distance L between two adjacent data points (i.e. the centers of regular hexagons) 点 The length is:

[0059]

[0060] According to the side length of the regular hexagon and the distance between the two centers, ArcGIS tools are used to draw n regular hexagons covering the area.

[0061] After dividing the area to be measured into n identical regular hexagons, update the coordinate positions of the n point data to the center coordinates of the n regular hexagons. The same method as in step 2 can be used to calculate the sum of the distances D′ between all the point data in the assumed state. The formula is:

[0062]

[0063] Where D′ is the sum of the distances between all point data under the assumed state, n is the total number of points, and d′ ij is the distance from the i-th point to the j-th point assuming a uniform state, i≠j.

[0064] Step 4: Calculate the spatial aggregation degree A of the population or facility data within the area:

[0065]

[0066] Step 5: Classify the spatial aggregation calculated in step 4 into different levels. The smaller the spatial aggregation value, the higher the degree of aggregation.

[0067] When the spatial aggregation is closer to 0, the elements in the area are more concentrated. When it is equal to 0, the elements are concentrated at only one point. When the spatial aggregation is closer to 1, the elements in the area are more discrete. When the spatial aggregation is greater than 1, it means that the area is in a peripheral discrete state (such as Figure 4 Therefore, the levels of spatial aggregation can be divided according to research needs, as shown in Table 1.

[0068] Table 1 Classification of spatial aggregation levels

[0069]

[0070]

[0071] In a specific implementation of the present invention, when the area to be measured is a specific shape, such as a square or a circle, an approximate calculation method is proposed in this embodiment, which can significantly reduce the amount of calculation and improve the scope of application and practicality of the present invention.

[0072] Taking a square as an example, the average distance between all two points in the square (infinite points) is There is a direct proportional relationship with the side length L of the square, that is:

[0073]

[0074] In the case of a finite number of points, where the points are evenly distributed within a square, the greater the number of points, the closer the ratio of the average distance between them to the side length is to 0.5214. For example, when n = 36 and 100, the values ​​are 0.5281 and 0.5240, respectively, with evenly distributed point data, representing errors of only 1.2% and 0.50%, respectively.

[0075] Therefore, in a square area, when there are many point data (preferably not less than 100), the calculation process of the sum of the distances D′ between all point data in the assumed state can be approximately calculated by the following formula:

[0076]

[0077] in, is the average distance between points in a uniformly distributed state, Q is the number of distance pairs between all two points in the region, L is the side length of the square, and n is the number of data points.

[0078] Taking a circle as an example, the average distance between all two points in the circle (infinite points) is There is a direct proportional relationship with the circle radius r, that is:

[0079]

[0080] In the case of a finite number of points, within a uniformly distributed circular range, the greater the number of points, the closer the ratio of the average distance between them to the side length is to 0.9045.

[0081] Therefore, when there are many point data (preferably not less than 100) within the circular area, the calculation process of the sum of the distances D′ between all point data in the assumed state can be approximately calculated by the following formula:

[0082]

[0083] in, is the average distance between points in a uniformly distributed state, Q is the number of distance pairs between all two points in the region, r is the radius of the circle, and n is the number of data points.

[0084] The above approximate calculation method is applicable to the case where there are many data points in the area. In this embodiment, when the number of point data in the area to be measured is greater than 100 and the shape of the area to be measured is square or circular, the above simple approximate calculation method can significantly reduce the amount of calculation.

[0085] In a specific implementation of the present invention, the population data conversion method is:

[0086] The area to be measured is divided into several sub-areas according to the administrative area, and the population to be measured in each sub-area is obtained; the population in all different sub-areas is proportionally converted and rounded to obtain the converted population in each sub-area P i , convert the population data to be measured into the population center position P of the corresponding sub-region i Point data, P in each sub-area i The data positions of the points overlap;

[0087] The location distribution information converted from the population data to be measured into point data is expressed as S Q ={q1,q2,…,q i ,…,q m},q i =(c i ,P i ), Among them, q i Indicates the point data information corresponding to the i-th sub-region, m represents the number of sub-regions, c i represents the population center coordinates of the ith sub-region, P i represents the converted population corresponding to the ith sub-region, that is, the number of point data in the ith sub-region; n represents the total amount of point data in the area to be measured;

[0088] Taking the spatial concentration of population in a certain region as an example, the urbanization rate only measures the difference in population distribution between urban and rural areas, and it is difficult to show the degree of concentration and dispersion in space. The regional population spatial concentration measurement according to the present invention will make up for this shortcoming. The calculation process is as follows:

[0089] S01, determine the scope of the area: the actual scope shall prevail.

[0090] S02, determine population distribution: collect population data, and divide the area into the smallest units as much as possible according to the availability of population data. For example, assuming that the area to be measured is a county, the measurement accuracy of administrative villages is higher than that of towns (streets).

[0091] In this embodiment, the population distribution data of the entire county is obtained. The town is measured in town districts and the rural area is measured in administrative villages. The total population of the entire county is 201,928 people. The actual distribution of the data points is as follows: Figure 2 Some of the data are shown in Table 2.

[0092] Table 2 Population data of a certain county

[0093]

[0094]

[0095] S03, Data Point Conversion: Because regional populations are often large, using individuals as data points increases workload and computation time. Therefore, it's helpful to convert data to a uniform order of magnitude (such as thousands or hundreds) to simplify calculations. For example, if a village has a population of 563, rounding to the hundreds place would simplify to 6, meaning there are 6 data points for that village.

[0096] In this example, the population of each township and administrative village is converted to data points, rounded to the nearest hundred. For example, District A1 (a county seat) has a population of 29,922, which is converted to 299 data points. Village A3 has a population of 1,152, which is converted to 12 data points. And so on. The county has 7 townships, 15 market towns, and 346 administrative villages, for a total of 2,022 data points.

[0097] The location distribution information converted from the population data to be measured into point data is expressed as S Q ={q1,q2,…,q 368},q i =(c i ,P i ), Among them, q i Indicates the point data information corresponding to the i-th sub-region, c i represents the population center coordinates of the ith sub-region, P i It represents the converted population corresponding to the ith sub-region, that is, the number of point data in the ith sub-region.

[0098] S04, data point distance calculation: use ArcGIS tools to calculate the actual distance between each data point and its sum D.

[0099] S05, data point distance calculation in uniform state:

[0100] According to the side length Construct n evenly distributed regular hexagons and calculate the distance between each data point and its sum D′.

[0101] In this embodiment, the data points in the region are evenly distributed as shown in the figure below. Figure 3 shown.

[0102] S06, calculate spatial aggregation And classify them into levels.

[0103] In this embodiment, the calculation results are shown in Table 3.

[0104] Table 3 Calculation of population spatial concentration in a county

[0105]

[0106]

[0107] According to the calculation results in Table 3, the spatial concentration of the population in a certain county is 0.922, which belongs to the low concentration level. This also objectively reflects that the population distribution in the county is very dispersed, the urban development is relatively backward, the urban scale is small, and it is in urgent need of improvement.

[0108] In a specific implementation of the present invention, the facility data conversion method is:

[0109] Obtain the actual location information of the facility to be measured, regard each facility to be measured as a point data in the area to be measured, and directly convert the data of the facility to be measured into the location distribution information of the point data in the area, which is expressed as S F ={f1,f2,…,f i ,…,f n}, where f i represents the actual location coordinates of the i-th facility, and n represents the number of facilities in the area, that is, the number of point data in the area to be measured.

[0110] Taking the calculation of the spatial concentration of urban service facilities around a subway station in a certain city as an example, the calculation process is as follows:

[0111] S11, determine the block range: take the center of each subway station as the origin and a radius of 500 meters to construct a circular area around the center of the station.

[0112] S12, data preparation: obtain the data points of urban public service facilities (including education, medical care, culture and sports, and commercial services) within the above-mentioned areas, and directly convert the location data of urban public service facilities into the location distribution information of point data within the area, such as Figure 4 shown.

[0113] S13, data point distance calculation: use ArcGIS tools to calculate the distance between each data point and its sum D.

[0114] S14, calculate the spatial aggregation according to the formula:

[0115]

[0116] In this embodiment, r is the radius of the circle, which is 500 meters; n is the number of data points corresponding to each station. The calculation results are shown in Table 4.

[0117] Table 4 Calculation results of spatial concentration of public service facilities at subway stations in a certain city

[0118]

[0119]

[0120] The measurements show significant differences in the spatial concentration of each station, which is consistent with actual conditions. Urban public service facilities are most concentrated at Line 2 Station B4, with a spatial concentration of 0.413, indicating high concentration. Line 2 Station B3 has a spatial concentration of 0.727, indicating medium concentration. Line 2 Station B2 and Line 1 Station B1 have relatively low spatial concentrations of 0.976 and 1.108, respectively, indicating low concentration and dispersion.

[0121] The above results also reflect that the measurement method of the present invention can better reflect the actual concentration level of urban public service facilities at these sites, providing a basis for conducting such research.

[0122] According to the above two specific embodiments, the scientificity, practicality and operability of the method for measuring the spatial aggregation degree of point data in a certain area proposed by the present invention are fully demonstrated.

[0123] The embodiment described above is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Persons skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent substitution or equivalent transformation falls within the scope of protection of the present invention.

Claims

1. A method for measuring the spatial concentration of point data within a certain area, characterized in that: The following steps are involved: S1: For the area to be measured, the population or facility data to be measured within the area is converted into location distribution information of point data; S2: Calculate the sum D of the actual distances between all point data within the area to be measured based on the location distribution information of the point data; S3: Assume that all point data are uniformly distributed within the area to be measured, and calculate the sum D′ of the distances between all point data under the assumed state; S4: Calculate the spatial aggregation of population or facility data within the area: Among them, A represents the spatial aggregation degree; S5: The spatial aggregation calculated in step S4 is classified into different levels. The smaller the spatial aggregation value, the higher the degree of aggregation.

2. The method for measuring spatial concentration of point data in a certain area according to claim 1, characterized in that: In step S1, the conversion of the population or facility data to be measured within the regional range into the location distribution information of point data includes a population data conversion method for converting the population data to be measured into the location distribution information of point data, and a facility data conversion method for converting the facility data to be measured into the location distribution information of point data; The population data conversion method is: The area to be measured is divided into several sub-areas according to the administrative area, and the population to be measured in each sub-area is obtained; the population in all different sub-areas is proportionally converted and rounded to obtain the converted population in each sub-area P i , convert the population data to be measured into the population center position P of the corresponding sub-region i Point data, P in each sub-area i The data positions of the points overlap; The location distribution information converted from the population data to be measured into point data is expressed as S Q ={q1,q2,…,q i ,…,q m },q i =(c i ,P i ), Among them, q i Indicates the point data information corresponding to the i-th sub-region, m represents the number of sub-regions, c i represents the population center coordinates of the ith sub-region, P i represents the converted population corresponding to the ith sub-region, that is, the number of point data in the ith sub-region; n represents the total amount of point data in the area to be measured; The facility data conversion method is: Obtain the actual location information of the facility to be measured, regard each facility to be measured as a point data in the area to be measured, and directly convert the data of the facility to be measured into the location distribution information of the point data in the area, which is expressed as S F ={f1,f2,…,f i ,…,f n }, where f i represents the actual location coordinates of the i-th facility, and n represents the number of facilities in the area, that is, the number of point data in the area to be measured.

3. The method for measuring spatial concentration of point data in a certain area according to claim 1, characterized in that: In step S3, it is assumed that all point data are uniformly distributed within the area to be measured. Under the assumed state, the coordinate positions of all point data are updated in the following manner: The area to be measured is divided into n identical regular hexagons, and the coordinate positions of the n point data are updated to the center coordinates of the n regular hexagons.

4. The method for measuring spatial concentration of point data in a certain area according to claim 3, characterized in that: When the number of point data in the area to be measured is greater than 100 and the shape of the area to be measured is square or circular, the sum of the distances D′ in step S3 is expressed as: in, It represents the average distance between all point data in a uniformly distributed state, Q represents the number of distance pairs between all two points in the area to be measured, L represents the side length of the square, and r represents the radius of the circle.

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