CN113792105B - Geospatial point data sampling method based on half-variogram - Google Patents
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Abstract
The invention discloses a geospatial point data sampling method based on a half-variogram. The method comprises the steps of firstly, capturing geographic statistical characteristics of geographic space point data by using a half-variation function, and dynamically counting the difference of the half-variation function before and after sampling in real time in the sampling process; and then, with the aim of minimizing the difference, driving a simulated annealing optimization algorithm to replace the initial sampling points generated by Z-order sampling, so that the geographic statistical characteristics are maintained, the spatial distribution of geographic spatial point data is maintained in the sampling result, and the accuracy of attribute interpolation is improved. The method of the invention performs visual evaluation and quantitative comparison of sampling results from two aspects of spatial distribution and attribute interpolation, and enhances the visual representation of the difference before and after sampling through the contour map. The invention realizes a sampling model for large-scale geographic space point data, so that a user can easily restore the original data characteristics through the sampling points, and visually explore and analyze the geographic space.
Description
Technical Field
The invention belongs to the technical field of information, and relates to a geospatial point data sampling method based on a half-variogram.
Background
With the rapid development of geospatial information technology, geospatial point data is widely collected in the fields of epidemiology, economics, climatology, and the like. Scatter plots are typically used to visualize geospatial point data sets, describing spatial locations and data attributes with coordinates and visual elements, respectively. However, a scatter diagram obtained by using large-scale geospatial point data often has serious overdraft and visual confusion problems, so that the spatial distribution and attribute relationship of the scatter diagram are difficult to perceive. For this reason, many studies propose various sampling methods considering data characteristics to simplify large-scale geospatial point data to alleviate the problem of over-rendering of scatter plots. For example, Parada-Mayorga et al devised a blue noise sampling to generate a sample set that can simulate human visual perception, while preserving the spatial density of the original points. Chen et al propose a hierarchical multi-class sampling method to alleviate the cross-branch problem of scatter plots and preserve the relative density order of the multi-class points for quantitative analysis. Zhou et al designed an attribute-based sampling model for visual abstraction of large-scale geospatial point data while preserving spatial density and spatial autocorrelation of the data attributes.
Spatial interpolation is a widely used spatial analysis method, and estimates an unsampled attribute space according to spatial similarity or geostatistical features through a spatial prediction model. In addition, the accuracy of spatial interpolation is closely related to the representativeness of the sample points. Therefore, the effective interpolation using the representative geospatial point data is the key to mining the spatial information of unknown points and recovering the original data characteristics. However, the conventional sampling method does not take the interpolation factor of the attribute into good consideration, which will cause great uncertainty for spatial data mining, such as finding valuable patterns. Through close discussion with field experts, the field experts provide geostatistical features which effectively retain data attributes, and are beneficial to improving the accuracy of interpolation results. Therefore, generating a sample set with good geostatistical features is very important for the simplification and subsequent geospatial analysis of large-scale geospatial point data. However, there are three technical problems in considering spatial interpolation during sampling: (1) how to represent the geographic statistical characteristics of attributes to dynamically constrain the sampling process in real time and generate points more suitable for spatial interpolation; (2) how to define a sampling model based on a half-variation function, and further ensuring the accuracy of an attribute interpolation result on the basis of keeping the spatial distribution of geospatial point data; (3) how to evaluate the effectiveness of the sampling result in maintaining the spatial distribution and interpolation quality.
Disclosure of Invention
The invention aims to provide a geospatial point data sampling method based on a half-variogram.
In order to achieve the purpose, the invention adopts the technical scheme that:
step (1) capturing geographic statistical characteristics of geospatial point data by using a semi-variogram;
generating an initial sampling point by using Z-order sampling, calculating the difference of the variation functions of the front and the rear half of the sampling in real time, constructing a target function according to the difference, driving a simulated annealing optimization algorithm, replacing the initial sampling point generated by the Z-order sampling, optimizing the maintenance of the geographic statistical characteristics of the initial sampling point on the basis of maintaining the spatial distribution of data of geographic space points, and realizing the sampling;
and (3) performing visual evaluation and quantitative comparison on sampling results from two aspects of spatial distribution and attribute interpolation, and performing shape-enhanced visual display on the result difference.
Further, the specific method of the step (1) is as follows:
(1-1) modeling empirical half-variogram for geospatial point data:
wherein i and j are any two points with Euclidean distance h, γ (h) is the average half-variance between i and j, N (h) is the set of all point pairs with Euclidean distance h, | N (h) | is the number of point pairs in N (h), z i And z j Attribute values of i and j, respectively;
and (1-2) calculating the sum of the squares of errors between the empirical half-variogram and the fitting model, and selecting the fitting model corresponding to the minimum sum of the squares of errors as a best fitting model to meet the requirement of isotropy, wherein the best fitting model represents the geographic statistical characteristics of the geospatial point data.
Still further, the specific method in the step (2) is as follows:
(2-1) generating an initial sample set S according to the sampling rate by using a Z-order sampling algorithm 0 As the current sample set S;
(2-2) calculating the difference of the best fit models before and after sampling in real time, constructing an objective function according to the difference, driving a simulated annealing optimization algorithm, and performing Z-order optimizationInitial sampling point S generated by sampling 0 And (3) replacing, simulating an objective function of annealing:
off-base station value difference c 1 ＝|V s-psill -V 0-psill |，V s-psill And V 0-psill Respectively representing the bias station values of the best fit model of the current sample set S and the original geospatial point data O; variation value difference c 2 ＝|V s-range -V 0-range |，V s-range And V 0-range Respectively representing the variation range values of the best fit model of the current sample set S and the original geospatial point data O; root mean square error of half variance
N is the number of step size bar units in the empirical half-variation function,
and
respectively representing the half variances of the current sample set S corresponding to the nth step bar of the empirical half-variation function of the original geospatial point data O, where N is 1,2, …, N;
(2-3) selecting a Z-order subset by roulette, randomly selecting data points in the Z-order subset, and replacing original sampling points in the Z-order subset to generate a new sample set S';
probability of selecting Z-order subset for roulette
The number of times that the kth Z-order subset has been selected;
(2-4) according to the set objective function c of simulated annealing 1 、c 2 、c 3 Deciding whether to accept the new sample set S': if the new sample set S' satisfies Δ c 1 < 0 and Δ c 3 < 0, or Δ c 2 < 0 and Δ c 3 < 0, directly receiving the newAs the current sample set S; otherwise, determining whether to accept the new sample set S 'according to an acceptance mechanism of the simulated annealing algorithm probability, if so, taking the S' as the current sample set S, otherwise, taking the last sample set as the current sample set S; Δ c 1 、Δc 2 、Δc 3 Respectively representing c calculated from the new sample set S 1 、c 2 、c 3 With respect to c calculated from the current sample set S 1 、c 2 、c 3 An increment of (d);
(2-5) repeating (2-3) and (2-4), and iteratively replacing until a new sample set is continuously rejected for a time threshold value sigma, and terminating the sampling process, wherein sigma is more than or equal to 30; and taking the sample set accepted for the last time as a final sampling result.
Furthermore, the specific method of the step (3) is as follows:
(3-1) first, calculating indices for evaluating interpolation accuracy, including SI-RMSE (root mean square error between interpolation result and original data) and SI-R (correlation coefficient between interpolation result and original data); calculating KDE errors (kernel density estimation errors) for evaluating spatial distribution maintenance; calculating an absolute difference value between a kriging interpolation result of the sampling points and the original attribute value;
(3-2) the disparity values are mapped by using a thermodynamic diagram, and a shape-enhanced visual disparity expression is obtained by using a contour diagram.
The invention has the beneficial effects that: the method of the invention utilizes the half-variation function to capture the geographic statistical characteristics of the geographic space point data, and dynamically counts the half-variation function difference before and after sampling in real time in the sampling process; and then, with the aim of minimizing the difference, driving a simulated annealing optimization algorithm to replace the initial sampling points generated by Z-order sampling, so that the maintenance of geographic statistical characteristics is realized, the spatial distribution of geographic spatial point data is maintained in the sampling result, and the accuracy of attribute interpolation is improved. In addition, the sampling result is visually evaluated and quantitatively compared from the aspects of spatial distribution and attribute interpolation, and the visual representation of the difference before and after sampling is enhanced from the aspect of shape by using the contour map, so that the sampling method is intuitively evaluated and compared. The method realizes a sampling model for large-scale geographic space point data, so that a user can easily restore the characteristics of original data through sampling points, and visually explore and analyze geographic space.
Drawings
FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a schematic diagram of sampling raw geospatial point data in accordance with the present invention;
FIG. 3 is a schematic diagram illustrating the evaluation of spatial distribution according to the present invention;
FIG. 4 is a schematic diagram illustrating the evaluation of interpolation results in the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and the specific embodiments.
As shown in fig. 1, a geospatial point data sampling method based on a half variogram specifically includes the following steps:
step (1) capturing geographic statistical characteristics of geospatial point data by using a semi-variogram; the method utilizes a semi-variation function which is used as a precondition and an important input of an interpolation model to represent the geographic statistical characteristics, thereby realizing the improvement of the interpolation quality through the maintenance of the geographic statistical characteristics. The specific method comprises the following steps:
(1-1) modeling empirical half-variogram for geospatial point data:
wherein i and j are any two points with Euclidean distance h, γ (h) is the average half-variance between i and j, N (h) is the set of all point pairs with Euclidean distance h, | N (h) | is the number of point pairs in N (h), z i And z j Attribute values of i and j, respectively;
and (1-2) calculating the sum of the squares of errors between the empirical half-variogram and the fitting model, and selecting the fitting model corresponding to the minimum sum of the squares of errors as a best fitting model to meet the requirement of isotropy, wherein the best fitting model represents the geographic statistical characteristics of the geospatial point data.
And (2) generating initial sampling points by using Z-order sampling, calculating the difference of the variation functions of the front and the rear half of the sampling in real time, constructing a target function according to the difference, driving a simulated annealing optimization algorithm, replacing the initial sampling points generated by the Z-order sampling, optimizing the maintenance of the geographic statistical characteristics of the initial sampling points on the basis of maintaining the spatial distribution of data of geographic space points, further realizing the improvement of interpolation quality and realizing the sampling. The specific method is shown in fig. 2:
(2-1) generating an initial sample set S according to the sampling rate by using a Z-order sampling algorithm 0 As the current sample set S;
(2-2) calculating the difference of the best fit models before and after sampling in real time, constructing a target function according to the difference, driving a simulated annealing optimization algorithm, and sampling the Z-order to generate an initial sampling point S 0 And (3) replacing, simulating an objective function of annealing:
simulated annealing objective function: off-base station value difference c 1 ＝|V s-psill -V 0-psill |，V s-psill And V 0-psill Respectively representing the bias station values of the best fit model of the current sample set S and the original geospatial point data O; variation difference c 2 ＝|V s-range -V 0-range |，V s-range And V 0-range Respectively representing the variable range values of the best fit model of the current sample set S and the original geospatial point data O; root mean square error of half variance
N is the number of step size bar units in the empirical half-variation function,
and
respectively representing the half variances of the current sample set S corresponding to the nth step bar of the empirical half-variation function of the original geospatial point data O, where N is 1,2, …, N;
(2-3) selecting a Z-order subset by roulette, randomly selecting data points in the Z-order subset, and replacing original sampling points in the Z-order subset to generate a new sample set S';
probability of selection of Z-order subset by roulette
The number of times that the kth Z-order subset has been selected;
(2-4) according to the set objective function c of simulated annealing 1 、c 2 、c 3 Deciding whether to accept the new sample set S': if the new sample set S' satisfies Δ c 1 < 0 and Δ c 3 < 0, or Δ c 2 < 0 and Δ c 3 If the sample set S 'is less than 0, directly receiving a new sample set S' as a current sample set S; otherwise, determining whether to accept the new sample set S 'according to an acceptance mechanism of the simulated annealing algorithm probability, if so, taking the S' as the current sample set S, otherwise, taking the last sample set as the current sample set S; Δ c 1 、Δc 2 、Δc 3 Respectively representing c calculated from the new sample set S 1 、c 2 、c 3 With respect to c calculated from the current sample set S 1 、c 2 、c 3 An increment of (d);
(2-5) repeating (2-3) and (2-4), and iteratively replacing until the new sample set is continuously rejected for a threshold value sigma, terminating the sampling process, wherein sigma is more than or equal to 30, and the threshold value of the rejection is 30 in the embodiment; and taking the sample set accepted for the last time as a final sampling result.
It can be seen that the spatial distribution of the original geospatial point data can be well maintained by the initial solution generated by Z-order sampling and the operation of limiting the replacement points within the Z-order subset; further, the evaluation function of the simulated annealing is set to c described above 1 、c 2 And c 3 The search process may be directed to a good solution, with minimal change in the geostatistical features. Therefore, the sampling points generated by the method can realize the improvement of the interpolation quality on the basis of keeping the spatial distribution.
And (3) performing visual evaluation and quantitative comparison on sampling results from two aspects of spatial distribution and attribute interpolation, and performing shape-enhanced visual display on the result difference. The specific method comprises the following steps:
(3-1) first, calculating the indexes for evaluating Interpolation accuracy, including SI-RMSE (root mean square error between Interpolation result and original data, reference: radius rainless events company with Kriging interference of Gauged Rain), SI-R (correlation coefficient between Interpolation result and original data, reference: Detection of Interpolation using correlation coefficients);
KDE errors (kernel density estimation errors, reference: Quality and efficiency for kernel density estimates in large data) for evaluating spatial distribution maintenance are calculated;
calculating an absolute difference value between a kriging interpolation result of the sampling point and an original attribute value;
and (3-2) mapping the difference value by using a thermodynamic diagram, and obtaining the visual difference expression with enhanced shape by using a contour diagram.
Based on the sampling method provided by the invention, the sampling result not only keeps the spatial distribution of the geographic space point data, but also improves the accuracy of attribute interpolation. In order to illustrate the effectiveness of the method, the sampling result is visually evaluated and quantitatively compared from two aspects of spatial distribution and attribute interpolation respectively. However, in the conventional thermodynamic diagram for evaluation, in the case where the large-scale scatter diagram itself is over-plotted, the visual expressiveness of the difference is significantly reduced. Therefore, the method designs a shape-enhanced visual assessment optimization scheme: firstly, calculating an absolute difference value between a kriging interpolation result of a sampling point and an original attribute value; then, the contour map is used to map the absolute difference to obtain the shape-enhanced visual difference representation.
As shown in fig. 3, the use of contour plots brings two benefits: firstly, the visual confusion of a high-density area of a large-scale scatter diagram is avoided, and secondly, the fusion of shapes enhances the visual performance of differences. From a comparison of (a), (b), (c) and (d), (e), (f) of fig. 4, it can be seen that the shape-optimized disparity estimation has a better visual perception effect.
The method has the following validity evaluation:
the effectiveness of our proposed geospatial point data sampling method based on half variogram is demonstrated by quantitative comparison and visual evaluation. Evaluation was performed using 3 sets of geospatial point data (D1, D2, D3). As shown in the following table, the sampling method (denoted by "OUR") was compared with two sampling methods, Z-order sampling (denoted by "ZS") and random sampling (denoted by "RS"), which have universality and authority.
At three sampling rates of 1%, 5% and 10%, the above three indices were used: the root mean square error (SI-RMSE) between the interpolated results and the raw data is compared with the correlation coefficients (SI-R) and KDE errors to evaluate the spatial distribution preservation. As can be seen from the table, the SI-RMSE values of this method are superior to the others at different sampling rates, and only one of the SI-R values is inferior to ZS, which is considered to be effective in maintaining the spatial distribution of geographic points. This shows that the sampling result of the method of the present invention not only keeps the spatial distribution of the original geospatial point data, but also better keeps the accuracy of the spatial interpolation.
As shown in fig. 3, it is intuitive from the KDE thermodynamic diagram that the sampling results of the method of the present invention are similar to ZS sampling in terms of preservation of spatial distribution and are better than ZS in some areas, which indicates that the method of the present invention can achieve preservation of the spatial distribution of geospatial point data.
As shown in (d), (e) and (f) of fig. 4, the method interpolates the sampling results of the method, the Z-order sampling and the random sampling of the present invention by using a kriging interpolation value, and simultaneously visually displays the difference between the interpolation result and the original data by using a contour map, and as can be seen from the diagram, the difference between the interpolation result of the sampling point of the method and the original data is minimal, particularly at a highlighted area A, B, C, thereby showing that the sampling result of the method of the present invention can better improve the accuracy of the attribute interpolation result on the basis of maintaining the spatial distribution of the geospatial point data.
Claims (3)
1. A geospatial point data sampling method based on a half-variogram is characterized by comprising the following steps:
step (1) capturing geographic statistical characteristics of geospatial point data by using a semi-variogram;
generating initial sampling points by using Z-order sampling, calculating the difference of best fit models before and after sampling in real time, constructing a target function according to the difference, driving a simulated annealing optimization algorithm, replacing the initial sampling points generated by the Z-order sampling, optimizing the retention of geographic statistical characteristics of the initial sampling points on the basis of maintaining the spatial distribution of data of geographic space points, and realizing sampling;
step (3) performing visual evaluation and quantitative comparison of sampling results from two aspects of spatial distribution and attribute interpolation, and performing shape-enhanced visual display on the result difference;
the specific method of the step (1) is as follows:
(1-1) modeling empirical half-variogram for geospatial point data:
wherein i and j are any two points with Euclidean distance h, γ (h) is the average half-variance between i and j, N (h) is the set of all point pairs with Euclidean distance h, | N (h) | is the number of point pairs in N (h), z i And z j Attribute values of i and j, respectively;
(1-2) fitting the empirical half-variogram, calculating the sum of squares of errors between the empirical half-variogram and a corresponding fitting model, and selecting the fitting model corresponding to the minimum sum of squares of errors as a best fitting model to meet the requirement of isotropy, wherein the best fitting model represents the geographic statistical characteristics of the geographic space point data;
the specific method of the step (2) is as follows:
(2-1) generating an initial sample set S according to the sampling rate by using a Z-order sampling algorithm 0 As a current sample set S;
(2-2) calculating the difference of the best fit models before and after sampling in real time, constructing a target function according to the difference, driving a simulated annealing optimization algorithm, and sampling the Z-order to generate an initial sampling point S 0 And (3) replacing, simulating an objective function of annealing:
base station bias value
V s-psill And V 0-psill Respectively representing the bias station values of the best fit model of the current sample set S and the original geospatial point data O; variation difference c 2 ＝|V s-range -V 0-range |，V s-range And V 0-range Respectively representing the variable range values of the best fit model of the current sample set S and the original geospatial point data O; root mean square error of the half variance
N is the number of step size bar units in the empirical half-variation function,
and
respectively representing the half variances of the current sample set S corresponding to the nth step bar of the empirical half-variation function of the original geospatial point data O, where N is 1,2, …, N;
(2-3) selecting a Z-order subset according to a certain probability, randomly selecting data points in the Z-order subset, and replacing original sampling points in the Z-order subset to generate a new sample set S';
(2-4) according to the set objective function c of simulated annealing 1 、c 2 、c 3 Deciding whether to accept the new sample set S': if the new sample set S' satisfies Δ c 1 < 0 and Δ c 3 < 0, or Δ c 2 < 0 and Δ c 3 If the sample set S 'is less than 0, directly receiving a new sample set S' as a current sample set S; otherwise, determining whether to accept a new sample set S 'according to an acceptance mechanism of the simulated annealing algorithm probability, if so, taking S' as the current sample set S, otherwise, taking the last sample set as the current sample set S; Δ c 1 、Δc 2 、Δc 3 Respectively representing c calculated from the new sample set S 1 、c 2 、c 3 With respect to c calculated from the current sample set S 1 、c 2 、c 3 An increment of (d);
(2-5) repeating (2-3) and (2-4), and iteratively replacing until a new sample set is continuously rejected for a time threshold value sigma, and terminating the sampling process, wherein sigma is more than or equal to 30; and taking the sample set accepted for the last time as a final sampling result.
2. The method for sampling geospatial point data based on a semi-variogram as claimed in claim 1, wherein the specific method in step (3) is:
(3-1) first, calculating indexes for evaluating interpolation accuracy, including SI-RMSE and SI-R; calculating KDE errors for evaluating space distribution maintenance; calculating an absolute difference value between a kriging interpolation result of the sampling point and an original attribute value;
(3-2) the disparity values are mapped by using a thermodynamic diagram, and a shape-enhanced visual disparity expression is obtained by using a contour diagram.
3. The method for sampling geospatial point data based on a semi-variogram as claimed in claim 1, wherein the probability of selecting the subset of Z-orders in (2-3)
The number of times the kth Z-order subset has been selected.
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