Optimized hotspot analysis method for analyzing spatial distribution characteristics of land cover types

Abstract

The invention relates to the technical field of geographic spatial distribution identification, in particular to an optimized hotspot analysis method for analyzing spatial distribution characteristics of land cover types, which comprises the following steps of: performing further grade division on an identified initialized salient hotspot region by combining kernel density, a natural breakpoint method and a maximum entropy threshold segmentation method; the feature aggregation degree difference of different geographic units can be reflected more accurately, comprehensively and visually, and the spatial heterogeneity and spatial-temporal variation of the feature distribution of the geographic units can be reflected better.

Description

Technical Field

[0001] The invention relates to the technical field of geographic spatial distribution recognition, and in particular to an optimized hot spot analysis method for analyzing spatial distribution characteristics of surface cover types. Background Art

[0002] Hot spot analysis algorithm is a method commonly used in geographic information systems (GIS) to determine and analyze the spatial distribution of high-value clusters (hot spots) and low-value clusters (cold spots) of geographic unit characteristics (a certain geographical phenomenon or a certain attribute value). This method can mine and quantify deep spatial information and verify the spatial distribution pattern of clusters, such as urban area description, spatial distribution of economic activities, and crime hot spot analysis.

[0003] This method calculates the local sum of the geographic unit and its neighboring elements by comparing it to the sum of all elements. Statistical indices are used to determine and analyze hot spots of geographical unit aggregation and their changes, that is, to reflect the aggregation of high and low values ​​in the region.

[0004] The input to this method is a spatial feature class that describes the spatial relationships between geographic units. The value is actually the z-score in the statistical sense. Based on the normal distribution test assumption, the critical values ​​used to determine whether a geographical unit is a hotspot are different at different significance test levels. The significance test level is 10% and the corresponding critical value is +-1.65 (i.e. A geographical unit with a value greater than 1.65 is judged as a significant hot spot area, and a geographical unit with a value less than -1.65 is judged as a significant cold spot area, the same below). The critical value corresponding to the significance test level of 5% is +-1.96, and the critical value corresponding to the significance test level of 1% is +-2.58.

[0005] When different hot spots in the geographic space The value distribution range is wide (such as Figure 1 When the difference is large, it indicates that there are large differences in the degree of significant clustering of the characteristics of different hotspot geographical units in the geographic space. Only the critical values ​​of 1%, 5%, and 10% significance test levels ( Figure 1 The red line in the middle is the critical value corresponding to the 5% significance level) It is difficult to further reflect the differences in the degree of aggregation of the characteristics of different hotspot geographical units intuitively, comprehensively and accurately. And according to the principle of hotspot analysis, it can be seen that the characteristics of each geographical unit are The value is the "relative value" at a specific time phase, that is, the local sum of the geographical unit and its adjacent elements at the current time phase is compared with the sum of all elements within the study area. The benchmarks of different periods, that is, the sum of all elements within the study area, are different. It is difficult for the value to intuitively reflect the changes and developments of hot spots.

[0006] Therefore, it is necessary to design an optimized hotspot analysis method for analyzing the spatial distribution characteristics of surface cover types, and to further grade the identified initial significant hotspot areas by combining the kernel density, natural breakpoint method and maximum entropy threshold segmentation method, so as to more accurately, comprehensively and intuitively reflect the differences in the degree of characteristic aggregation of different geographic units, and better reflect the spatial heterogeneity of the characteristic distribution of geographic units and their spatiotemporal changes. Summary of the invention

[0007] The purpose of the present invention is to overcome the shortcomings of the prior art and provide an optimized hotspot analysis method for analyzing the spatial distribution characteristics of surface cover types. The method combines kernel density, natural breakpoint method and maximum entropy threshold segmentation method to further grade the identified initial significant hotspot areas, which can more accurately, comprehensively and intuitively reflect the differences in the degree of aggregation of characteristics of different geographic units, and better reflect the spatial heterogeneity of the distribution of geographic unit characteristics and their spatiotemporal changes.

[0008] In order to achieve the above object, the present invention provides an optimized hot spot analysis method for analyzing the spatial distribution characteristics of land cover types:

[0009] The following steps are involved:

[0010] S1, identify the geographic entity to be analyzed and obtain raster data representing the spatial distribution of the geographic entity;

[0011] S2, preprocessing of spatially distributed raster data, including:

[0012] S2-1, raster data converted to point vector data: raster data is converted to point vector data using the raster to point tool, where each vector point corresponds to a pixel on the raster data;

[0013] S2-2, calculate the building distribution density characteristics: take the building spatial distribution vector point data as input, calculate the kernel density by the following formula 1, and obtain the building spatial distribution kernel density raster data;

[0014] Formula 1:

[0015] Where Density(x,y) is the kernel density value of the pixel at (x,y), h is the search radius, and the default search radius function calculation setting is 1000. i ,y i is the coordinate of the input spatial element;

[0016] S2-3, raster data conversion to vector data: using the building spatial distribution kernel density raster data as input, the raster data is converted into vector point data to obtain the building spatial distribution kernel density vector point data. Each pixel corresponds to a point feature, and the construction land kernel density on the pixel corresponds to the attribute value of the point feature.

[0017] S3, calculate and extract significant initial construction land hotspot areas, including:

[0018] S3-1, using building kernel density vector point data as input, point elements as the smallest geographic unit, and building spatial distribution kernel density as the eigenvalue, calculate the density of each geographic unit using the following formula 2 The significant initial construction land hotspots were extracted by using a threshold of 1.96 at a significance test level of 5%, i.e., when the geographic unit When the value is greater than 1.96, it is marked as a significant hotspot and used to obtain significant building spatial distribution hotspot vector point data: Formula 2:

[0019] Where n is the total number of geographical units, x j is the kernel density value of the building spatial distribution in the ith geographic unit, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units, a i,j is the spatial weight coefficient of geographic unit i and geographic unit j, which is used to describe the spatial relationship between geographic units, where:

[0020] Formula 3:

[0021] Formula 4:

[0022] S3-2, conversion data type: using the building spatial distribution hot spot vector point data as input, converting the building spatial distribution hot spot vector point data into raster data, by setting the pixel value of the hot spot area to 1 and the pixel value of the non-hot spot area to 0 to obtain the building spatial distribution hot spot area raster data;

[0023] S4, further dividing the significant initial construction land hotspot areas based on kernel density, including the following steps:

[0024] S4-1, calculate and obtain the building kernel density distribution within the initial construction land hotspot area, take the building spatial distribution kernel density raster data and the building spatial distribution hotspot area raster data as input, and obtain the kernel density value raster data within the building spatial distribution hotspot area by performing an intersection operation between the two types of data, as follows: when the pixel value of the building spatial distribution hotspot area raster data is 1, retain the pixel value of the corresponding position of the building spatial distribution kernel density raster data, otherwise set it to NULL until the traversal is completed;

[0025] S5, based on the kernel density calculation segmentation threshold, the initial construction land hotspot area is graded: the kernel density value raster data in the hotspot area of ​​the building spatial distribution is used as input, and the segmentation threshold N is used to calculate the initial construction land hotspot area. 1 、N 2 、N 3 and N 4 The kernel density values ​​in the hot spots of building spatial distribution are divided into three levels to obtain the graded raster data of construction land hot spots;

[0026] Among them, the segmentation threshold N 1 、N 2 、N 3 and N 4 Calculated by the maximum entropy classification method; entropy is an indicator to measure the uncertainty or information content of the system. The maximum entropy classification method is based on the maximum entropy principle in information theory. It maximizes the entropy value of the classified data in each interval to find the best segmentation threshold, thereby retaining as much original data information as possible. The specific calculation steps are as follows:

[0027] S5-1, taking the kernel density value grid data in the hot spots of building spatial distribution as input, sorting the data according to the value size, and selecting a set of initial segmentation thresholds N 01 、N 02 、N 03 and N 04 The data is divided into three groups, where the initial segmentation threshold N 01 、N 02 、N 03 and N 04 It is calculated by the natural breakpoint method, as follows:

[0028] S5-1-1, using the kernel density value grid data in the hot spots of building spatial distribution as input, calculate the mean deviation square sum SDAM by the following formula 5:

[0029] Formula 5:

[0030] Where n is the total number of geographical units within the hotspot area of ​​building spatial distribution, x jis the kernel density value of the building spatial distribution in the ith geographic unit, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units;

[0031] S5-1-2, for each possible threshold group N i (N i1 <N i2 <N i3 <N i4 ), all geographical units are divided into three levels according to the thresholds, and for each possible data combination, the squared deviation sum of the category means SDCM is calculated by the following formula:

[0032] Formula 6:

[0033] Where k is the classification level, n is the total number of geographical units in the kth level, and x kj is the kernel density value of the building spatial distribution in the jth geographic unit within the kth level, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units within the kth level;

[0034] S5-1-3, for each possible threshold group N i (N i1 <N i2 <N i3 <N i4 ), the variance goodness of fit GVF is calculated by the following formula:

[0035] Formula 7:

[0036] Select the threshold group N corresponding to the maximum GVF i (N i1 、N i2 、N i3 and N i4 ) as the optimal initial segmentation threshold group N 01 、N 02 、N 03 and N 04 ;

[0037] S5-2, by initializing the segmentation threshold group N 01 、N 02 、N 03 and N 04 The kernel density value grid data in the hot spots of building spatial distribution are divided into three groups and the entropy value of each group is calculated by the following formula, and the entropy values ​​of all groups are summed to obtain the total entropy value:

[0038] Formula 8:

[0039] Where X represents a random variable, p i Represents the probability that a random variable takes the value i. The larger the entropy value, the greater the uncertainty of the random variable and the greater the amount of information.

[0040] S5-3, segmentation threshold iteration based on entropy maximization:

[0041] S5-3-1, with a as the step size, -b and +b as the maximum negative and positive change values, respectively, for the segmentation threshold group N 01 、N 02 、N 03 and N 04 Fine-tune, and use the adjusted segmentation threshold group N each time. i1 、N i2 、N i3 and N i4 The kernel density value raster data within the hot spots of the building spatial distribution are grouped and the entropy value of each group is recalculated, where a and b are determined according to the order of magnitude of the initial segmentation threshold.

[0042] S5-3-2, compare the adjusted total entropy value with the current entropy value, and select the segmentation threshold group N corresponding to the higher entropy value i1 、N i2 、N i3 and N i4 is the current threshold;

[0043] S5-3-3, repeat the above steps S5-3-1 and S5-3-2 until the entropy value no longer increases significantly or reaches the predetermined number of iterations. At this time, the segmentation threshold group N 1 、N 2 、N 3 and N 4 is the optimal segmentation threshold;

[0044] The kernel density values ​​in the hot spots of the building spatial distribution are classified by the optimal threshold group. i1 Less than or equal to N i2 When the pixel value is greater than or equal to N, the pixel value is set to 3, indicating a third-level hot spot; i1 Less than or equal to N i1 When the pixel value is greater than or equal to N, the pixel value is set to 2, indicating a secondary hotspot; i3 Less than or equal to N i4 When , the pixel value is set to 1, indicating a first-level hotspot, which has the highest degree of significant aggregation.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The kernel density, natural breakpoint method and maximum entropy classification method are combined to further grade the identified initial significant hotspot areas, which can more accurately, comprehensively and intuitively reflect the differences in the degree of characteristic aggregation of different geographical units, and better reflect the spatial heterogeneity of the distribution of geographical unit characteristics and their spatiotemporal changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the hotspot analysis results in the background technology of the present invention and a schematic diagram of the Z score distribution of different hotspot units in the region.

[0048] Figure 2 The figure is a schematic diagram of converting raster data into point vector data according to an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of obtaining building spatial distribution kernel density raster data by calculating building spatial distribution vector point data in an embodiment of the present invention.

[0050] Figure 4 Schematic diagram of converting kernel density raster data into vector data in an embodiment of the present invention.

[0051] Figure 5 This is a schematic diagram of obtaining hotspot vector point data of building spatial distribution based on kernel density vector point data calculation in an embodiment of the present invention.

[0052] Figure 6 This is a schematic diagram of obtaining raster data of hot spots in the spatial distribution of buildings from hot spot vector point data in an embodiment of the present invention.

[0053] Figure 7 This is a schematic diagram of obtaining kernel density value raster data in hot spots of building spatial distribution according to an embodiment of the present invention.

[0054] Figure 8 A schematic diagram of classifying kernel density values ​​according to an embodiment of the present invention.

[0055] Fig. 9 Schematic diagram of comparison of two hot spot analysis results in the embodiment of the present invention Figure 1 .

[0056] Fig.10 Schematic diagram of comparison of two hot spot analysis results in the embodiment of the present invention Figure 2 . DETAILED DESCRIPTION

[0057] See also Figures 1 to 10, the present invention is further described in conjunction with the accompanying drawings. This embodiment analyzes the spatial distribution characteristics of the surface cover type (construction land). Taking the construction land in the Three Gorges Reservoir area as an example, based on the public data set (1985-2021 30m National Land Cover Data (CLCD) https: / / zenodo.org / record / 5816591, spatial resolution 30 meters), the spatial distribution raster data of the construction land in the Three Gorges Reservoir area in 2020 is obtained for further explanation:

[0058] The following steps are involved:

[0059] (1) Identify the geographic entities to be analyzed and obtain spatial raster data representing the spatial distribution of the geographic entities:

[0060] This study takes the construction land in the Three Gorges Reservoir area as an example, and obtains the spatial distribution raster data of the construction land in the Three Gorges Reservoir area in 2020 based on a public dataset (30m National Land Cover Data (CLCD) from 1985 to 2021 https: / / zenodo.org / record / 5816591, with a spatial resolution of 30 meters);

[0061] (2) Preprocessing of the spatial distribution raster data of construction land in the Three Gorges Reservoir area, including:

[0062] (2-1) Convert raster data into vector data (such as Figure 2 As shown in the figure): The raster data is converted into point vector data through the ArcGIS software RasterToPoint tool. Each vector point corresponds to a pixel on the raster data.

[0063] (2-2) Calculate the building distribution density characteristics (such as Figure 3 As shown): Taking the building spatial distribution vector point data as input, the kernel density is calculated by the following formula 1 to obtain the building spatial distribution kernel density raster data;

[0064] Kernel density analysis is a spatial analysis algorithm that reflects the aggregation of spatial elements in a region by calculating the density of spatial elements in their surrounding neighborhoods. This method takes each spatial element in the input feature class as the center, and calculates the density contribution value of each spatial element to the center point of each grid unit within a specified radius through the kernel function. The density values ​​of the center points of each grid unit are spatially superimposed to generate kernel density raster data. The kernel function used in this study is based on the quartic kernel function of Silverman et al., and the expression is as follows:

[0065] Formula 1:

[0066] Where Density(x,y) is the kernel density value of the pixel at (x,y), h is the search radius, which is set to 1000 in this embodiment according to the default search radius function calculation provided by ArcGIS software, and x i ,y i The coordinates of the input spatial features.

[0067] (2-3) Convert raster data into vector data (such as Figure 4 As shown in the figure): Taking the building spatial distribution kernel density raster data as input, the raster data is converted into vector point data through the RasterToPoint tool of ArcGIS software to obtain the building spatial distribution kernel density vector point data. Each pixel corresponds to a point feature, and the construction land kernel density on the pixel corresponds to the attribute value of the point feature.

[0068] (3) Calculate and extract significant initial construction land hotspot areas, including:

[0069] (3-1) Taking the building kernel density vector point data as input, point elements as the smallest geographic unit, and the building spatial distribution kernel density as the eigenvalue, the following formula is used to calculate the density of each geographic unit. The significant initial construction land hotspots were extracted by using a threshold of 1.96 at a significance test level of 5%, i.e., when the geographic unit When the value is greater than 1.96, it is marked as a significant hotspot to obtain the significant building spatial distribution hotspot vector point data (such as Figure 5 shown):

[0070]

[0071] Where n is the total number of geographical units, x j is the kernel density value of the building spatial distribution in the ith geographic unit, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units, a i,j is the spatial weight coefficient of geographic unit i and geographic unit j, which is used to describe the spatial relationship between geographic units, where:

[0072]

[0073]

[0074] (3-2) Data conversion: Taking the hot spot vector point data of the building spatial distribution as input, the feature to raster tool of ArcGIS software is used to convert the hot spot vector point data of the building spatial distribution into raster data. The pixel value of the hot spot area is set to 1, and the pixel value of the non-hot spot area is set to 0 to obtain the raster data of the hot spot area of ​​the building spatial distribution (such as Figure 6 shown);

[0075] (4) Further division of significant initial construction land hotspots based on kernel density, including:

[0076] (4-1) Calculate and obtain the building kernel density distribution within the initial construction land hotspot area. Take the building spatial distribution kernel density raster data and the building spatial distribution hotspot area raster data as input, and perform an intersection operation between the two types of data to obtain the kernel density value raster data within the building spatial distribution hotspot area. The details are as follows: When the pixel value of the building spatial distribution hotspot area raster data is 1, the pixel value of the corresponding position of the building spatial distribution kernel density raster data is retained, otherwise it is set to NULL until the traversal is completed (such as Figure 7 shown);

[0077] (5) Based on the kernel density calculation segmentation threshold, the initial construction land hotspot area is graded. The kernel density value raster data in the hotspot area of ​​the building spatial distribution is used as input, and the segmentation threshold N is used to calculate the initial construction land hotspot area. 1 、N 2 、N 3 and N 4 The kernel density values ​​within the hot spots of building spatial distribution are divided into three levels to obtain the graded raster data of construction land hot spots.

[0078] Among them, the segmentation threshold N 1 、N 2 、N 3 and N 4 Calculated by the maximum entropy classification method. Entropy is an indicator of system uncertainty or information volume. The maximum entropy classification method is based on the maximum entropy principle in information theory. It maximizes the entropy value of the classified data in each interval to find the best segmentation threshold, thereby retaining as much original data information as possible. The specific calculation steps are as follows:

[0079] (a) Taking the kernel density value grid data in the hot spots of building spatial distribution as input, sort the data according to the value size and select a set of initial segmentation thresholds N 01 、N 02 、N 03 and N 04 The data is divided into three groups, where the initial segmentation threshold N01 、N 02 、N 03 and N 04 It is calculated by the natural breakpoint method, as follows:

[0080] (a-1) Taking the kernel density value raster data in the hotspot area of ​​the spatial distribution of buildings as input, the sum of squared deviations from the mean (SDAM) is calculated by the following formula;

[0081]

[0082] Where n is the total number of geographical units within the hotspot area of ​​building spatial distribution, x j is the kernel density value of the building spatial distribution in the ith geographic unit, is the mean of the kernel density values ​​of the spatial distribution of buildings in all geographic units:

[0083] (a-2) For each possible threshold set N i (N i1 <N i2 <N i3 <N i4 ), all geographical units are divided into three levels according to the thresholds, and for each possible data combination, the sum of squared deviations of the category means (SDCM) is calculated by the following formula;

[0084]

[0085] Where k is the classification level, n is the total number of geographical units in the kth level, and x kj is the kernel density value of the building spatial distribution in the jth geographic unit within the kth level, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units within the kth level;

[0086] (a-3) For each possible threshold set N i (N i1 <N i2 <N i3 <N i4 ), and the goodness of fit (GVF) is calculated by the following formula:

[0087]

[0088] Select the threshold group N corresponding to the maximum GVF i (N i1 、N i2 、N i3 and N i4 ) as the optimal initial segmentation threshold group N 01 、N 02 、N 03and N 04 .

[0089] (b) By initializing the segmentation threshold group N 01 、N 02 、N 03 and N 04 The kernel density value raster data in the hot spots of building spatial distribution are divided into three groups and the entropy value of each group is calculated by the following formula. The entropy values ​​of all groups are summed up to obtain the total entropy value.

[0090]

[0091] Where X represents a random variable, p i It represents the probability that a random variable takes the value i. The larger the entropy value is, the greater the uncertainty of the random variable is and the greater the amount of information is.

[0092] (c) Segmentation threshold iteration based on entropy maximization.

[0093] (c-1) With a step size of 0.1, -3 and 3 are the maximum negative and positive changes respectively, and the segmentation threshold group N is 01 、N 02 、N 03 and N 04 Fine-tune, and use the adjusted segmentation threshold group N each time. i1 、N i2 、N i3 and N i4 The kernel density value raster data within the hot spots of the building spatial distribution are grouped, and the entropy value of each group is recalculated, where 0.1, 3, and -3 are determined according to the order of magnitude of the initial segmentation threshold.

[0094] (c-2) Compare the adjusted total entropy value with the current entropy value and select the segmentation threshold group N corresponding to the higher entropy value i1 、N i2 、N i3 and N i4 is the current threshold.

[0095] (c-3) Repeat the above steps until the entropy value no longer increases significantly or reaches the predetermined number of iterations. At this time, the segmentation threshold group N 1 、N 2 、N 3 and N 4 is the optimal segmentation threshold.

[0096] The kernel density values ​​in the hot spots of the building spatial distribution are classified by the optimal threshold group. i1 Less than or equal to N i2 When the pixel value is greater than or equal to N, the pixel value is set to 3, indicating a third-level hot spot;i2 Less than or equal to N i1 When the pixel value is greater than or equal to N, the pixel value is set to 2, indicating a secondary hotspot; i3 Less than or equal to N i4 When , the pixel value is set to 1, indicating a first-level hotspot, which has the highest degree of significant aggregation (such as Figure 8 shown).

[0097] Comparison of results (such as Fig. 9 , Fig.10 shown):

[0098] In order to intuitively reflect the difference between the two methods, the Z score range, mean and standard deviation of the hot spot areas obtained based on different methods were calculated respectively (table). The results show that the Z score range of the first-level hot spot, second-level hot spot and third-level hot spot divided by the method of the present invention is much smaller than the results of the traditional method, indicating that the data in the results obtained by the method of the present invention is less discrete and relatively more concentrated; the mean Z scores of hot spot areas of different levels are significantly different, indicating that there are significant differences in the degree of building aggregation in different areas.

[0099] Further verification and analysis combined with the field remote sensing images of the study area found that the kernel density-based optimization hotspot analysis method proposed in this invention is more sensitive to the differences in the concentration of construction land in different regions, and can perform more detailed level division of the significant construction land concentration areas obtained based on the traditional hotspot analysis method. Based on the field remote sensing images, it is found that the construction land in the actual area corresponding to hotspots of different levels has obvious differences in the number of buildings, building scale and construction land area. This shows that this method can provide richer spatial distribution information of surface elements, can more accurately and comprehensively reflect the heterogeneity of spatial distribution of surface elements, and can more accurately reflect the spatial distribution of surface elements than traditional hotspot analysis methods.

[0100] Comparison table of the results of the two methods based on statistical analysis

[0101]

[0102] The above are only preferred embodiments of the present invention, which are only used to help understand the method and core ideas of the present application. The protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

[0103] The above embodiments can be implemented in whole or in part by software or hardware. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When a computer instruction or computer program is loaded or executed on a computer, a process or function according to an embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. Computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium.

[0104] The present invention solves the problem in the prior art that different hot spots in the geographic space are When the value distribution range is wide and the difference is large, it indicates that there are large differences in the significant aggregation degree of the characteristics of different hot spot geographic units in the geographic space. It is difficult to further reflect the differences in the degree of aggregation of the characteristics of different hot spot geographic units intuitively, comprehensively and accurately by using only the critical values ​​of the 1%, 5% and 10% significance test levels. By combining the kernel density, natural breakpoint method and maximum entropy classification method, the identified initial significant hot spot areas are further graded, which can more accurately, comprehensively and intuitively reflect the differences in the degree of aggregation of the characteristics of different geographic units, and better reflect the spatial heterogeneity of the distribution of geographic unit characteristics and their spatiotemporal changes.

Claims

1. An optimized hotspot analysis method for analyzing the spatial distribution characteristics of land cover types, characterized in that: The following steps are involved: S1, identify the geographic entity to be analyzed and obtain spatial raster data representing the spatial distribution of the geographic spatial entity; S2, preprocessing the spatially distributed grid data, including: S2-1, raster data converted to point vector data: raster data is converted to point vector data using the raster to point tool, where each vector point corresponds to a pixel on the raster data; S2-2, calculate the building distribution density characteristics: take the building spatial distribution vector point data as input, calculate the kernel density by the following formula 1, and obtain the building spatial distribution kernel density raster data; Formula 1: Where Density(x,y) is the kernel density value of the pixel at (x,y), h is the search radius, and the default search radius function calculation setting is 1000. i ,y i is the coordinate of the input spatial element; S2-3, raster data conversion to vector data: using the building spatial distribution kernel density raster data as input, the raster data is converted into vector point data to obtain the building spatial distribution kernel density vector point data. Each pixel corresponds to a point feature, and the construction land kernel density on the pixel corresponds to the attribute value of the point feature. S3, calculate and extract significant initial construction land hotspot areas, including: S3-1, using building kernel density vector point data as input, point elements as the smallest geographic unit, and building spatial distribution kernel density as the eigenvalue, calculate the density of each geographic unit using the following formula 2 The significant initial construction land hotspots were extracted by using a threshold of 1.96 at a significance test level of 5%, i.e., when the geographic unit When the value is greater than 1.96, it is marked as a significant hotspot and used to obtain significant building spatial distribution hotspot vector point data; Formula 2: Where n is the total number of geographical units, x j is the kernel density value of the building spatial distribution in the ith geographic unit, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units, a i,j is the spatial weight coefficient of geographic unit i and geographic unit j, which is used to describe the spatial relationship between geographic units, where: Formula 3: Formula 4: S3-2, conversion data type: using the building spatial distribution hot spot vector point data as input, converting the building spatial distribution hot spot vector point data into raster data, by setting the pixel value of the hot spot area to 1 and the pixel value of the non-hot spot area to 0 to obtain the building spatial distribution hot spot area raster data; S4, further dividing the significant initial construction land hotspot areas based on kernel density, including the following steps: S4-1, calculate and obtain the building kernel density distribution within the initial construction land hotspot area, take the building spatial distribution kernel density raster data and the building spatial distribution hotspot area raster data as input, and obtain the kernel density value raster data within the building spatial distribution hotspot area by performing an intersection operation between the two types of data, as follows: when the pixel value of the building spatial distribution hotspot area raster data is 1, retain the pixel value of the corresponding position of the building spatial distribution kernel density raster data, otherwise set it to NULL until the traversal is completed; S5, classifying the initialized construction land hotspot area based on the kernel density calculation segmentation threshold: taking the kernel density value raster data in the building spatial distribution hotspot area as input, the kernel density value in the building spatial distribution hotspot area is divided into three levels by segmentation thresholds N1, N2, N3 and N4, so as to obtain the graded raster data of the construction land hotspot area; Among them, the segmentation thresholds N1, N2, N3 and N4 are calculated by the maximum entropy classification method; entropy is an indicator to measure the uncertainty or information amount of the system. The maximum entropy classification method is based on the maximum entropy principle in information theory. It maximizes the entropy value of the classified data in each interval to find the optimal segmentation threshold, thereby retaining as much original data information as possible. The specific calculation steps are as follows: S5-1, taking the kernel density value grid data in the hot spots of building spatial distribution as input, sorting the data according to the value size, and selecting a set of initial segmentation thresholds N 01 、N 02 、N 03 and N 04 The data is divided into three groups, where the initial segmentation threshold N 01 、N 02 、N 03 and N 04 It is calculated by the natural breakpoint method, as follows: S5-1-1, using the kernel density value grid data in the hot spots of building spatial distribution as input, calculate the mean deviation square sum SDAM by the following formula 5: Formula 5: Where n is the total number of geographical units in the hotspot area of ​​building spatial distribution, x j is the kernel density value of the building spatial distribution in the ith geographic unit, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units; S5-1-2, for each possible threshold group N i (N i1 <N i2 <N i3 <N i4 ), all geographical units are divided into three levels according to the thresholds, and for each possible data combination, the squared deviation sum of the category means SDCM is calculated by the following formula: Formula 6: Where k is the classification level, n is the total number of geographical units in the kth level, and x kj is the kernel density value of the building spatial distribution in the jth geographic unit within the kth level, is the mean value of the kernel density of the spatial distribution of buildings in all geographic units within the kth level; S5-1-3, for each possible threshold group N i (N i1 <N i2 <N i3 <N i4 ), the variance goodness of fit GVF is calculated by the following formula: Formula 7: Select the threshold group N corresponding to the maximum GVF i (N i1 、N i2 、N i3 and N i4 ) as the optimal initial segmentation threshold group N 01 、N 02 、N 03 and N 04 ; S5-2, by initializing the segmentation threshold group N 01 、N 02 、N 03 and N 04 The kernel density value grid data in the hot spots of building spatial distribution are divided into three groups and the entropy value of each group is calculated by the following formula, and the entropy values ​​of all groups are summed to obtain the total entropy value: Formula 8: Where X represents a random variable, p i Represents the probability that a random variable takes the value i. The larger the entropy value, the greater the uncertainty of the random variable and the greater the amount of information. S5-3, segmentation threshold iteration based on entropy maximization: S5-3-1, with a as the step size, -b and +b as the maximum negative and positive change values, respectively, for the segmentation threshold group N 01 、N 02 、N 03 and N 04 Fine-tune, and use the adjusted segmentation threshold group N each time. i1 、N i2 、N i3 and N i4 The kernel density value raster data within the hot spots of the building spatial distribution are grouped and the entropy value of each group is recalculated; where a and b are determined according to the order of magnitude of the initial segmentation threshold. S5-3-2, compare the adjusted total entropy value with the current entropy value, and select the segmentation threshold group N corresponding to the higher entropy value i1 、N i2 、N i3 and N i4 is the current threshold; S5-3-3, repeat the above steps S5-3-1 and S5-3-2 until the entropy value no longer increases significantly or reaches the predetermined number of iterations, at which time the segmentation threshold group N1, N2, N3 and N4 are the optimal segmentation thresholds; The kernel density values ​​in the hot spots of the building spatial distribution are classified by the optimal threshold group. i1 Less than or equal to N i2 When the pixel value is greater than or equal to N, the pixel value is set to 3, indicating a third-level hot spot; i2 Less than or equal to N i1 When the pixel value is greater than or equal to N, the pixel value is set to 2, indicating a secondary hotspot; i3 Less than or equal to N i4 When , the pixel value is set to 1, indicating a first-level hotspot, which has the highest degree of significant aggregation.

Images