Adaptive KDE method and system considering local spatial distribution differences of POI points

Abstract

The present invention discloses an adaptive KDE method and system that takes into account the differences in the local spatial distribution of POI points. First, a statistical neighborhood range X is preset, and the number of POI points in the four quadrants of each POI point within the range of 0 to X is counted at set intervals to construct a four-quadrant neighborhood spatial distribution trend curve for each POI point; then, based on the mutation point of the spatial distribution trend curve, the adaptive bandwidth of different quadrants of each POI point is determined, and the mutation point is the point where the first-order derivative or second-order derivative of the spatial distribution trend curve is 0; finally, based on the local adaptive bandwidth of each quadrant of each POI point obtained, the kernel density value is calculated in each quadrant and summed in the four quadrants to obtain the final kernel density value of the POI point. The present invention takes into account the differences in local geographic spatial structure characteristics, analyzes the local adaptive bandwidth of each POI point from four quadrants, and can more accurately measure the spatial distribution density of POI points.

Description

Technical Field

[0001] The present invention relates to an adaptive KDE method and system that takes into account the local spatial distribution differences of POI points, and belongs to the fields of geography, data mining, spatiotemporal big data analysis, etc. Background Art

[0002] Kernel Density Estimation (KDE) is a spatial density analysis method often used to analyze point data and detect spatial "hotspots," such as traffic accidents, retail sales, public service facilities, and regional crime. Due to its simple principle and ease of operation, KDE has been an important tool for exploring issues related to urban commercial space based on POI (Point of Interest) data. For example, Feng Daici used KDE based on Shenzhen POI data and combined it with commercial development planning to explore the current status and problems of Shenzhen's commercial center. Hao Feilong et al. combined KDE with location entropy index and other methods to study the industry distribution and agglomeration characteristics of Changchun's commercial space. Wei Zhongyu et al. used KDE and other methods based on POI point data and road network data to reveal Xi'an's "one axis, multiple cores" commercial distribution model and explore the spatial distribution pattern of hot and cold spots in its commercial districts.

[0003] The kernel function and bandwidth are two key parameters of the KDE method. Previous studies have revealed that bandwidth determination is the core technique of the KDE method and has a more significant impact on research results than the choice of kernel function. When the bandwidth is too large, the constructed kernel density surface is too smooth, resulting in the neglect of local "hot spots." When the bandwidth is too small, the constructed kernel density surface is too sharp, resulting in local "hot spots" being too prominent and making global patterns difficult to observe. Although compared with traditional empirical methods (such as Yang Jing et al.'s selection of a 300-meter bandwidth based on the walking distance of a commercial center), the global optimal fixed bandwidth determined by the minimum mean integrated squared error method proposed by relevant scholars (such as Goldenshluger et al.) is more objective, it still fails to account for the differences in local density in different quadrants on the global density surface, which are affected by the spatial distribution characteristics of point elements. Summary of the Invention

[0004] Purpose of the invention: In response to the above problems, the purpose of the present invention is to provide an adaptive KDE method and system that takes into account the differences in the local spatial distribution of POI points. Based on the mutation of the spatial distribution trend curves of POI points in different quadrant neighborhoods, combined with the traditional kernel density estimation method, the kernel density estimation value of the adaptive local bandwidth of the POI point is determined, which can more scientifically and objectively reflect the spatiotemporal distribution density of urban commercial POI points, and help to further reveal the urban geographic spatial structure, pattern and its evolution law.

[0005] Technical solution: To achieve the above-mentioned purpose, the present invention adopts the following technical solution:

[0006] An adaptive KDE method that takes into account the local spatial distribution differences of POIs includes the following steps:

[0007] Preset the statistical neighborhood range X, count the number of POI points within the range of 0 to X in the four quadrants of each POI point at the set interval, and construct the four-quadrant neighborhood spatial distribution trend curve of each POI point;

[0008] Determine the adaptive bandwidth of different quadrants of each POI point based on the mutation point of the spatial distribution trend curve. The mutation point is the point where the first-order derivative or second-order derivative of the spatial distribution trend curve is 0, and the neighborhood range corresponding to the mutation point is the adaptive bandwidth;

[0009] According to the local adaptive bandwidth of each quadrant of each POI point, the kernel density value is calculated in each quadrant and summed up in four quadrants to obtain the final kernel density value of the POI point.

[0010] Preferably, the mutation point is determined according to the following method: calculating the first-order derivative and the second-order derivative of the spatial distribution trend curve function, obtaining the neighborhood range corresponding to when the first-order derivative and the second-order derivative are 0, and selecting the minimum neighborhood range as the adaptive bandwidth.

[0011] Preferably, if there is a POI point within the neighborhood range X that does not obtain the adaptive bandwidth, the neighborhood range X is increased until the local adaptive bandwidth of each quadrant of each POI point is within the neighborhood range X.

[0012] As a preference, the kernel density value K of the i-th POI point is calculated according to the following formula: i :

[0013]

[0014] Among them, r i,k is the local adaptive bandwidth of the k-th quadrant of the determined ith POI point, n k is the total number of POI points within the local adaptive bandwidth of the k-th quadrant of the i-th POI point, d i,j,k is the distance from the i-th POI point in the k-th quadrant to the j-th POI point within the bandwidth, k(d i,j,k ,r i,k ) represents the Gaussian kernel function.

[0015] An adaptive KDE system that takes into account the local spatial distribution differences of POIs, including:

[0016] The local spatial distribution trend calculation module is used to preset the statistical neighborhood range X, count the number of POI points within the range of 0 to X in the four quadrants of each POI point at set intervals, and construct the four-quadrant neighborhood spatial distribution trend curve of each POI point;

[0017] An adaptive bandwidth determination module is used to determine the adaptive bandwidth of different quadrants of each POI point based on the mutation point of the spatial distribution trend curve. The mutation point is the point where the first-order derivative or second-order derivative of the spatial distribution trend curve is 0, and the neighborhood range corresponding to the mutation point is the adaptive bandwidth;

[0018] And a global kernel density value calculation module is used to calculate the kernel density value of each quadrant according to the local adaptive bandwidth of each quadrant of each POI point obtained, and perform the summation of the four quadrants to obtain the final kernel density value of the POI point.

[0019] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the steps of the adaptive KDE method taking into account the local spatial distribution differences of POI points are implemented.

[0020] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the adaptive KDE method that takes into account the local spatial distribution differences of POI points.

[0021] Beneficial effects: The present invention determines the four-quadrant spatial distribution clustering range of POI points by identifying different types of mutation points in the spatial distribution trend curves of neighborhood points in different quadrants of POI points, thereby solving the problem of identifying the local bandwidth of each POI point in different quadrants. Compared with the traditional kernel density estimation method and the adaptive kernel density estimation method, the present invention takes into account the differences in local geographic spatial structure characteristics, analyzes the local adaptive bandwidth of each POI point from four quadrants respectively, and can more accurately measure the spatial distribution density of POI points. From the experimental results, it can be found that the commercial kernel density surface constructed based on the adaptive kernel density estimation method proposed in the present invention has a good evaluation effect and can provide a basis for urban space optimization and physical examination evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Flowchart of adaptive kernel density construction according to an embodiment of the present invention.

[0023] Figure 2 Schematic diagram of determining local adaptive bandwidth in an embodiment of the present invention, wherein (a) is the local adaptive bandwidth of different quadrants; (b) is the spatial distribution trend curve of neighborhood points in different quadrants.

[0024] Figure 3This is an example diagram of an embodiment of the present invention applied to Nanjing in 2017. (a) is a spatial distribution map of commercial POIs; (b) is a commercial kernel density surface of Nanjing constructed based on the adaptive kernel density estimation method.

[0025] Figure 4 This is the spatial distribution map of night light intensity in Nanjing in 2017. DETAILED DESCRIPTION

[0026] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0027] In order to take into account the difference characteristics of the local spatial distribution of commercial POI points and solve the problem of determining the adaptive bandwidth of kernel density, the embodiment of the present invention proposes an adaptive kernel density estimation method based on the mutation of the spatial distribution trend curve of the neighborhood commercial points, which is used to measure the spatial distribution density of commercial POI points. First, the statistical neighborhood range X is preset, and the number of POI points in the four quadrants of 0 to X for each POI point is counted at set intervals to construct a four-quadrant neighborhood spatial distribution trend curve for each POI point; then, based on the mutation point of the spatial distribution trend curve, the adaptive bandwidth of different quadrants of each POI point is determined; finally, based on the local adaptive bandwidth of each quadrant of each POI point, the kernel density value is calculated in each quadrant and summed up in the four quadrants to obtain the final kernel density value of the POI point. The specific process is as follows: Figure 1 As shown:

[0028] S1: Trend diagram of the spatial distribution of commercial POI points in different quadrant neighborhoods.

[0029] The present invention first sets the neighborhood range of each commercial POI point to X meters, with an interval of 100 meters, and counts the number of neighborhood points within the range of 0 to X meters in the four quadrants of each POI point. For the set of commercial POI points, a set of spatial distribution trend curves of commercial points in the four quadrants of the POI point neighborhood is constructed.

[0030] S2: Adaptive bandwidth determination for different quadrants of each POI.

[0031] Influenced by natural and human factors, the spatial distribution of commercial POIs in different quadrants exhibits local variations, resulting in varying local bandwidths for each POI in different quadrants. The spatial distribution trend curves for neighborhood commercial POIs in different quadrants exhibit a monotonically increasing trend, but there are three types of "mutation points": 1) the increasing rate of the neighborhood commercial point spatial distribution trend curve is zero, meaning that there are no more commercial POIs within a certain area outside the neighborhood; 2) the increasing rate of the neighborhood commercial point spatial distribution trend curve accelerates, meaning that commercial POIs outside the neighborhood become more concentrated; and 3) the increasing rate of the neighborhood commercial point spatial distribution trend curve slows, meaning that commercial POIs outside the neighborhood become increasingly dispersed. The first "mutation point" corresponds to a first-order derivative of the neighborhood commercial point spatial distribution trend curve equal to 0, while the second and third "mutation points" correspond to second-order derivatives of the neighborhood commercial point spatial distribution trend curve equal to 0.

[0032] Using the formula shown below, we can identify three mutation points in the spatial distribution trend curve of each POI point in different quadrants:

[0033]

[0034] Among them, f′ i,k (x) and f″ i,k (x) represents the spatial distribution trend curve function f of the k-th quadrant (k = 1, 2, 3, 4) of commercial POI point i i,k The first and second derivatives of (x) are expressed as (a i,k ,b i,k ) represents the neighborhood range a corresponding to the first-order derivative and the second-order derivative being equal to 0 i,k and neighborhood range a i,k The number of commercial POI points within the i,k When the spatial distribution trend curve has only one mutation point, the neighborhood range a corresponding to the mutation point is i,k is the adaptive bandwidth r of the k-th quadrant of commercial POI point i i,k When there is more than one mutation point in the spatial distribution trend curve, we default to the minimum neighborhood range a i,k is the adaptive bandwidth r of the k-th quadrant of commercial POI point i i,k .

[0035] S3: Setting of domain range X.

[0036] Commercial POI features vary in both global and local spatial distribution. Therefore, the neighborhood ranges for different POI feature sets vary. This paper uses an iterative method to analyze the locations of trend curve abrupt changes in different quadrants for all POI features within different neighborhood ranges, using 500-meter intervals. When the location of a trend curve abrupt change for each POI feature falls within neighborhood range X, the corresponding neighborhood range X is considered the neighborhood range X for this commercial POI dataset.

[0037] S4: Calculation of global commercial POI kernel density values.

[0038] The kernel density value of commercial POI elements is an important parameter for evaluating the spatial distribution density of commercial POI points and is mainly affected by the bandwidth selection. The present invention combines the adaptive local bandwidth obtained above and calculates the kernel density value of each commercial POI element according to formulas 2 and 3. The formula is as follows:

[0039]

[0040] where k(d i,j,k ,r i,k ) represents the Gaussian kernel function, d i,j,k is the bandwidth r from the center point of the i-th POI in the k-th quadrant i,k The distance to the jth POI point, r i,k is the k-th quadrant local adaptive bandwidth of the i-th POI point determined using the above method.

[0041]

[0042] where K i is the kernel density value of the i-th POI point, n k is the total number of POI points within the local adaptive bandwidth of the k-th quadrant of the i-th POI point. i The larger the value, the more commercial points are gathered in the neighborhood of the POI point.

[0043] Figure 2The process of determining the local adaptive bandwidth of an embodiment of the present invention is illustrated. To address the problem that the traditional KDE method cannot take into account the local spatial distribution characteristics of point elements in different quadrants, this experiment uses first-order and second-order derivatives to detect the spatial aggregation range of neighboring points in different quadrants of each commercial POI point, that is, the KDE local bandwidth of different quadrants. First, we select a commercial POI point (the coordinate origin in (a)) as a sample point, and statistically calculate the spatial distribution trend curve of commercial POI points within its neighborhood range of X meters in different quadrants. By identifying the mutation points of the trend curves in different quadrants (the dots in (b)). The mutation point of the trend curve graph of the first quadrant is (700, 130), the mutation point of the trend curve graph of the second quadrant is (1100, 97), the mutation point of the trend curve graph of the third quadrant is (900, 116), and the mutation point of the trend curve graph of the fourth quadrant is (800, 134), indicating that the local adaptive bandwidths of the four quadrants are 700m, 1100m, 900m, and 800m, respectively. Considering that in traditional kernel density estimation methods, the bandwidth of each center point is fixed, the differences in local adaptive bandwidths in different quadrants and their impact on the estimated kernel density value of the center point are not considered. This experiment combines the first-order and second-order derivatives to determine the local adaptive bandwidths in different quadrants. The Gaussian kernel function of each commercial POI in different quadrants is calculated using Formula 2. Substituting this into Formula 3, the kernel density estimate of the sample point at each commercial POI is calculated under the combined effect of the four quadrants.

[0044] Figure 3 (a) is the spatial distribution map of commercial POI points in Nanjing in 2017. Figure 3 (b) The commercial kernel density surface constructed using the above four steps takes into account the local spatial distribution differences of commercial POI points. The following is a test and analysis based on the above calculation results.

[0045] Previous studies have confirmed that there is a significant spatial correlation between the urban commercial core density surface and nighttime light intensity. This paper compares the correlation between the constructed 2017 Nanjing commercial core density surface and the 2017 Nanjing nighttime light data, and calculates the global Pearson correlation coefficient, as shown below:

[0046]

[0047] Where r is the Pearson correlation coefficient between the constructed commercial density surface and the night light intensity, X i and Y i They represent the commercial kernel density and night light intensity of commercial POI point i, and represents the average kernel density value and the average nighttime light intensity of all commercial POIs in Nanjing in 2017, respectively, and n represents the total number of commercial POIs. When |r| > 0.8, the constructed commercial kernel density surface is highly correlated with nighttime light intensity, indicating that the constructed commercial kernel density surface is more realistic and objective.

[0048] Statistics show that the commercial kernel density surface of Nanjing City constructed by the adaptive kernel density estimation method designed by the present invention is consistent with the night light intensity ( Figure 4 ) has a Pearson correlation coefficient of up to 0.897. This finding indicates that the adaptive kernel density estimation method proposed in this invention, which takes into account the differences in local spatial distribution, has better prediction results, which is helpful for further analyzing the commercial space structure of Nanjing and providing a basis for urban space optimization and physical examination evaluation.

[0049] It should be noted that the above embodiment uses urban commercial POI points as an example to illustrate the implementation process and effects of the present invention. The adaptive KDE method of the present invention is also applicable to the analysis of other types of POI point data such as transportation facilities and service equipment.

[0050] Based on the same inventive concept, an embodiment of the present invention discloses an adaptive KDE system that takes into account the local spatial distribution differences of POI points, including: a local spatial distribution trend calculation module, which is used to preset a statistical neighborhood range X, count the number of POI points within the range of 0 to X in the four quadrants of each POI point at set intervals, and construct a four-quadrant neighborhood spatial distribution trend curve for each POI point; an adaptive bandwidth determination module, which is used to determine the adaptive bandwidth of different quadrants of each POI point based on the mutation point of the spatial distribution trend curve, wherein the mutation point is a point where the first-order derivative or second-order derivative of the spatial distribution trend curve is 0, and the neighborhood range corresponding to the mutation point is the adaptive bandwidth; and a global kernel density value calculation module, which is used to calculate the kernel density value of each quadrant based on the local adaptive bandwidth of each quadrant of each POI point, and sum the values across the four quadrants to obtain the final kernel density value of the POI point.

[0051] The specific working process of each module described above can refer to the corresponding process in the aforementioned method embodiment and will not be repeated here. The division of the modules is only a logical function division. In actual implementation, there may be other division methods, such as combining multiple modules or integrating them into another system.

[0052] Based on the same inventive concept, an embodiment of the present invention discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the steps of the aforementioned adaptive KDE method that takes into account the differences in the local spatial distribution of POI points are implemented.

[0053] Based on the same inventive concept, an embodiment of the present invention discloses a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the aforementioned adaptive KDE method that takes into account the local spatial distribution differences of POI points.

[0054] Those skilled in the art will appreciate that the technical solution of the present invention, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes instructions for causing a computer system (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in the embodiments of the present invention. Storage media include various media capable of storing computer programs, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random-access memories (RAMs), magnetic disks, or optical disks.

Claims

1. An adaptive KDE method that takes into account the local spatial distribution differences of POI points, characterized by: The steps include: The statistical neighborhood range is preset to X meters. The number of urban commercial POI points within the range of 0 to X meters in the four quadrants of each urban commercial POI point is counted at the set interval, and the spatial distribution trend curve of the four-quadrant neighborhood of each urban commercial POI point is constructed; Determine the adaptive bandwidth of different quadrants of each city's commercial POI point based on the mutation point of the spatial distribution trend curve. The mutation point is the point where the first-order derivative or second-order derivative of the spatial distribution trend curve is 0, and the neighborhood range corresponding to the mutation point is the adaptive bandwidth; Based on the local adaptive bandwidth of each quadrant of each urban commercial POI point, kernel density values are calculated for each quadrant and summed across the four quadrants to obtain the final kernel density value of the urban commercial POI point. The kernel density value is used to construct an urban commercial kernel density surface, which is used to perform spatial correlation analysis with nighttime light intensity. The kernel density value K of the commercial POI point in the i-th city is calculated according to the following formula: i : Among them, r i,k is the local adaptive bandwidth of the k-th quadrant of the commercial POI point in the i-th city, n k is the total number of urban commercial POI points within the local adaptive bandwidth of the k-th quadrant of the i-th urban commercial POI point, d i,j,k is the distance from the commercial POI point of the i-th city in the k-th quadrant to the commercial POI point of the j-th city within the bandwidth, k(d i,j,k ,r i,k ) represents the Gaussian kernel function.

2. The adaptive KDE method considering the local spatial distribution differences of POI points according to claim 1, characterized in that: The mutation point is determined by the following method: calculating the first-order derivative and the second-order derivative of the spatial distribution trend curve function, obtaining the neighborhood range corresponding to when the first-order derivative and the second-order derivative are 0, and selecting the smallest neighborhood range as the adaptive bandwidth.

3. The adaptive KDE method considering the local spatial distribution differences of POI points according to claim 1, characterized in that: If there is a city commercial POI point within the neighborhood range of X meters that does not obtain the adaptive bandwidth, the neighborhood range is increased by X meters until the local adaptive bandwidth of each quadrant of each city commercial POI point is within the neighborhood range of X meters.

4. An adaptive KDE system that takes into account the local spatial distribution differences of POIs, characterized by: include: The local spatial distribution trend calculation module is used to preset a statistical neighborhood range of X meters, count the number of urban commercial POI points within the range of 0 to X meters in the four quadrants of each urban commercial POI point at set intervals, and construct a four-quadrant neighborhood spatial distribution trend curve for each urban commercial POI point; An adaptive bandwidth determination module is used to determine the adaptive bandwidth of different quadrants of each city's commercial POI point based on the mutation point of the spatial distribution trend curve. The mutation point is the point where the first-order derivative or second-order derivative of the spatial distribution trend curve is 0, and the neighborhood range corresponding to the mutation point is the adaptive bandwidth; And a global kernel density value calculation module is used to calculate the kernel density value of each quadrant according to the local adaptive bandwidth of each quadrant of each urban commercial POI point obtained, and perform the summation of the four quadrants to obtain the final kernel density value of the urban commercial POI point. The kernel density value is used to construct the urban commercial kernel density surface, and the urban commercial kernel density surface is used to perform spatial correlation analysis with the night light intensity; the kernel density value K of the i-th urban commercial POI point is calculated according to the following formula i : Among them, r i,k is the local adaptive bandwidth of the k-th quadrant of the commercial POI point in the i-th city, n k is the total number of urban commercial POI points within the local adaptive bandwidth of the k-th quadrant of the i-th urban commercial POI point, d i,j,k is the distance from the commercial POI point of the i-th city in the k-th quadrant to the commercial POI point of the j-th city within the bandwidth, k(d i,j,k ,r i,k ) represents the Gaussian kernel function.

5. The adaptive KDE system considering the local spatial distribution differences of POI points according to claim 4, characterized in that: The mutation point is determined by the following method: calculating the first-order derivative and the second-order derivative of the spatial distribution trend curve function, obtaining the neighborhood range corresponding to when the first-order derivative and the second-order derivative are 0, and selecting the smallest neighborhood range as the adaptive bandwidth.

6. The adaptive KDE system according to claim 4, wherein: If there is a city commercial POI point within the neighborhood range of X meters that does not obtain the adaptive bandwidth, the neighborhood range is increased by X meters until the local adaptive bandwidth of each quadrant of each city commercial POI point is within the neighborhood range of X meters.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the computer program is loaded into a processor, the steps of the adaptive KDE method taking into account the differences in local spatial distribution of POI points according to any one of claims 1 to 3 are implemented.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the adaptive KDE method considering the local spatial distribution differences of POI points according to any one of claims 1 to 3 are implemented.

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