Data point set feature analysis method, system and terminal of road network K function based on sampling and spatial threshold sharing, and storage medium

Abstract

The present application relates to the technical field of geographic information analysis, and discloses a data point set feature analysis method, system, terminal and storage medium based on sampling and spatial threshold sharing of road network K function, which comprises the following steps: obtaining the sampling point set of each route by using a sampling method, and then constructing the corresponding positions between the sampling point set and the data point set on another edge based on the sampling point set, so as to calculate the set aggregation function by using the method of spatial threshold sharing, so as to obtain the approximate K value of each edge, and finally analyze the aggregation features of all data points on the entire target road network based on the approximate K values of all edges. The present application can greatly improve the analysis efficiency of data points in the road network and reduce the analysis time of the aggregation features under the condition of ensuring the accuracy and spatial overhead.

Description

Technical Field

[0001] This invention relates to the field of geographic information analysis technology, and in particular to a method, system, terminal, and computer-readable storage medium for analyzing data point set features based on road network K-functions using sampling and spatial threshold sharing. Background Technology

[0002] The road network K-function is a commonly used tool in point pattern analysis. Many fields (including transportation science and urban planning) use this tool to analyze data points on the road network in order to determine whether the data points have meaningful clusters or hotspots.

[0003] However, using the road network K-function tool to analyze road network data points has the following drawbacks: First, the computational complexity of the road network K-function tool is very high; even the most basic method requires at least... (in This refers to the number of data points on the road network. Secondly, in the era of big data, many large-scale datasets can be collected and analyzed by users (i.e.,...). (Very large). Third, when users analyze data using the road network K-function tool, they need to generate road network K-function graphs, which requires calculating multiple road network K-functions (based on multiple spatial thresholds), further exacerbating the efficiency problem.

[0004] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0005] The main objective of this invention is to provide a method, system, terminal, and computer-readable storage medium for analyzing the data point set features of a road network K-function based on sampling and spatial threshold sharing. This aims to solve the problem of high computational complexity and extremely low efficiency in road network analysis when constructing a road network K-function graph for a certain region in the prior art.

[0006] To achieve the above objectives, this invention provides a method for analyzing the feature of a road network K-function based on sampling and spatial threshold sharing. The method includes the following steps: Obtain the data point set on each edge within the target road network. Based on the defined absolute error parameter, sample the data points on each edge to obtain the corresponding sampled point set. For each edge, based on the set of sampled points on the first edge and the set of data points on the second edge, a one-to-two point aggregation function is constructed between the first edge and the second edge. Based on the one-to-two point aggregation function, a set aggregation function is constructed between the set of sampled points and the set of data points. For each sampling point in the sampling point set of the first side, the set aggregation function is equivalently replaced to obtain an equivalent aggregation function, and an approximate K function is constructed based on the equivalent aggregation function; All spatial thresholds on the second side are sorted, and corresponding scan lines are constructed at both ends of the second side according to the spatial threshold sorting results. Based on the process of scanning each data point-spatial threshold pair by each scan line, the approximate K value of the target road network is calculated using the approximate K function. Based on iterative calculations using multiple random data point sets, the maximum approximate road network K value and the minimum approximate road network K value of the target road network are obtained. Based on the approximate K value, the maximum approximate road network K value, and the minimum approximate road network K value, the clustering characteristics of the data points on the target road network are displayed.

[0007] Optionally, the method for analyzing the data point set features of a road network based on sampling and spatial threshold sharing, wherein obtaining the data point set on each edge within the target road network, and sampling data points on each edge based on a defined absolute error parameter to obtain the corresponding sampled point set, specifically includes: Based on the user-defined absolute error parameters, data points are sampled from the data point set on each edge of the target road network to obtain the sampling point set corresponding to each edge. Wherein, the difference between the network K value and the approximate K value of the target road network is less than the absolute error parameter: ; in, Indicates spatial threshold The approximate K value below, Indicates spatial threshold K-value of the road network Represents the absolute error parameter. This represents the set of data points representing all edges. This represents the set of sampled points for all edges.

[0008] Optionally, the method for analyzing data point set features of a road network K-function based on sampling and spatial threshold sharing, wherein for each edge, constructing a one-to-two point set aggregation function between the first edge and the second edge based on the sampling point set on the first edge and the data point set on the second edge, and constructing a set aggregation function between the sampling point set and the data point set based on the one-to-two point set aggregation function, specifically includes: Based on multiple user-defined spatial thresholds, the approximate K value of the target road network is initialized to 0; Define any edge as the first edge, and construct a point aggregation function between the first edge and the second edge based on any data point on the second edge and the sampled point set on the first edge: ; in, This represents the aggregation function for a set of one or two points. Indicates the first side, Indicates the second side of the first... Data points, This represents the set of sampled points on the first side. Indicates the first side of the first edge. One sampling point express and In the target road network The shortest path on, Indicates an indicator function, Indicates spatial threshold; Based on the first and second point set aggregation function, construct a set aggregation function between the sampling point set of the first side and the data point set of the second side: ; in, Represents aggregate functions for sets. This represents the set of data points on the second side. Indicates the second side.

[0009] Optionally, the method for analyzing the data point set features of a road network K-function based on sampling and spatial threshold sharing, wherein the step of performing an equivalent substitution on the set aggregation function for each sampling point in the sampling point set of the first edge to obtain an equivalent aggregation function, and constructing an approximate K-function based on the equivalent aggregation function, specifically includes: Construct a two-point set aggregation function between each sampling point on the first edge and the set of data points on the second edge: ; in, This represents the aggregation function of a two-point set. express and In the target road network The shortest path on; Based on the two-point set aggregation function, construct an equivalent aggregation function for the set aggregation function to perform an equivalent replacement on the set aggregation function: ; in, Represents equivalent aggregate functions; Construct an approximate K-function for the target road network based on the equivalent aggregation function: ; in, Indicates the target road network at the spatial threshold The approximate K value below, Describe the set of edges of the target road network. This represents the total number of data points on the first side. This represents the total number of sampling points on the first side.

[0010] Optionally, the method for analyzing the data point set features of a road network based on sampling and spatial threshold sharing, wherein the steps of sorting all spatial thresholds of the second side, constructing corresponding scan lines at both ends of the second side according to the spatial threshold sorting results, and calculating the approximate K value of the target road network using the approximate K function based on the process of scanning each data point-spatial threshold pair by each scan line, specifically includes: Sort all the spatial thresholds of the second side to obtain the spatial threshold sorting result of the second side, and fill the two endpoints of the second side with the spatial threshold sorting result; A corresponding scan line is constructed at each endpoint. For each endpoint, the scan line is used to scan from the endpoint to the other endpoint. When the scan line passes through each data point-spatial threshold pair, the function value of the corresponding two-point set aggregation function is constructed. Based on each of the function values, construct an approximate K function for the target road network at each of the spatial thresholds, and calculate the corresponding approximate K value.

[0011] Optionally, the method for analyzing the data point set features of a road network K-function based on sampling and spatial threshold sharing, wherein sorting all the spatial thresholds of the second side to obtain the spatial threshold sorting result of the second side, and filling the spatial threshold sorting result into the two endpoints of the second side, specifically includes: Two endpoints are constructed on the second side. For each sampling point data point-spatial threshold pair, all spatial thresholds are sorted according to the distance between the sampling point and any endpoint of the second side, and finally the first sorting result corresponding to each sampling point is obtained. The two first sorting results corresponding to any two adjacent sampling points are merged and sorted to obtain the second sorting result; Merge and sort any two adjacent second sorting results until the spatial threshold sorting result of the second side is obtained.

[0012] Optionally, the method for analyzing data point set features based on road network K-function using sampling and spatial threshold sharing, wherein the step of iteratively calculating the maximum and minimum approximate road network K-values ​​of the target road network based on multiple random data point sets, and displaying the clustering features of data points on the target road network based on the approximate K-values, the maximum approximate road network K-values, and the minimum approximate road network K-values, specifically includes: Based on multiple random data point sets provided by the user, a random approximate K value for the target road network is calculated for each of the random data point sets, and a maximum and minimum approximate road network K value are defined from all the random approximate K values: ; ; in, Indicates the first A spatial threshold, Indicates spatial threshold The minimum approximate road network K value is given below. Indicates spatial threshold The maximum approximate road network K value is given below. , and These represent the spatial thresholds. The first random dataset, the second random dataset, and the third random dataset are listed below. A random approximation of K values ​​for a random dataset. , and These represent the first set of random data points. The second set of random data points and the A set of random data points The sampling point set; Based on the approximate K value, the maximum approximate road network K value, and the minimum approximate road network K value, a schematic diagram of the target road network is constructed, and the aggregation characteristics of the total data point set under each spatial threshold are obtained.

[0013] Furthermore, to achieve the above objectives, the present invention also provides a data point set feature analysis system based on sampling and spatial threshold sharing of a road network K-function, wherein the data point set feature analysis system based on sampling and spatial threshold sharing of a road network K-function includes: The sampling module is used to obtain the data point set on each edge in the target road network. Based on the defined absolute error parameter, the data points are sampled on each edge to obtain the corresponding sampling point set. The aggregation function construction module is used to construct a one-to-two point aggregation function between the first edge and the second edge for each edge, based on the sampling point set on the first edge and the data point set on the second edge, and to construct a set aggregation function between the sampling point set and the data point set based on the one-to-two point aggregation function. An approximate K-function construction module is used to perform an equivalent substitution on the set aggregation function for each sampling point in the sampling point set of the first side to obtain an equivalent aggregation function, and to construct an approximate K-function based on the equivalent aggregation function; The approximate K-value calculation module is used to sort all spatial thresholds of the second side, and construct corresponding scan lines at both ends of the second side according to the spatial threshold sorting results. Based on the process of scanning each data point-spatial threshold pair by each scan line, the approximate K-value of the target road network is calculated using the approximate K function. The clustering feature display module is used to iteratively calculate the maximum approximate road network K value and the minimum approximate road network K value of the target road network based on multiple random data point sets, and display the clustering features of the data points on the target road network according to the approximate K value, the maximum approximate road network K value and the minimum approximate road network K value.

[0014] Furthermore, to achieve the above objectives, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a data point set feature analysis program based on a road network K function of sampling and spatial threshold sharing, stored in the memory and executable on the processor. When the data point set feature analysis program based on a road network K function of sampling and spatial threshold sharing is executed by the processor, it implements the steps of the data point set feature analysis method based on a road network K function of sampling and spatial threshold sharing as described above.

[0015] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a data point set feature analysis program based on a road network K function of sampling and spatial threshold sharing, and when the data point set feature analysis program based on a road network K function of sampling and spatial threshold sharing is executed by a processor, it implements the steps of the data point set feature analysis method based on a road network K function of sampling and spatial threshold sharing as described above.

[0016] In this invention, a data point set is obtained on each edge of the target road network. Based on a defined absolute error parameter, data points are sampled on each edge to obtain a corresponding sampled point set. For each edge, a one-to-two point aggregation function is constructed between the first edge and the second edge based on the sampled point set on the first edge and the data point set on the second edge. Based on the one-to-two point aggregation function, a set aggregation function is constructed between the sampled point set and the data point set. For each sampled point in the sampled point set of the first edge, the set aggregation function is equivalently replaced to obtain an equivalent aggregation function. An approximate K-function is constructed based on the equivalent aggregation function; all spatial thresholds of the second side are sorted, and corresponding scan lines are constructed at both ends of the second side according to the spatial threshold sorting results. Based on the process of each scan line scanning to each data point-spatial threshold pair, the approximate K-value of the target road network is calculated using the approximate K-function; based on iterative calculations using multiple random data point sets, the maximum and minimum approximate road network K-values ​​of the target road network are obtained. Based on the approximate K-values, the maximum approximate road network K-values, and the minimum approximate road network K-values, the aggregation characteristics of the data points on the target road network are displayed. This invention, while ensuring accuracy and space overhead, can greatly improve the analysis efficiency of data points in the road network and reduce the analysis time of aggregation features. Attached Figure Description

[0017] Figure 1 This is a flowchart of a preferred embodiment of the data point set feature analysis method of the road network K function based on sampling and spatial threshold sharing of the present invention; Figure 2 This is a schematic diagram of the road network K-function, which is a preferred embodiment of the road network K-function data point set feature analysis method based on sampling and spatial threshold sharing of the present invention. Figure 3 This is a schematic diagram of data point sampling in a preferred embodiment of the data point set feature analysis method of the road network K function based on sampling and spatial threshold sharing of the present invention. Figure 4 This is a schematic diagram showing the reversed calculation order of a preferred embodiment of the data point set feature analysis method for road network K-function based on sampling and spatial threshold sharing of the present invention; Figure 5 This is a schematic diagram of the spatial threshold sorting of a preferred embodiment of the data point set feature analysis method of the road network K function based on sampling and spatial threshold sharing of the present invention. Figure 6 This is a schematic diagram of iterative sorting of a preferred embodiment of the data point set feature analysis method of the road network K function based on sampling and spatial threshold sharing of the present invention; Figure 7This is a schematic diagram of the scan line of a preferred embodiment of the data point set feature analysis method of the road network K function based on sampling and spatial threshold sharing of the present invention; Figure 8 This is a schematic diagram of the features of a road network K-function graph, representing a preferred embodiment of the road network K-function data point set feature analysis method based on sampling and spatial threshold sharing of the present invention. Figure 9 This is a schematic diagram illustrating the change in response time of different methods for generating road network K-function graphs as the number of spatial thresholds varies, based on a preferred embodiment of the road network K-function data point set feature analysis method of the present invention, which is based on sampling and spatial threshold sharing. Figure 10 This is a schematic diagram illustrating the change in response time of different methods for generating road network K-function graphs as the amount of dataset varies, based on a preferred embodiment of the road network K-function data point set feature analysis method of the present invention, which is based on sampling and spatial threshold sharing. Figure 11 This is a schematic diagram illustrating the maximum range of response time for generating road network K-function graphs using different methods of the preferred embodiment of the road network K-function data point set feature analysis method based on sampling and spatial threshold sharing of the present invention, as well as the variation of spatial threshold. Figure 12 This is a schematic diagram illustrating the response time of generating a road network K-function graph using different methods as a function of absolute error, based on a preferred embodiment of the road network K-function data point set feature analysis method of the present invention, which is based on sampling and spatial threshold sharing. Figure 13 This is a schematic diagram illustrating the variation of the spatial overhead of generating a road network K-function graph with the number of spatial thresholds in a preferred embodiment of the road network K-function data point set feature analysis method based on sampling and spatial threshold sharing of the present invention. Figure 14 This is a schematic diagram illustrating the spatial overhead of generating road network K-function graphs using different methods as the amount of data in a preferred embodiment of the road network K-function data point set feature analysis method based on sampling and spatial threshold sharing of the present invention. Figure 15 This is a schematic diagram illustrating the spatial overhead of generating a road network K-function graph using different methods as a function of absolute error, based on a preferred embodiment of the road network K-function data point set feature analysis method of the present invention, which is based on sampling and spatial threshold sharing. Figure 16 This is a schematic diagram showing the results of generating a road network K-function graph for the total data point set using precise and approximate methods under different spatial thresholds, according to a preferred embodiment of the road network K-function feature analysis method based on sampling and spatial threshold sharing of the present invention. Figure 17This is a schematic diagram showing the results of generating road network K-function graphs for random data point sets using precise and approximate methods under different spatial thresholds, based on a preferred embodiment of the road network K-function feature analysis method of the present invention, which is based on sampling and spatial threshold sharing. Figure 18 This is a schematic diagram showing the results of generating a complete road network K-function graph for location D using precise and approximate methods under different spatial thresholds, based on a preferred embodiment of the data point set feature analysis method for road network K-functions based on sampling and spatial threshold sharing of the present invention. Figure 19 This is a schematic diagram illustrating the absolute and relative errors of the road network K-function graph generated by this method for different spatial thresholds under different spatial thresholds, based on a preferred embodiment of the data point set feature analysis method of the road network K-function using sampling and spatial threshold sharing of the present invention. Figure 20 This is a schematic diagram illustrating the average absolute percentage error of generating a road network K-function graph using this method under different absolute errors in a preferred embodiment of the data point set feature analysis method of the road network K-function based on sampling and spatial threshold sharing in the present invention; Figure 21 This is a schematic diagram illustrating the average absolute percentage error of generating a road network K-function graph using this method under random data point sets, based on a preferred embodiment of the road network K-function data point set feature analysis method of the present invention, which is based on sampling and spatial threshold sharing. Figure 22 This is a structural diagram of a preferred embodiment of the data point set feature analysis system of the road network K function based on sampling and spatial threshold sharing of the present invention; Figure 23 This is a structural diagram of a preferred embodiment of the terminal of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0019] The preferred embodiment of the present invention describes a data point set feature analysis method based on sampling and spatial threshold sharing of a road network K-function, such as... Figure 1 As shown, the data point set feature analysis method based on road network K-function using sampling and spatial threshold sharing includes the following steps: Step S10: Obtain the data point set on each edge in the target road network. Based on the defined absolute error parameter, sample the data points on each edge to obtain the corresponding sampled point set.

[0020] In the embodiments disclosed in this invention, the target area is first defined as the form of a target road network: ,in and Let these represent the set of nodes and the set of edges of the road network, respectively. This target road network contains a set of size [value missing]. Total dataset , , and They represent the 1st, 2nd, and 3rd respectively. Given a set of data points, if a spatial threshold is defined for the target road network... Then the road network K function of the target road network is: ; at this time, Indicates spatial threshold Approximate K value below Indicates the first Data points, Indicates the first Data points, Indicates an indicator function, express and In the target road network The distance on.

[0021] Among them, such as Figure 2 As shown, the distance to each data point needs to be accumulated. The total number of all data points is then divided by the total number of all pairs, for example... Figure 2 (a) refers to data points. , , and The value of the road network K function is ,like Figure 2 (b) refers to data points. , , and The value of the road network K function is .

[0022] Specifically, based on the absolute error parameters defined by the user, data points are sampled from the data point set on each edge of the target road network to obtain the sampling point set corresponding to each edge; Wherein, the difference between the network K value and the approximate K value of the target road network is less than the absolute error parameter: ; in, Indicates spatial threshold The approximate K value below, Indicates spatial threshold K-value of the road network Represents the absolute error parameter. This represents the set of data points representing all edges. This represents the set of sampled points for all edges.

[0023] To improve the efficiency of generating road network K-function graphs, this invention proposes a Sampling and Threshold Sharing Solution (STARS). The sampling method involves observing the equivalence between calculating the road network K-function and kernel density estimation, and then using a kernel density estimation sampling method on the road network. Each edge in the dataset is sampled to obtain a dataset, and based on this, an approximate calculation formula with absolute error theory guarantee is proposed.

[0024] Specifically, this invention utilizes a kernel density estimation sampling method and sets its absolute error. For each edge, data points are sampled, such as... Figure 3 As shown, and They represent the edges respectively ( and Representing an edge The data point of one of the total data point sets on the node (i.e., Belongs to the edge (data point set) and the sampled data on the edge ( and Representing an edge The data points (nodes). Based on this, it can be proved that the relationship between the aggregation function of the data points on the second side to the data point set on the first side and the aggregation function of the data points on the second side to the sampled point set on the first side is as follows: ; in, This represents the aggregation function that represents the set of data points from the second side to the first side. This represents the aggregation function that represents the set of sampled points from the second side to the first side. Representing an edge The data point set.

[0025] Based on this relationship, this invention proposes that if the absolute error parameter of the sampling method is set... If the difference between the target road network's K value and the approximate K value is less than the absolute error parameter, then up to this step, the time complexity of generating the sampled dataset is... ,in Indicates the number of edges.

[0026] Step S20: For each edge, construct a one-to-two point aggregation function between the first edge and the second edge based on the sampling point set on the first edge and the data point set on the second edge, and construct a set aggregation function between the sampling point set and the data point set based on the one-to-two point aggregation function.

[0027] The spatial threshold sharing method avoids repeatedly calculating multiple spatial thresholds. The road network K-function is then used to reduce the computation of multiple spatial thresholds. This reduces the time complexity of generating the road network K-function graph, thus lowering the time complexity of generating the road network K-function graph.

[0028] Specifically, based on multiple user-defined spatial thresholds, the approximate K value of the target road network is initialized to 0; Define any edge as the first edge, and construct a point aggregation function between the first edge and the second edge based on any data point on the second edge and the sampled point set on the first edge: ; in, This represents the aggregation function for a set of one or two points. Indicates the first side, Indicates the second side of the first... Data points, This represents the set of sampled points on the first side. Indicates the first side of the first edge. One sampling point express and In the target road network The shortest path on, Indicates an indicator function, Indicates spatial threshold; Based on the first and second point set aggregation function, construct a set aggregation function between the sampling point set of the first side and the data point set of the second side: ; in, Represents aggregate functions for sets. This represents the set of data points on the second side. Indicates the second side.

[0029] In order to calculate the approximate K value, it is necessary to define the relationship between the approximate K function and various aggregation functions. For the current first side, a set aggregation function can be defined between the data point set of the second side and the sampling point set of the first side. At the same time, the expression of the approximate K function constructed based on the set aggregation function can also be obtained. At this time, it is only necessary to calculate the value of the set aggregation function to obtain the approximate K value. Based on this, the present invention can further describe the method of spatial threshold sharing.

[0030] Step S30: For each sampling point in the sampling point set of the first side, perform an equivalent substitution on the set aggregation function to obtain an equivalent aggregation function, and construct an approximate K function based on the equivalent aggregation function.

[0031] Specifically, a two-point set aggregation function is constructed between each sampling point on the first edge and the set of data points on the second edge: ; in, This represents the aggregation function of a two-point set. express and In the target road network The shortest path on; Based on the two-point set aggregation function, construct an equivalent aggregation function for the set aggregation function to perform an equivalent replacement on the set aggregation function: ; in, Represents equivalent aggregate functions; Construct an approximate K-function for the target road network based on the equivalent aggregation function: ; in, Indicates the target road network at the spatial threshold The approximate K value below, Describe the set of edges of the target road network. This represents the total number of data points on the first side. This represents the total number of sampling points on the first side.

[0032] From the expression of the set aggregation function, it can be seen that to obtain the value of the set aggregation function, it is necessary to calculate the value of the one- or two-point set aggregation function, such as... Figure 4 As shown, from the data points ( On the second side (Up) to the first side Only then can an approximate value of K be calculated, but this only requires reversing the calculation order, making it from... ( First side (Up) to the second side That is, to calculate the aggregation function of a two-point set. and the corresponding equivalent aggregate functions Its (equivalent aggregation function) Results and aggregate functions They are equivalent; at this point, the objective of this invention to calculate an approximate K value is to calculate the aggregation function of the set. It has been transformed into calculating equivalent aggregation functions. .

[0033] Step S40: Sort all spatial thresholds of the second side, and construct corresponding scan lines at both ends of the second side according to the spatial threshold sorting results. Based on the process of scanning each data point-spatial threshold pair by each scan line, calculate the approximate K value of the target road network using the approximate K function.

[0034] Specifically, all the spatial thresholds of the second side are sorted to obtain the spatial threshold sorting result of the second side, and the spatial threshold sorting result is filled into the two endpoints of the second side; A corresponding scan line is constructed at each endpoint. For each endpoint, the scan line is used to scan from the endpoint to the other endpoint. When the scan line passes through each data point-spatial threshold pair, the function value of the corresponding two-point set aggregation function is constructed. Based on each of the function values, construct an approximate K function for the target road network at each of the spatial thresholds, and calculate the corresponding approximate K value.

[0035] In order to calculate multiple spatial thresholds Equivalent aggregate functions, such as Figure 5 As shown, this invention requires each data point-spatial threshold pair statistics( Indicates the first (using spatial thresholds) to obtain the data point set on the second side. spatial threshold The number of data points within the range, of which All are sampling points on the first side. Therefore, this data point-spatial threshold pair Corresponding to the two dashed lines, one from the node To begin, a path starts from node start.

[0036] like Figure 6 As shown, first from the node Starting data point-spatial threshold pair, from node The same method was used initially. The purpose of this invention is to determine the endpoints and nodes... The distances are sorted from smallest to largest among the endpoints. In the embodiments disclosed in this invention, the spatial thresholds are related as follows: In the sampling point set on the first side, different data points (such as...) Figure 5 Data points in and The corresponding Each spatial threshold (endpoint) is sorted, therefore in Figure 6 Each of the 0th floor All endpoints of the same color (corresponding to a specific data point) are already sorted; in each layer (each iteration), the already sorted endpoints are further merged and sorted until a single sorted endpoint is obtained (i.e., ... Figure 6 The second level (at this point, it has undergone two merge sorts). Since the merge sort at each level takes time... There are a total of Therefore, the time complexity at this step is... .

[0037] Furthermore, two endpoints are constructed on the second side. For each data point-spatial threshold pair of the sampling point, all spatial thresholds are sorted according to the distance between the sampling point and any endpoint of the second side, and finally the first sorting result corresponding to each sampling point is obtained. The two first sorting results corresponding to any two adjacent sampling points are merged and sorted to obtain the second sorting result; Merge and sort any two adjacent second sorting results until the spatial threshold sorting result of the second side is obtained.

[0038] Where the endpoint has been based on the node (or node) When sorting by distance, corresponding scan lines can be constructed at both ends of this edge (e.g., ...). Figure 7 (As shown), scan lines From node To the node Scan, scan line From node To the node Scanning involves counting the number of data points scanned during the scanning process. When a scan line reaches a data point, the spatial threshold is calculated. The corresponding endpoints can then be used to calculate the aggregation function of the two-point set. Value: ; in, and They represent and The number of data points scanned when a data point is reached - the spatial threshold corresponds to the endpoint of the corresponding endpoint; for example... Figure 7 As shown, The value is 5. The value is 4.

[0039] Furthermore, from the expression of the aggregation function of a two-point set ( )and Figure 5 It can be seen that the scanning line processing method can be calculated. Equivalent aggregation functions for spatial thresholds Furthermore, this method only needs to access all endpoints and data points, so the time complexity is O(n). .

[0040] Step S50: Based on iterative calculation of multiple random data point sets, obtain the maximum approximate road network K value and the minimum approximate road network K value of the target road network. Based on the approximate K value, the maximum approximate road network K value and the minimum approximate road network K value, display the clustering characteristics of the data points on the target road network.

[0041] Specifically, based on multiple random data point sets provided by the user, a random approximate K value for the target road network is calculated for each of the random data point sets, and a maximum and minimum approximate road network K value are defined from all the random approximate K values: ; ; in, Indicates the first A spatial threshold, Indicates spatial threshold The minimum approximate road network K value is given below. Indicates spatial threshold The maximum approximate road network K value is given below. , and These represent the spatial thresholds. The first random dataset, the second random dataset, and the third random dataset are listed below. A random approximation of K values ​​for a random dataset. , and These represent the first set of random data points. The second set of random data points and the A set of random data points The sampling point set; Based on the approximate K value, the maximum approximate road network K value, and the minimum approximate road network K value, a schematic diagram of the target road network is constructed, and the aggregation characteristics of the total data point set under each spatial threshold are obtained.

[0042] After visiting one edge, the process continues to visit other edges (other data point sets) until all edges have been visited, and the approximate K values ​​under all spatial thresholds are updated. Based on this, the maximum and minimum approximate road network K values ​​can be selected from all spatial thresholds and visualized (e.g., Figure 8 As shown), it can be concluded that when the spatial threshold is small (within the spatial threshold... Previously, the data points of the target road network exhibited clustering properties, while the spatial threshold... Subsequently, the data points exhibited a dispersed nature.

[0043] Through some mathematical derivation, the time complexity of generating the K-function graph of the target road network using the STARS method for the total data point set and multiple random data point sets is O(n). The resulting space complexity is .

[0044] To address the shortcomings of existing road network K-function graph analysis (i.e., very high computational complexity, large dataset size, and low efficiency in calculating road network K-functions), although existing NS (Neighbor Sharing) methods can partially solve these shortcomings, they cannot support the rapid generation of road network K-function graphs. This invention, however, can achieve this, and the results are shown in Table 1. Table 1: Theoretical Results of Different Methods

[0045] in, This represents the time complexity of the shortest path. This represents the space complexity of the shortest path.

[0046] To further demonstrate the effectiveness of this invention, multiple experiments were conducted on four large-scale datasets (the largest dataset containing over 8.19 million data points). The results show that the STARS method disclosed in this invention, compared to existing precise methods (the first method, Range-query-based solution, RQS), (the second method, Shortest path sharing solution, SPS), and the third method (NS), achieves a speed improvement of 1.52 to 21.57 times with minimal additional space overhead and a negligible reduction in accuracy. Specific results are as follows: Figures 9-21 As shown: in, Figure 9 A schematic diagram illustrating how the response time of different methods for generating road network K-function graphs varies with the number of spatial thresholds; Figure 9 (a) Figure 9 (b) Figure 9 (c) and Figure 9 (d) in the figure shows the results in locations A, B, C and D respectively.

[0047] Figure 10 A schematic diagram illustrating how the response time of different methods for generating road network K-function graphs varies with the amount of dataset; Figure 10 (a) Figure 10 (b) Figure 10 (c) and Figure 10 (d) in the figure shows the results in locations A, B, C and D respectively.

[0048] Figure 11 A schematic diagram illustrating the maximum range of response time variations of different methods for generating road network K-function graphs as a function of spatial thresholds is presented. Figure 11 (a) Figure 11 (b) Figure 11 (c) and Figure 11 (d) in the figure shows the results in locations A, B, C and D respectively.

[0049] Figure 12 A schematic diagram illustrating the response time of different methods for generating road network K-function graphs as a function of absolute error is presented. Figure 12 (a) Figure 12 (b) Figure 12 (c) and Figure 12 (d) in the figure shows the results in locations A, B, C and D respectively.

[0050] Figure 13 A schematic diagram illustrating how the spatial cost of generating road network K-function graphs varies with the number of spatial thresholds using different methods is presented. Figure 13 (a) Figure 13 (b) Figure 13 (c) and Figure 13 (d) in the figure shows the results in locations A, B, C and D respectively.

[0051] Figure 14 A schematic diagram illustrating how the spatial cost of generating road network K-function graphs varies with the size of the dataset using different methods; Figure 14 (a) Figure 14 (b) Figure 14 (c) and Figure 14 (d) in the figure shows the results in locations A, B, C and D respectively.

[0052] Figure 15 A schematic diagram illustrating the spatial cost of generating road network K-function graphs using different methods as a function of absolute error is presented. Figure 15 (a) Figure 15 (b) Figure 15 (c) and Figure 15 (d) in the figure shows the results in locations A, B, C and D respectively.

[0053] Figure 16 The diagram illustrates the results of generating road network K-function graphs for the total data point set using both exact and approximate methods under different spatial thresholds. Figure 16 (a) Figure 16 (b) Figure 16 (c) and Figure 16 (d) in the figure shows the results in locations A, B, C and D respectively.

[0054] Figure 17 The diagram illustrates the results of generating road network K-function graphs for random data point sets using exact and approximate methods under different spatial thresholds. Figure 17 (a) Figure 17 (b) Figure 17 (c) and Figure 17 (d) in the figure shows the results in locations A, B, C and D respectively.

[0055] Figure 18 The diagram illustrates the results of generating a complete road network K-function graph for location D using both exact and approximate methods under different spatial thresholds. Figure 18 (a) shows the precise results of calculating the road network K-function graph of location D using an exact method. Figure 18 (b) shows the approximate results of calculating the road network K function graph of location D using an approximation method.

[0056] Figure 19 The diagram illustrates the absolute error (represented by solid lines) and relative error (represented by dashed lines) of the road network K-function graph generated using this method for the total data point set under different spatial thresholds (ranging from 0 to 2000 meters); Figure 19 (a) Figure 19 (b) Figure 19 (c) and Figure 19 (d) in the figure shows the results in locations A, B, C and D respectively.

[0057] Figure 20A schematic diagram illustrating the mean absolute percentage error of generating a road network K-function graph using this method on a total data point set under different absolute errors is shown. Figure 20 (a) Figure 20 (b) Figure 20 (c) and Figure 20 (d) in the figure shows the results in locations A, B, C and D respectively.

[0058] Figure 21 A schematic diagram illustrating the mean absolute percentage error of generating road network K-function graphs using this method on random data point sets under different absolute error conditions is presented. Figure 21 (a) Figure 21 (b) Figure 21 (c) and Figure 21 (d) in the figure shows the results in locations A, B, C and D respectively.

[0059] This invention can greatly improve the analysis efficiency of data points in road networks and reduce the analysis time of aggregated features while ensuring accuracy and space overhead.

[0060] Furthermore, such as Figure 22 As shown, based on the above-mentioned method for analyzing the feature of road network K-functions based on sampling and spatial threshold sharing, this invention also provides a system for analyzing the feature of road network K-functions based on sampling and spatial threshold sharing, wherein the system includes: The sampling module 51 is used to obtain the data point set on each edge in the target road network, and to sample the data points on each edge based on the defined absolute error parameter to obtain the corresponding sampling point set. The aggregation function construction module 52 is used to construct a one-to-two point aggregation function between the first edge and the second edge for each edge, based on the sampling point set on the first edge and the data point set on the second edge, and to construct a set aggregation function between the sampling point set and the data point set based on the one-to-two point aggregation function. The approximate K-function construction module 53 is used to perform an equivalent substitution on the set aggregation function for each sampling point in the sampling point set of the first side to obtain an equivalent aggregation function, and construct an approximate K-function based on the equivalent aggregation function; The approximate K-value calculation module 54 is used to sort all spatial thresholds of the second side, and construct corresponding scan lines at both ends of the second side according to the spatial threshold sorting results. Based on the process of scanning each data point-spatial threshold pair by each scan line, the approximate K-value of the target road network is calculated using the approximate K function. The clustering feature display module 55 is used to iteratively calculate based on multiple random data point sets to obtain the maximum approximate road network K value and the minimum approximate road network K value of the target road network, and display the clustering features of the data points on the target road network according to the approximate K value, the maximum approximate road network K value and the minimum approximate road network K value.

[0061] Furthermore, such as Figure 23 As shown, based on the above-mentioned method and system for analyzing the data point set features of the road network K function based on sampling and spatial threshold sharing, the present invention also provides a terminal, which includes a processor 10, a memory 20 and a display 30. Figure 23 Only some of the terminal components are shown. However, it should be understood that it is not required to implement all of the components shown, and more or fewer components can be implemented instead.

[0062] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc. Further, the memory 20 may include both internal and external storage devices. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a data point set feature analysis program 40 based on a road network K function using sampling and spatial threshold sharing. This data point set feature analysis program 40 can be executed by the processor 10 to implement the data point set feature analysis method based on a road network K function using sampling and spatial threshold sharing in this application.

[0063] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as executing the data point set feature analysis method based on the road network K function of sampling and spatial threshold sharing.

[0064] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. The display 30 is used to display information on the terminal and to display a visual user interface. The components of the terminal communicate with each other via a system bus.

[0065] In one embodiment, when the processor 10 executes the data point set feature analysis program 40 based on the road network K function of sampling and spatial threshold sharing in the memory 20, it implements the steps of the data point set feature analysis method based on the road network K function of sampling and spatial threshold sharing described above.

[0066] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a data point set feature analysis program based on a road network K function of sampling and spatial threshold sharing, and the data point set feature analysis program based on a road network K function of sampling and spatial threshold sharing, when executed by a processor, implements the steps of the data point set feature analysis method based on a road network K function of sampling and spatial threshold sharing as described above.

[0067] In summary, this invention provides a method and related equipment for analyzing data point set features of a road network based on sampling and spatial threshold sharing using a K-function. The method includes: acquiring a data point set on each edge within a target road network; sampling data points on each edge based on a defined absolute error parameter to obtain a corresponding sampled point set; for each edge, constructing a one-to-two point aggregation function between the first edge and the second edge based on the sampled point set on the first edge and the data point set on the second edge; constructing a set aggregation function between the sampled point set and the data point set based on the one-to-two point aggregation function; and for each sampled point in the sampled point set of the first edge, performing a feature analysis on the K-function. The aggregation functions are equivalently replaced to obtain equivalent aggregation functions, and an approximate K function is constructed based on these equivalent aggregation functions. All spatial thresholds on the second side are sorted, and corresponding scan lines are constructed at both ends of the second side based on the sorting results. The approximate K value of the target road network is calculated using the approximate K function based on the process of scanning each data point-spatial threshold pair using each scan line. The maximum and minimum approximate road network K values ​​are obtained through iterative calculation based on multiple random data point sets. The aggregation characteristics of the data points on the target road network are then displayed based on these approximate K values, the maximum approximate road network K value, and the minimum approximate road network K value. This invention significantly improves the analysis efficiency of data points in a road network and reduces the analysis time for aggregation features while ensuring accuracy and space overhead.

[0068] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal that includes that element.

[0069] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The computer-readable storage medium can be a memory, magnetic disk, optical disk, etc.

[0070] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for analyzing the features of a road network K-function based on sampling and spatial threshold sharing, characterized in that, The data point set feature analysis method based on road network K-function sampling and spatial threshold sharing includes: Obtain the data point set on each edge within the target road network. Based on the defined absolute error parameter, sample the data points on each edge to obtain the corresponding sampled point set. For each edge, based on the set of sampled points on the first edge and the set of data points on the second edge, a one-to-two point aggregation function is constructed between the first edge and the second edge. Based on the one-to-two point aggregation function, a set aggregation function is constructed between the set of sampled points and the set of data points. For each sampling point in the sampling point set of the first side, the set aggregation function is equivalently replaced to obtain an equivalent aggregation function, and an approximate K function is constructed based on the equivalent aggregation function; All spatial thresholds on the second side are sorted, and corresponding scan lines are constructed at both ends of the second side according to the spatial threshold sorting results. Based on the process of scanning each data point-spatial threshold pair by each scan line, the approximate K value of the target road network is calculated using the approximate K function. Based on iterative calculations using multiple random data point sets, the maximum approximate road network K value and the minimum approximate road network K value of the target road network are obtained. Based on the approximate K value, the maximum approximate road network K value, and the minimum approximate road network K value, the clustering characteristics of the data points on the target road network are displayed.

2. The method for analyzing data point set features of a road network K-function based on sampling and spatial threshold sharing as described in claim 1, characterized in that, The process of obtaining the data point set on each edge within the target road network involves sampling data points on each edge based on a defined absolute error parameter to obtain the corresponding sampled point set. Specifically, this includes: Based on the user-defined absolute error parameters, data points are sampled from the data point set on each edge of the target road network to obtain the sampling point set corresponding to each edge. Wherein, the difference between the network K value and the approximate K value of the target road network is less than the absolute error parameter: ； in, Indicates spatial threshold The approximate K value below, Indicates spatial threshold K-value of the road network Represents the absolute error parameter. This represents the set of data points representing all edges. This represents the set of sampled points for all edges.

3. The method for analyzing data point set features of a road network K-function based on sampling and spatial threshold sharing as described in claim 1, characterized in that, For each edge, based on the sampling point set on the first edge and the data point set on the second edge, a one-to-two point set aggregation function is constructed between the first edge and the second edge. Based on the one-to-two point set aggregation function, a set aggregation function is constructed between the sampling point set and the data point set. Specifically, this includes: Based on multiple user-defined spatial thresholds, the approximate K value of the target road network is initialized to 0; Define any edge as the first edge, and construct a point aggregation function between the first edge and the second edge based on any data point on the second edge and the sampled point set on the first edge: ； in, This represents the aggregation function for a set of one or two points. Indicates the first side, Indicates the second side of the first... Data points, This represents the set of sample points on the first side. Indicates the first side of the first edge One sampling point express and In the target road network The shortest path on, Indicates an indicator function, Indicates spatial threshold; Based on the first and second point set aggregation function, construct a set aggregation function between the sampling point set of the first side and the data point set of the second side: ； in, Represents aggregate functions for sets. This represents the set of data points on the second side. Indicates the second side.

4. The data point set feature analysis method for road network K-function based on sampling and spatial threshold sharing according to claim 3, characterized in that, For each sampling point in the sampling point set of the first side, the set aggregation function is equivalently replaced to obtain an equivalent aggregation function, and an approximate K function is constructed based on the equivalent aggregation function, specifically including: Construct a two-point set aggregation function between each sampling point on the first edge and the set of data points on the second edge: ； in, This represents the aggregation function of a two-point set. express and In the target road network The shortest path on; Based on the two-point set aggregation function, construct an equivalent aggregation function for the set aggregation function to perform an equivalent replacement on the set aggregation function: ； in, Represents equivalent aggregate functions; Construct an approximate K-function for the target road network based on the equivalent aggregation function: ； in, Indicates the target road network at the spatial threshold The approximate K value below, Describe the set of edges of the target road network. This represents the total number of data points on the first side. This represents the total number of sampling points on the first side. express The number of elements in the data.

5. The method for analyzing data point set features of a road network K-function based on sampling and spatial threshold sharing as described in claim 4, characterized in that, The process involves sorting all spatial thresholds on the second side, constructing corresponding scan lines at both ends of the second side based on the sorting results, and calculating the approximate K value of the target road network using the approximate K function based on the process of scanning each data point-spatial threshold pair using each scan line. Specifically, this includes: Sort all the spatial thresholds of the second side to obtain the spatial threshold sorting result of the second side, and fill the two endpoints of the second side with the spatial threshold sorting result; A corresponding scan line is constructed at each endpoint. For each endpoint, the scan line is used to scan from the endpoint to the other endpoint. When the scan line passes through each data point-spatial threshold pair, the function value of the corresponding two-point set aggregation function is constructed. Based on each of the function values, construct an approximate K function for the target road network at each of the spatial thresholds, and calculate the corresponding approximate K value.

6. The data point set feature analysis method for road network K-function based on sampling and spatial threshold sharing according to claim 5, characterized in that, The process of sorting all the spatial thresholds of the second side to obtain a spatial threshold sorting result for the second side, and then filling the two endpoints of the second side with the spatial threshold sorting result, specifically includes: Two endpoints are constructed on the second side. For each sampling point data point-spatial threshold pair, all spatial thresholds are sorted according to the distance between the sampling point and any endpoint of the second side, and finally the first sorting result corresponding to each sampling point is obtained. The two first sorting results corresponding to any two adjacent sampling points are merged and sorted to obtain the second sorting result; Merge and sort any two adjacent second sorting results until the spatial threshold sorting result of the second side is obtained.

7. The method for analyzing data point set features of a road network K-function based on sampling and spatial threshold sharing as described in claim 1, characterized in that, The process involves iterative calculation based on multiple random data point sets to obtain the maximum and minimum approximate road network K values ​​for the target road network. Based on these approximate K values, the maximum and minimum approximate road network K values, the aggregation characteristics of the data points on the target road network are displayed, specifically including: Based on multiple random data point sets provided by the user, a random approximate K value for the target road network is calculated for each of the random data point sets, and a maximum and minimum approximate road network K value are defined from all the random approximate K values: ； ； in, Indicates the first A spatial threshold, Indicates spatial threshold The minimum approximate road network K value is given below. Indicates spatial threshold The maximum approximate road network K value is given below. , and These represent the spatial thresholds. The first random dataset, the second random dataset, and the third random dataset are listed below. A random approximation of K values ​​for a random dataset. , and These represent the first set of random data points. The second set of random data points and the A set of random data points The sampling point set; Based on the approximate K value, the maximum approximate road network K value, and the minimum approximate road network K value, a schematic diagram of the target road network is constructed, and the aggregation characteristics of the total data point set under each spatial threshold are obtained.

8. A data point set feature analysis system for road networks based on sampling and spatial threshold sharing, characterized in that, The data point set feature analysis system based on sampling and spatial threshold sharing of the road network K function is used to implement the data point set feature analysis method based on sampling and spatial threshold sharing of the road network K function as described in any one of claims 1-7. The data point set feature analysis system based on sampling and spatial threshold sharing of the road network K function includes: The sampling module is used to obtain the data point set on each edge in the target road network. Based on the defined absolute error parameter, the data points are sampled on each edge to obtain the corresponding sampling point set. The aggregation function construction module is used to construct a one-to-two point aggregation function between the first edge and the second edge for each edge, based on the sampling point set on the first edge and the data point set on the second edge, and to construct a set aggregation function between the sampling point set and the data point set based on the one-to-two point aggregation function. An approximate K-function construction module is used to perform an equivalent substitution on the set aggregation function for each sampling point in the sampling point set of the first side to obtain an equivalent aggregation function, and to construct an approximate K-function based on the equivalent aggregation function; The approximate K-value calculation module is used to sort all spatial thresholds of the second side, and construct corresponding scan lines at both ends of the second side according to the spatial threshold sorting results. Based on the process of scanning each data point-spatial threshold pair by each scan line, the approximate K-value of the target road network is calculated using the approximate K function. The clustering feature display module is used to iteratively calculate the maximum approximate road network K value and the minimum approximate road network K value of the target road network based on multiple random data point sets, and display the clustering features of the data points on the target road network according to the approximate K value, the maximum approximate road network K value and the minimum approximate road network K value.

9. A terminal, characterized in that, The terminal includes: a memory, a processor, and a data point set feature analysis program based on a road network K function with sampling and spatial threshold sharing, stored in the memory and executable on the processor. When the data point set feature analysis program based on a road network K function with sampling and spatial threshold sharing is executed by the processor, it implements the steps of the data point set feature analysis method based on a road network K function with sampling and spatial threshold sharing as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a data point set feature analysis program based on a road network K function with sampling and spatial threshold sharing. When the data point set feature analysis program based on a road network K function with sampling and spatial threshold sharing is executed by a processor, it implements the steps of the data point set feature analysis method based on a road network K function with sampling and spatial threshold sharing as described in any one of claims 1-7.

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