Urban group identification method based on complex network and heterogeneous remote sensing images

Abstract

The application provides a kind of city group identification method based on complex network and heterogeneous remote sensing image, and relates to remote sensing image processing technical field.The application realizes the unified description of the structure of heterogeneous remote sensing image to ground objects by constructing a composite complex network model composed of night light data complex network and Landsat image complex network, can unify remote sensing images from different sensors under the complex network structure, and can fuse the information of the two data sources.At the same time, the application embeds spatial attributes into the connection expectation function of community structure identification, improves the reliability of the community structure identification method for spatial analysis of ground objects, and improves the identification accuracy.The application establishes the geographical mapping relationship between remote sensing image community and urban spatial structure, so that the geographical boundary of city group can be quantitatively described, and visualization is possible.

Description

Technical Field

[0001] This invention relates to the field of remote sensing image processing technology, and in particular to a method for identifying urban clusters based on complex networks and heterogeneous remote sensing images. Background Technology

[0002] Urban clusters are an important component of the spatial structure of polycentric cities; they are collections of geographical units with similar functions or development orientations that develop around a city center. The community structure of a complex network is a set of highly correlated nodes formed around a central node. Constructing a complex network model from remote sensing images allows for the identification of community structures within remote sensing images. Based on the above analysis, urban clusters and complex network community structures have a natural structural consistency; therefore, identifying urban clusters can be achieved through the identification of community structures in remote sensing images.

[0003] After applying complex network theory to the field of remote sensing image structure recognition, several problems remain to be solved. Two typical issues stand out: First, the formation of urban clusters is influenced by a combination of socioeconomic and land cover factors, making it difficult for single-source remote sensing images to simultaneously capture both socioeconomic and land cover information. While nighttime light images can reflect socioeconomic information and Landsat data can reflect land cover information, these two types of data originate from different sensors and are considered heterogeneous data. Constructing complex networks from these two types of data separately reveals inconsistencies in the node sets of the heterogeneous remote sensing images due to differences in radiometry. This makes it difficult to integrate and describe image elements when modeling composite complex networks, severely limiting its in-depth application in remote sensing image community structure recognition. Second, current remote sensing image community structure recognition methods primarily focus on basic topological attributes, neglecting the influence of spatial attributes on their formation. For example, spatial distance causes spatial non-stationarity in node proximity relationships, aggregation attraction, and spatial relationships, resulting in the loss of spatial meaning in the obtained remote sensing image community structure and reducing the accuracy of urban cluster recognition. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for identifying urban clusters based on complex networks and heterogeneous remote sensing images.

[0005] A method for identifying urban clusters based on complex networks and heterogeneous remote sensing images, specifically including the following steps:

[0006] Step 1: Acquire nighttime light images, extract grayscale feature points from the nighttime light images and construct a complete map. Use cosine spectral similarity to establish a complete map of the Landsat remote sensing image. Use a horizontal visualization algorithm to evolve the complete maps of the nighttime light images and the Landsat image into a complex network of nighttime light data and a complex network of Landsat image with small-world properties, respectively. Reconstruct a composite complex network model composed of the complex network of nighttime light data and the complex network of Landsat image under spatial homogeneity constraints.

[0007] The complete graph can be a directed or undirected graph;

[0008] Step 1.1: Extract grayscale feature points from nighttime light images and construct a complete image;

[0009] The complete graph nodes of the luminous light image are grayscale features, and the edges between nodes represent the connections between them, described by the similarity between grayscale feature points. The luminous light image is considered as a continuous three-dimensional surface model, which is a smooth function that is differentiable at any time. Let the grayscale feature point p(x0,y0) be a point with a first-order partial derivative of 0. Its type is obtained by calculating the number of non-negative eigenvalues ​​of the Hessian matrix at outlier points. The Hessian matrix is:

[0010]

[0011] Where f xx (x0,y0),f xy (x0,y0),f yx (x0, y0) and f yy (x0, y0) is the second-order partial derivative. The similarity between nodes is proportional to the reciprocal of the difference in their gray values.

[0012] Step 1.2: Construct a complete map of the Landsat image using cosine spectral similarity;

[0013] The complete image of the Landsat image above was obtained by establishing the connection relationship of the geometric centroids of the segmented image objects through cosine spectral similarity.

[0014] A fractal network evolution algorithm is used to segment Landsat images into image objects with spectral homogeneity. The geometric centroids of the image objects are extracted as nodes in the complete graph. The cosine distance similarity between nodes is calculated and used to describe the node connectivity. The cosine distance similarity is shown in the following formula:

[0015]

[0016] Where A and B represent the spectral feature vectors of different image objects, and ||A|| and ||B|| are norms; the larger D(A,B) is, the higher the similarity, and vice versa; the cosine distance similarity is used to establish the connection relationship between nodes to form the complete graph of the Landsat image;

[0017] Step 1.3: Using a horizontal visualization algorithm, the complete graphs of the above-mentioned night light light images and Landsat images are evolved into complex network models, respectively, to obtain the night light complex network and the Landsat complex network.

[0018] The horizontal visualization algorithm uses the node attribute values ​​of the complete graph as measurement values. If the difference between the measurement values ​​of two nodes is the smallest, then these two nodes are connected; otherwise, the original connection is abandoned. The node attribute values ​​of the complete graphs of the night light image and the Landsat image are the sum of all similarities between each node and other nodes in the above complete graph. Nodes with higher attribute values ​​tend to have more unique topological structures.

[0019] Step 1.4: Reconstruct the complex network model under spatial homogeneity constraints;

[0020] Under spatial homogeneity, nodes are merged. If a geographic unit contains more than one node from the Noctilucent Complex Network, these nodes are merged. The merged node's location aligns with the Landsat Complex Network node's location, and node weights are increased based on the number of nodes. Connections between nodes within the same geographic unit are denoted as homogeneous connections, while connections between nodes from different geographic units are denoted as heterogeneous connections. Homogeneous connections from the Noctilucent Complex Network are removed, while heterogeneous connections are retained and appended to the merged nodes, forming a composite complex network model. The mathematical expression of the composite complex network model is as follows:

[0021] Consider a complex network with N nodes and an L-layer network as follows:

[0022]

[0023] Where V N =[v0,...,v i ,...,v N ] is a set of nodes, V N For a set of nodes, v N For node E [l] =V N ×V N It is the set of edges in a layer l network, V L For network sets. [l] The corresponding binary nearest neighbor matrix is:

[0024]

[0025] in, The value is 1 when nodes are adjacent and 0 otherwise, where i and j refer to any two nodes. The complex network model is an undirected network, so A... [l] It is a symmetric matrix.

[0026] Step 2: Calculation of the contribution of single-layer networks in composite networks; By analyzing the correlation between the centrality of single-layer networks and composite networks and the change of the contribution of single-layer networks, the contribution of single-layer networks to multi-layer networks is quantitatively evaluated, and the composite proximity matrix of composite complex networks is constructed.

[0027] Constructing the composite proximity matrix of complex networks

[0028] W(c) = cW [1] +(1-c)W [2] (5)

[0029] Among them, W [1] and W [2] G represents the complex network of nighttime light data. [1] and Landsat Image Complex Network G [2] The spatial weight matrix, where c is the contribution of a single-layer network, and W is the weight matrix. [1] for:

[0030]

[0031] in, Let W be the connection weight between any node i and node j in network 1. [2] for:

[0032]

[0033] in, Let be the connection weights of any node i and node j in network 2.

[0034] When c takes equally spaced values ​​within the interval [0,1], the eigenvector centrality E(c) of W(c) is calculated for different c values, and the network G is calculated and obtained. [1] and G [2] Eigenvector centrality E [1] and E [2] Calculate E respectively [1] and E [2] Kendall correlation coefficient with E(c) was calculated, and the correlation coefficient curve was fitted using the least squares method. [1] and Curve [2] Curve [1] and Curve [2] When placed in the same coordinate system, the x-coordinate of the intersection point of the two curves is the contribution c of the single-layer network.

[0035] Step 3: Community structure identification in remote sensing images considering spatial attributes;

[0036] Composite modularity is used as a function to measure community structure. The NG connection expectation weight function is improved by spatial gravity model to optimize its inability to describe the nonlinear changes in node gravity caused by spatial distance. The community structure is obtained by maximizing composite modularity using Louvain algorithm. The community structure of remote sensing image is expressed by mapping the relationship between community structure nodes and image elements.

[0037] Step 3.1: Construction of a spatial gravity model with composite modularity;

[0038] The modularity Q of the composite module is

[0039]

[0040] Where m is the number of edges, c i and c j For node v i and v j The community to which it belongs, δ(c i ,c j Let ) be a binary discriminant function, if node v i and v j If they belong to the same community, then δ(c) i ,c j ) = 1, otherwise δ(c) i ,c j ) = 0. It is node v on network l i and v j The expected weight function for the connections between them. L is the total number of networks. Let be the connection weights between any node i and node j in network l. Let be the expected connection between any node i and node j in the l-th layer.

[0041] The connection expectation weight function uses the NG connection expectation weight function, as shown in the following equation:

[0042]

[0043] Wherein, the degree of node i in network l Degree of node j in network l NG connection expectation weight function The effect of spatial distance on the gravitational force between nodes was not considered; m [l] Let be the total number of edges in network l; the gravity model is introduced into the expected weight function of the composite network connection as shown in the following equation:

[0044]

[0045] in, Let gravitational force be the function of force. and This represents the node weight. For the expected weight function of the composite network connection, Let d be the Euclidean distance between any node i and node j in network l, and d be a numerical value. The spatial weight matrix is... Where l is 1 or 2, substituting into formulas (11) and (12), the improved composite modularity index is:

[0046]

[0047]

[0048] Q M The improved composite modularity index. This is the expected weight function for the improved composite network connection.

[0049] Step 3.2: Calculate the optimal solution for the Louvain algorithm for the community structure, i.e., use the Louvain algorithm to maximize Q. M Perform optimization and solution;

[0050] Step 3.2.1: Treat each node in the network as a separate community;

[0051] Step 3.2.2: Traverse all neighboring nodes of each node, calculate the modularity gain brought by adding the node to the neighboring node community, select the neighboring node with the largest gain, and add it to its community. Iterate this process continuously until the community attribute of each node is fixed.

[0052] Step 3.2.3: Merge nodes belonging to the same community into one node. The connection weights between nodes in the same community are no longer used. The weight between the current community and other communities is the sum of the weights of all nodes in the two communities, thus obtaining a new network structure. Return to step 3.2.2 until the community structure is fixed.

[0053] Step 4: Constructing the spatial mapping relationship between remote sensing community structure and urban clusters;

[0054] The image object is the Landsat image segmentation result and has segmentation boundaries. The spatial range of each node is obtained. Multiple image objects belonging to the same community are merged into one community image object. Since there are multiple communities, multiple community image objects are obtained. The image object of this community is the urban cluster, and the outline of the community image object is the spatial range of the urban cluster.

[0055] The beneficial effects of adopting the above technical solution are as follows:

[0056] This invention provides a method for identifying urban clusters based on complex networks and heterogeneous remote sensing images, which has the following beneficial effects:

[0057] (1) Fully explore the spatial common constraints of heterogeneous remote sensing image data, establish a node integration mechanism under spatial homogeneity, and effectively fuse remote sensing images from different sensors, thus integrating the influence of socio-economic factors and land cover factors on urban cluster analysis.

[0058] (2) By embedding the influence of spatial attributes into the topology identification process, a spatial optimization mechanism for community structure is established, which improves the spatial adaptability of complex network topology and enhances the effectiveness and accuracy of community structure identification.

[0059] (3) Applying remote sensing image community structure recognition to urban cluster recognition enables quantitative description of its morphology and evolution in space, providing a reliable solution for quantitative description of urban spatial structure. Attached Figure Description

[0060] Figure 1 This is an overall flowchart of the urban cluster identification method according to an embodiment of the present invention;

[0061] Figure 2 This is a flowchart illustrating the modeling process of a complex network with spatial homogeneity constraints according to an embodiment of the present invention.

[0062] Figure 3 This is a flowchart illustrating the optimization of the aggregation gravity space of the composite community structure according to an embodiment of the present invention. Detailed Implementation

[0063] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0064] A method for urban cluster identification based on complex networks and heterogeneous remote sensing images, such as Figure 1 As shown, the specific steps include:

[0065] Step 1: Acquire nighttime light images, extract grayscale feature points from the nighttime light images and construct a complete map. Use cosine spectral similarity to establish a complete map of the Landsat remote sensing image. Use a horizontal visualization algorithm to evolve the complete maps of the nighttime light images and the Landsat image into a complex network of nighttime light data and a complex network of Landsat image with small-world properties, respectively. Reconstruct a composite complex network model composed of the complex network of nighttime light data and the complex network of Landsat image under spatial homogeneity constraints.

[0066] The complete graph can be directed or undirected, and can provide a basic network for complex network models.

[0067] Step 1.1: Extract grayscale feature points from nighttime light images and construct a complete image;

[0068] The complete graph nodes of the luminous light image are grayscale features, and the edges between nodes represent the connections between them, described by the similarity between grayscale feature points. The luminous light image is considered as a continuous three-dimensional surface model, which is a smooth function that is differentiable at any time. Let the grayscale feature point p(x0,y0) be a point with a first-order partial derivative of 0. Its type is obtained by calculating the number of non-negative eigenvalues ​​of the Hessian matrix at outlier points. The Hessian matrix is:

[0069]

[0070] Where f xx (x0,y0),f xy (x0,y0),f yx (x0, y0) and f yy (x0, y0) is the second-order partial derivative. The similarity between nodes is proportional to the reciprocal of the difference in their gray values.

[0071] Step 1.2: Construct a complete map of the Landsat image using cosine spectral similarity;

[0072] The complete image of the Landsat image above was obtained by establishing the connection relationship of the geometric centroids of the segmented image objects through cosine spectral similarity.

[0073] A fractal network evolution algorithm is used to segment Landsat images into image objects with spectral homogeneity. The geometric centroids of the image objects are extracted as nodes in the complete graph. The cosine distance similarity between nodes is calculated and used to describe the node connectivity. The cosine distance similarity is shown in the following formula:

[0074]

[0075] Where A and B represent the spectral feature vectors of different image objects, and ||A|| and ||B|| are norms; the larger D(A,B) is, the higher the similarity, and vice versa; the cosine distance similarity is used to establish the connection relationship between nodes to form the complete graph of the Landsat image;

[0076] Step 1.3: Using a horizontal visualization algorithm, the complete graphs of the above-mentioned night light light images and Landsat images are evolved into complex network models with high clustering coefficients and a certain average path length, respectively, to obtain the night light complex network and the Landsat complex network, highlighting the physical attribute of strong clustering characteristics of remote sensing images.

[0077] The horizontal visualization algorithm uses the node attribute values ​​of the complete graph as measurement values. If the difference between the measurement values ​​of two nodes is the smallest, then these two nodes are connected; otherwise, the original connection is abandoned. The node attribute values ​​of the complete graphs of the night light image and the Landsat image are the sum of all similarities between each node and other nodes in the above complete graph. Nodes with higher attribute values ​​tend to have more unique topological structures.

[0078] Step 1.4: Reconstruct the complex network model under spatial homogeneity constraints;

[0079] The goal of complex network reconstruction is to use spatial homogeneity as a constraint to merge nodes representing the same geographic unit in a complex network model, forming a unified expression of the composite network model. For remote sensing images, spatial homogeneity is reflected in a uniform spectral distribution, a characteristic possessed by image objects representing unique or similar land cover categories. Due to the low spatial resolution of nighttime light images, image objects in Landsat 8 images are treated as shared geographic units, with geographic unit boundaries serving as the representation of spatial heterogeneity constraints.

[0080] Image elements are the basic units that form the structure of an image. The image elements of nighttime light images and high-resolution images are pixels and image objects, respectively, and are described by network nodes. When heterogeneous remote sensing image elements describe the same geographic unit, they have spatial consistency. This is used as a spatial commonality, and based on this, the two types of node datasets are merged to obtain a unified dataset.

[0081] Under spatial homogeneity, nodes are merged. If a geographic unit contains more than one node from the Noctilucent Complex Network, these nodes are merged. The merged node's position aligns with the Landsat Complex Network node's position, and the node weight is increased based on the number of nodes, ensuring that this geographic unit is represented by one Noctilucent Complex Network node and one Landsat8 Complex Network node. Node connections within the same geographic unit are denoted as homogeneous connections, while connections between nodes in different geographic units are denoted as heterogeneous connections. Homogeneous connections from the Noctilucent Complex Network are removed, while heterogeneous connections are retained and appended to the merged node. Through this process, each geographic unit is represented by at least one Landsat8 Complex Network node or one Noctilucent Complex Network node, and the connection relationships between different nodes are constructed, forming a composite complex network model. The mathematical expression of the composite complex network model is as follows:

[0082] Consider a complex network with N nodes and an L-layer network as follows:

[0083]

[0084] Where V N =[v0,...,v i ,...,v N ] is a set of nodes, V N For a set of nodes, v N For node E [l] =V N ×V N It is the set of edges in a layer l network, V L For network sets. [l] The corresponding binary nearest neighbor matrix is:

[0085]

[0086] in, The value is 1 when nodes are adjacent and 0 otherwise, where i and j refer to any two nodes. The complex network model is an undirected network, so A... [l] It is a symmetric matrix.

[0087] Step 2: Calculation of the contribution of single-layer networks in the composite network; By analyzing the correlation between the centrality of single-layer networks and composite networks and the change of the contribution of single-layer networks, the contribution of single-layer networks to multi-layer networks is quantitatively evaluated, and a composite proximity matrix of the spatial relationship of nodes in the composite network is constructed.

[0088] Constructing the composite proximity matrix of complex networks

[0089] W(c) = cW [1] +(1-c)W [2] (5)

[0090] Among them, W [1] and W [2] G represents the complex network of nighttime light data. [1] and Landsat Image Complex Network G [2] The spatial weight matrix, where c is the contribution of a single-layer network, and W is the weight matrix. [1] for:

[0091]

[0092] in, Let W be the connection weight between any node i and node j in network 1. [2] for:

[0093]

[0094] in, Let be the connection weights of any node i and node j in network 2.

[0095] When c takes equally spaced values ​​within the interval [0,1], the eigenvector centrality E(c) of W(c) is calculated for different c values, and the network G is calculated and obtained. [1] and G [2] Eigenvector centrality E [1] and E [2] Calculate E respectively [1] and E [2] Kendall correlation coefficient with E(c) was calculated, and the correlation coefficient curve was fitted using the least squares method. [1] and Curve [2] Curve [1] and Curve [2] The slope change at each point reflects the change in the degree of influence of the two single-layer networks as c increases. The curve... [1] and Curve [2] When placed in the same coordinate system, the x-coordinate of the intersection point of the two curves is the contribution c of the single-layer network.

[0096] Step 3: Community structure identification in remote sensing images considering spatial attributes;

[0097] Composite modularity is used as a function to measure community structure. The NG connectivity expectation weight function is improved through a spatial gravity model to address its inability to describe the nonlinear changes in node gravity caused by spatial distance. The Louvain algorithm is used to maximize composite modularity to obtain the community structure. The community structure of remote sensing images is expressed through a mapping of relationships between community structure nodes and image elements, as shown in the appendix. Figure 2 As shown.

[0098] Step 3.1: Construction of a spatial gravity model with composite modularity;

[0099] The modularity Q of the composite module is

[0100]

[0101] Where m is the number of edges, c i and c j For node v i and v j The community to which it belongs, δ(c i ,c j Let ) be a binary discriminant function, if node v i and v j If they belong to the same community, then δ(c) i ,c j ) = 1, otherwise δ(c) i ,c j ) = 0. It is node v on network l i and v j The expected weight function for the connections between them. L is the total number of networks. Let be the connection weights between any node i and node j in network l. Let be the expected connection between any node i and node j in the l-th layer.

[0102] The connection expectation weight function uses the NG connection expectation weight function, as shown in the following equation:

[0103]

[0104] Wherein, the degree of node i in network l Degree of node j in network l NG connection expectation weight function The effect of spatial distance on the gravitational force between nodes was not considered; m [l] Let be the total number of edges in network l; the gravity model is introduced into the expected weight function of the composite network connection as shown in the following equation:

[0105]

[0106] in, Let gravitational force be the function of force. and This represents the node weight. For the expected weight function of the composite network connection, Let d be the Euclidean distance between any node i and node j in network l, and d be a numerical value, where d is a higher value. This indicates that node v in network l i and v j Within a distance d, there is higher connection strength. Furthermore, to reflect the impact of spatial distance on the spatial relationships between nodes in community structure analysis, a spatial weight matrix is ​​used. Where l is 1 or 2, substituting into formulas (11) and (12), the improved composite modularity index is:

[0107]

[0108]

[0109] Q M The improved composite modularity index. This is the expected weight function for the improved composite network connection.

[0110] Step 3.2: Calculate the optimal solution using the Louvain algorithm for community structure.

[0111] Due to its high Q MCorresponding to a high-quality community structure, the community structure identification problem is transformed into maximizing Q. M Louvain's algorithm is used to maximize Q. M An optimized solution is performed to identify the community structure. Furthermore, based on the importance of the central structural nodes, they belong to different community structures.

[0112] Step 3.2.1: Treat each node in the network as a separate community;

[0113] Step 3.2.2: Traverse all neighboring nodes of each node, calculate the modularity gain brought by adding the node to the neighboring node community, select the neighboring node with the largest gain, and add it to its community. Iterate this process continuously until the community attribute of each node is fixed.

[0114] Step 3.2.3: Merge nodes belonging to the same community into one node. The connection weights between nodes in the same community are no longer used. The weight between the current community and other communities is the sum of the weights of all nodes in the two communities, thus obtaining a new network structure. Return to step 3.2.2 until the community structure is fixed.

[0115] Step 4: Constructing the spatial mapping relationship between remote sensing community structure and urban clusters.

[0116] Since each node originates from the image object obtained in step 1.2, the above steps enable each node to acquire a community affiliation attribute. Consequently, the image object corresponding to each node also acquires a community affiliation attribute. The image object is the Landsat image segmentation result and has segmentation boundaries, thus obtaining the spatial range of each node. Multiple image objects belonging to the same community are merged into one community image object. Since there are multiple communities, multiple community image objects are obtained. This community image object represents the urban cluster, and the outline of the community image object represents the spatial range of the urban cluster. Figure 3 As shown.

[0117] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for urban cluster identification based on complex network and heterogeneous remote sensing images, characterized in that, The method comprises the following steps: Step 1: collecting a night light image, extracting a gray feature point of the night light image and constructing a complete graph, establishing a complete graph of a remote sensing image Landsat by using cosine spectral similarity, and evolving the complete graph of the night light image and the complete graph of the Landsat image into a night light data complex network and a Landsat image complex network with small-world characteristics respectively by using a horizontal visualization algorithm, and reconstructing a composite complex network model composed of the night light data complex network and the Landsat image complex network under the constraint of spatial homogeneity; Step 2: calculating a single-layer network contribution degree of the composite network; quantitatively evaluating the contribution degree of the single-layer network to the multi-layer network by analyzing the change rule of the correlation between the center degree of the single-layer network and the composite network with the single-layer network contribution degree, and constructing a composite adjacent matrix of the composite complex network; Step 3: identifying a community structure of the remote sensing image considering spatial attributes; a composite modularity is used as a function for measuring the community structure, and a spatial gravity model is used to improve an NG connection expected weight function, so as to optimize the nonlinearity change of node gravity caused by the inability of the NG connection expected weight function to describe spatial distance, the community structure is obtained by maximizing the composite modularity by using a Louvain algorithm, and the community structure of the remote sensing image is expressed by mapping the relationship between the nodes of the community structure and image elements; Step 3.1: constructing a spatial gravity model of the composite modularity; the composite modularity Q is as follows: （8）； where m is the number of edges, and is the number of nodes and belongs to, is a binary decision function, if node and belongs to the same community, then , otherwise , is the expected weight function of the connection between nodes and on network l, is the total number of networks, is the connection weight between any node and node in network ; the connection expected weight function uses an NG connection expected weight function, as shown in the following formula: （9）； Wherein, the network The degree of the node The degree of the node The degree of the node The degree of the node The degree of the node NG connection expected weight function The influence of spatial distance on the attraction between nodes is not considered; The total number of edges in the network The gravity model is introduced into the composite network connection expected weight function as follows: （10）； where, is the gravitational function, and is the node weight, is the expected weight function of the composite network connection, is the network The Euclidean distance between any node and node , is a numerical value, and the space weight matrix , where is 1 or 2, is substituted into formulas (11) and (12), and the improved composite modularity index is: （11）； （12）； wherein is the improved composite modularity index, is the improved composite network connection expected weight function; Step 3.2: Compute the optimal solution of the Louvain algorithm for community structure, i.e. maximize the modularity using the Louvain algorithm and optimize the solution; Step 3.2.1: regarding each node in the network as a separate community; Step 3.2.2: traversing all neighbor nodes of each node, calculating the modularity gain brought by adding the node to the community of the neighbor node, selecting the neighbor node with the maximum gain, and adding it to the community, and iteratively implementing the process until the community attribute of each node is fixed; Step 3.2.3: fusing the nodes belonging to the same community into one node, and no longer using the connection weight between the nodes before the same community nodes, and the weight between the current community and other communities is the sum of the weights of all nodes of the two communities, and then a new network structure is obtained, and the process returns to step 3.2.2 until the community structure is fixed; Step 4: constructing a spatial mapping relationship between the remote sensing community structure and urban groups; image objects are Landsat image segmentation results and have segmentation boundaries, the spatial range of each node is obtained, multiple image objects belonging to the same community are merged into one community image object, and since there are multiple communities, multiple community image objects are obtained, and the image object of the community is the urban group, and the outline of the community image object is the spatial range of the urban group.

2. The urban group identification method based on complex network and heterogeneous remote sensing images according to claim 1, characterized in that, The complete graph in step 1 is a directed or undirected graph. 3.The urban group identification method based on complex network and heterogeneous remote sensing images according to claim 1, characterized in that, The step 1 specifically comprises the following steps: Step 1.1: extracting a gray feature point of the night light image and constructing a complete graph; The complete graph nodes of the night light image are gray scale features, and the edges between the nodes are the connection relationship between the nodes, which is described by the similarity between the gray scale feature points; the night light image is regarded as a continuous three-dimensional surface model, which is a smooth function that can be differentiated at any time; the gray scale feature points are points with first-order partial derivatives of 0, and the type is obtained by calculating the number of non-negative eigenvalues of the Hessian matrix at the abnormal points, and the Hessian matrix is: （1）； wherein , , and are second order partial derivatives, the similarity between nodes is proportional to the inverse of the difference in gray values from each other; Step 1.2: establishing a complete graph of a Landsat image by using cosine spectral similarity; the complete graph of the Landsat image is obtained by establishing a connection relationship of geometric gravity centers of segmented image objects by using cosine spectral similarity; The Landsat image is segmented into image objects with spectral homogeneity by using a fractal network evolution algorithm, and the geometric barycenter of the image object is extracted as a complete graph node, the cosine distance similarity between nodes is calculated, and the cosine distance similarity is used to describe the connection relationship between nodes, and the cosine distance similarity is shown in the following formula: （2）； wherein, and represent the spectral feature vectors of different image objects, respectively, and are norms; The greater the similarity, otherwise the opposite; using the cosine distance similarity to establish the connection between nodes, forming a complete graph of Landsat image; Step 1.3: The complete graph of the above night light image and the complete graph of the Landsat image are evolved into complex network models respectively by using a horizontal visualization algorithm, and a night light complex network and a Landsat complex network are obtained; The horizontal visualization algorithm takes the node attribute value of the complete graph as the measurement value, if the difference between the measurement values of two nodes is the smallest, the two nodes are connected, otherwise the original connection is abandoned; The node attribute value of the complete graph of the night light image and the complete graph of the Landsat image is the sum of all similarities of each node of the complete graph with other nodes, and the node with higher attribute value often has more special topological structure; Step 1.4: Reconstruct the composite complex network model under the constraint of spatial homogeneity; Under the constraint of spatial homogeneity, the nodes are merged; if there are more than one night light complex network node in a geographical unit, the nodes are merged, the position of the merged node is consistent with the position of the Landsat complex network node, and the weight of the node is increased according to the number of nodes, the connection between the nodes in the same geographical unit is recorded as isomorphic connection, and the connection between the nodes in different geographical units is recorded as heterogeneous connection, the isomorphic connection of the night light complex network is removed, the heterogeneous connection is retained, and the heterogeneous connection relationship is attached to the merged node, forming a composite complex network model; The mathematical expression of the composite complex network model is as follows: Let us consider a complex network with nodes and layers. （3）； wherein is a set of nodes, is a set of nodes, v N is a node, is a set of network edges of layer l, is a set of networks, the corresponding binary adjacency matrix is: （4）； wherein, 1 when adjacent, otherwise 0, and refers to any two nodes, wherein the complex network model is a non-directional network, so is a symmetric matrix.

4. The urban group identification method based on complex network and heterogeneous remote sensing images according to claim 3, characterized in that, The composite adjacency matrix of the composite complex network constructed in step 2 is shown in the following formula: （5）； in, and They represent complex networks of nighttime light data. Landsat Image Complex Network The spatial weight matrix is ​​given by , where c represents the contribution of a single-layer network. for: （6）； wherein, is the connection weight of any node and node in network 1, is: （7）； wherein, is the connection weight of any node and node in network 2; When c takes equally spaced values ​​within the interval [0,1], calculate the eigenvector centrality of W(c) for different c values. Calculate and obtain the network and eigenvector centrality and Calculate separately and and The Kendall correlation coefficient was calculated, and the correlation coefficient curve was fitted using the least squares method. and , the curve and When placed in the same coordinate system, the x-coordinate of the intersection point of the two curves represents the contribution of a single-layer network. .

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