A method for calculating similarity of spatial datasets based on convolution and pooling

Abstract

The application belongs to the field of spatial data set sample search, and discloses a spatial data set similarity calculation method based on convolution and pooling, which comprises (1) a data set feature map generation stage: a grid coordinate system is established for a spatial data set warehouse, and the number of two-dimensional coordinates is counted to generate a feature map; (2) a convolution and pooling stage: a Gaussian smoothing convolution kernel is used to smooth the feature map, structural features of the feature map are extracted, and a pooling feature map is generated by selecting the maximum value through a pooling window; (3) a similarity calculation stage: the final feature map is flattened into a feature vector and normalized, the relative cosine similarity is calculated, and the similarity between data sets is obtained. The application solves the similarity problem of spatial data sets with complex structures, effectively extracts main features of the data sets and reduces the calculation scale, and takes into account accuracy and efficiency, efficiently processes large-scale spatial data sets with complex structures, and accurately reflects the similarity between data sets.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of spatial data set sample search, and specifically relates to a spatial data set similarity calculation method based on convolution and pooling. BACKGROUND

[0002] In today's accelerating urbanization process, cities, as the main carriers of human activities, their development and planning have attracted widespread attention. With the popularization of geographic information systems (GIS), Internet of Things (IoT) and big data technology, the collection, processing and analysis capabilities of urban data have been significantly improved. These data not only cover geographic location information, but also integrate complex features such as economy, society and culture, providing a wealth of information for urban planning, policy making and smart city construction. At the same time, as the core of GIS systems, spatial data sets contain geographic location information and complex spatial relationships, which play a key role in many fields. Measuring the similarity between urban spatial data sets plays an important role in guiding urban construction planning, helping to optimize resource allocation, improve urban management efficiency, and promote the construction and development of smart cities.

[0003] However, existing similarity measurement methods have different degrees of limitations when faced with complex and diverse spatial data sets. Traditional methods such as Euclidean distance and Manhattan distance are effective in handling continuous data, but they are not suitable for complex spatial structures. EMD and Hausdorff distance are widely applicable, but they are limited by high time complexity and sensitivity to outliers. The minimum bounding rectangle (MBR) method focuses on overlapping areas, but ignores the subtle differences in spatial distribution. Therefore, there is an urgent need to explore a new method that can efficiently process large-scale spatial data and accurately reflect the similarity between data sets. SUMMARY

[0004] To solve the above technical problems, the present application provides a spatial data set similarity calculation method based on convolution and pooling, which integrates multi-dimensional similarity evaluation between cities and the ability to process complex geographic location and spatial relationships of spatial data sets. The innovation will inject new momentum into spatial data set query technology and promote the in-depth development and research application in the fields of urban planning and smart city construction.

[0005] To achieve the above purpose, the present application is realized by the following technical scheme:

[0006] The present application is a spatial data set similarity calculation method based on convolution and pooling, which includes three stages: the first stage is the data set feature map generation stage; the second stage is the convolution and pooling stage; the third stage is the similarity calculation stage.

[0007] Step 1, data set feature map generation stage: a grid coordinate system R is established for a spatial data set warehouse D i , and the number of two-dimensional coordinates is counted to generate a two-dimensional coordinate original feature map A i ;

[0008] Step 2, convolution and pooling stage: a Gaussian smoothing convolution kernel is used to smooth the two-dimensional coordinate original feature map A i , the two-dimensional coordinate original feature map A i structure features are extracted, and a sample pooling feature map C i is generated by selecting the maximum value through a pooling window.

[0009] Step 3, similarity calculation stage: the pooling feature map C i and the sample pooling feature map C generated according to the sample data set D e are flattened into feature vectors and normalized, the relative cosine similarity is calculated, and the similarity between the data sets is obtained.

[0010] Further improvement of the application is that step 2 specifically comprises the following steps:

[0011] Step 2.1, a 3x3 window and a Gaussian smoothing convolution kernel with a standard deviation of a are selected, which is used to smooth the two-dimensional coordinate original feature map A i in the subsequent feature extraction, and the structure features of the spatial data set are retained.

[0012] Step 2.2, for the two-dimensional coordinate original feature map set A={A1, A2, …, A n}, each two-dimensional coordinate original feature map A i in A is zero-filled (Zero Padding), and then the Gaussian smoothing convolution kernel is placed in the upper left corner of the two-dimensional coordinate original feature map A i after zero padding, that is, A i the first 3x3 region after zero padding, then slide the Gaussian smoothing convolution kernel and locally weighted sum until the two-dimensional coordinate original feature map A i is traversed to generate a convolution feature map B i , and a convolution feature map set B={B1, B2, …, B n} corresponding to each spatial data set in the spatial data set warehouse D is obtained.

[0013] Step 2.3, for each convolution feature map B n in the convolution feature map set B={B1, B2, …, B i}, a 2 p x 2 p pooling window is selected, and the step size is set to 2 pWherein, 1≤p≤θ-1 places the initial position of the pooling window at the upper left corner of the convolution feature map B i , that is, the first 2 i ×2 p region of B p , selects the maximum value in the region and places it in the corresponding position c i,j,k of the pooled feature map, where 1≤j≤2 θ-p , 1≤k≤2 θ-p , slides the pooling window until the convolution feature map B i is traversed, and the corresponding pooled feature map C i is obtained. n Finally, the set of pooled feature maps C={C1,C2,…,C θ-p} corresponding to each spatial data set in the spatial data set warehouse D is obtained, and the formula is as follows:

[0014]

[0015] Wherein, 1≤j≤2 θ-p , 1≤k≤2 θ-p , c i,j,k is the value of the jth row and kth column of the pooled feature map C i , b i,j,k is the value of the jth row and kth column of the convolution feature map B i , and the upper left quarter region of the pooling window covers the j0th row and k0th column of the convolution feature map B i .

[0016] Further improvement of the application is that in step 2.1, a 3×3 Gaussian smoothing kernel with a standard deviation of α is selected as the window, and the specific steps include the following steps:

[0017] Step 2.1.1, calculate each value of the convolution kernel:

[0018]

[0019] Wherein, (x,y) is the coordinate relative to the center of the convolution kernel, σ is the standard deviation, x,y∈{0,±1}, take σ=α, calculate all possible values of (x,y) (-1,-1), (-1,0), (-1,1), (0,-1), (0,0), (0,1), (1,-1), (1,0), (1,1), and obtain the convolution kernel Kernel, which is represented as follows:

[0020] Kernel i,j =G(i-2,j-2);

[0021] Step 2.1.2, calculate the sum Sum of all elements of the convolution kernel, and then normalize each element by dividing the sum to obtain the normalized convolution kernel NK, which is represented as follows:

[0022]

[0023] wherein Kernel i,j is the value of the i-th row and j-th column of the convolution kernel Kernel, 1≤i,j≤3.

[0024] The further improvement of the present application is that the two-dimensional coordinate original feature map A i is padded with zeros and the convolution kernel is slid and locally weighted summation, specifically comprising the following steps:

[0025] Step 2.2.1, one row of 0 is added above the first row and below the last row, and one column of 0 is added left of the first column and right of the last column of the two-dimensional coordinate original feature map A i , i.e. Padding=1, so that the size of the two-dimensional coordinate original feature map A i is changed from 2 θ ×2 θ to (2 θ +2)×(2 θ +2), to ensure that the size of the feature map after convolution is unchanged;

[0026] Step 2.2.2, slide the Gaussian smoothing convolution kernel on the two-dimensional coordinate original feature map A i with a step of 1, each position corresponds to a local region, i.e. a receptive field, in the local region covered by the Gaussian smoothing convolution kernel, multiply the Gaussian smoothing convolution kernel and the corresponding position of the two-dimensional coordinate original feature map A i element by element, then sum all the products to get an element value b i,j,k of the convolution feature map, where 1≤j≤2 θ , 1≤k≤2 θ , this process is repeated until the convolution kernel traverses A i , to generate the corresponding convolution feature map B i , to get the convolution feature map set B={B1,B2,…,B n} corresponding to each feature map in the two-dimensional coordinate original feature map set A, represented as:

[0027]

[0028] wherein NK u,v is the value of the u-th row and v-th column of the normalized convolution kernel NK, 1≤u,v≤3.

[0029] The further improvement of the present application is that the step 3 specifically comprises the following steps:

[0030] Step 3.1: For the given query sample dataset D e Based on the query sample dataset D e Establish a coordinate system R by finding the minimum and maximum values ​​of the x and y axes of all two-dimensional coordinates. e Count the number of two-dimensional coordinates to generate sample two-dimensional coordinate original feature map A e Then, the original feature map A of the two-dimensional coordinates of the sample is smoothed using a Gaussian smoothing convolution kernel. e Obtain the sample convolutional feature map B e Then, the maximum value is selected through the pooling window to generate the sample pooling feature map C. e ;

[0031] Step 3.2: For the sample pooling feature map C e The pooling feature map set C = {C1, C2, ..., C} n Each feature map C in} i ∈C, respectively flattened into eigenvectors v e and v i :

[0032]

[0033] Step 3.3: Normalize the eigenvectors and calculate v. e and v i The similarity is denoted as the similarity of the corresponding two-dimensional coordinate space dataset D. i And query sample dataset D e The similarity is calculated using the following formula:

[0034]

[0035] Where θ is the partitioning parameter, v e,t It is a vector v e The t-th element, v i,t It is a vector v i The t-th element.

[0036] A further improvement of the present invention is that step 1 specifically includes the following steps:

[0037] Step 1.1: Given a spatial dataset repository D = {D1, D2, ..., D...} n}, D i ∈D is a spatial dataset of two-dimensional coordinates, where D i ={(x1,y1),(x2,y2),…,(x m ,y m Find D i Let xi be the minimum and maximum values ​​of the x-axis and y-axis of all two-dimensional coordinates. min yimin , xi max , yi max ;

[0038] Step 1.2, establish a rectangular region with (xi min , yi min ) and (xi max , yi max ) as the diagonal, then extend the width of the rectangle to both ends equally to expand the rectangular region into a square, and then divide the square region into 2 θ ×2 θ equal grids according to the division parameter θ to establish a grid coordinate system R i ;

[0039] Step 1.3, for each spatial data set D n in the spatial data set warehouse D={D1, D2, …, D i}, count the number of two-dimensional coordinate points of the spatial data set D i in the grid g i in the jth row and kth column of the grid coordinate system R j,k , denoted as a i,j,k , where 1≤j≤2 θ ,1≤k≤2 θ , to obtain the two-dimensional coordinate feature map A i of the spatial data set D i , and traverse the spatial data set warehouse D to obtain the two-dimensional coordinate original feature map set A={A1, A2, …, A n}.

[0040] The beneficial effects of the present application are:

[0041] The present application ingeniously combines convolution and pooling with spatial data set query to provide an efficient and adaptable spatial data set similarity calculation method.

[0042] The present application not only effectively overcomes the challenge of traditional technology in dealing with the diversity and complexity of spatial data through the careful design of convolution kernel selection and pooling process, but also reduces the calculation scale through the generation of data set feature map and improves the search efficiency. At the same time, in the similarity calculation stage, the method of normalized feature vector is adopted to ensure the balance and comparability between different spatial data set features, further improving the practicality and accuracy of the method.

[0043] This invention achieves efficient processing of spatial datasets with complex structures through a carefully designed three-stage process. It not only reduces computational scale but also improves search efficiency, meeting the needs of large-scale spatial data processing. Compared to traditional methods, this invention better reflects the complexity and diversity of spatial datasets, providing strong technical support for fields such as urban planning and smart city construction. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the present invention.

[0045] Figure 2 This is a schematic diagram illustrating the process of generating a two-dimensional coordinate original feature map during the dataset feature map generation stage of this invention.

[0046] Figure 3 This is a schematic diagram illustrating the process of generating pooling feature maps during the convolution and pooling stages of this invention. Detailed Implementation

[0047] Embodiments of the present invention will now be disclosed with reference to the accompanying drawings of the embodiments of this application. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the present invention, these practical details are not essential.

[0048] For ease of description, the relevant symbols are defined as follows: Spatial dataset repository D = {D1, D2, ..., D...} n}, containing n spatial datasets, D i ∈D is a spatial dataset of two-dimensional coordinates, where D i ={(x1,y1),(x2,y2),…,(x m ,y m The set of original two-dimensional coordinate feature maps corresponding to each spatial dataset in D is A = {A1, A2, ..., A}. n};The set of convolutional feature maps B corresponding to each spatial dataset in D = {B1, B2, ..., B} n}; The set of pooled feature maps corresponding to each spatial dataset in D is C = {C1, C2, ..., C} n}; Query sample dataset D e and sample pooling feature map C e .

[0049] like Figure 1 As shown, this invention is a spatial dataset similarity calculation method based on convolution and pooling. The similarity calculation method includes three stages: the first stage: dataset feature map generation stage; the second stage: convolution and pooling stage; and the third stage: similarity calculation stage.

[0050] The data set feature map generation stage includes the following steps:

[0051] (1a) Given a spatial data set warehouse D = {D1, D2, …, D n}, D i ∈D is a two-dimensional coordinate spatial data set, where D i = {(x1, y1), (x2, y2), …, (x m , y m )}, find the minimum and maximum values of the x-axis and y-axis of all two-dimensional coordinates in D i , denoted as xi min , yi min , xi max , yi max .

[0052] (1b) As shown in Figure 2 , establish a rectangular region with (xi min , yi min ) and (xi max , yi max ) as the opposite corners, then extend the width of the rectangle to both ends to expand the rectangular region into a square, and then divide the square region into 2 θ ×2 θ equal-sized grids according to the division parameter θ to establish a grid coordinate system R i .

[0053] (1c) For each spatial data set D n in the spatial data set warehouse D = {D1, D2, …, D i}, count the number of two-dimensional coordinate points in the grid g j,k in the jth row and kth column in the coordinate system R, denoted as a i,j,k , where 1≤j≤2 θ , 1≤k≤2 θ , to obtain the two-dimensional coordinate original feature map A i of D i . Traverse the spatial data warehouse D to obtain the two-dimensional coordinate original feature map set A = {A1, A2, …, A n}.

[0054] The convolution and pooling stage includes the following steps:

[0055] (2a) Select a 3×3 window and a Gaussian smoothing convolution kernel with a standard deviation of α to smooth the feature map in the subsequent feature extraction and retain the larger structural features of the spatial data set.

[0056] In this step, a window of 3x3 and a Gaussian smoothing kernel with a standard deviation of a is selected, which includes the following steps:

[0057] (2a1) Calculate each value of the kernel according to the formula, as follows:

[0058]

[0059] where (x, y) is the coordinate relative to the center of the kernel, and σ is the standard deviation, so x, y ∈ {0, ±1}. Taking σ = a, calculate all possible combinations of (x, y) (-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1) to obtain the kernel Kernel, which can be expressed as follows:

[0060] Kernel i,j = G(i-2, j-2)

[0061] where Kernel i,j is the value of the i-th row and j-th column of the kernel Kernel, 1≤i,j≤3.

[0062] (2a2) Calculate the sum of all elements of the kernel Sum, and then normalize each element by dividing it by the sum to ensure that the total amount of features remains essentially unchanged, to obtain the normalized kernel NK, which can be expressed as follows:

[0063]

[0064] (2b) As shown in Figure 3 , for a two-dimensional coordinate original feature map set A = {A1, A2, …, A n}, each two-dimensional coordinate original feature map A i ∈A is "zero padded", and the kernel is placed in the upper left corner of the two-dimensional coordinate original feature map A i , i.e. A i "zero padded" in the first 3x3 region, then slide the kernel and locally weighted sum until the entire A i is traversed to obtain the convolution feature map B i . Finally, the convolution feature map set B = {B1, B2, …, B n} corresponding to each spatial data set in D is obtained.

[0065] In this step, the two-dimensional coordinate original feature map A i is "zero padded" and the kernel is slid and locally weighted summed, which includes the following steps:

[0066] (2b1) In A i Add a row of 0s above the first row and below the last row, and add a column of 0s to the left of the first column and to the right of the last column, i.e., Padding = 1, so that A i Size from 2 θ ×2 θ It becomes (2) θ +2)×(2 θ +2) to ensure that the size of the feature map after convolution remains unchanged.

[0067] (2b2) ​​Place the convolution kernel on A i Slide upwards with a stride of 1. Each position corresponds to a local region, or receptive field. Within the local region covered by the convolution kernel, the convolution kernel is connected to A. i Element-wise multiplication is performed at the corresponding positions, and then all products are summed to obtain an element value b of the convolutional feature map. i,j,k where 1≤j≤2 θ ,1≤k≤2 θ This process is repeated until the convolution kernel has traversed all of A. i The corresponding convolutional feature map B is obtained. i Finally, we obtain the set of convolutional feature maps B = {B1, B2, ..., B...} corresponding to each feature map in A. n The formula is as follows:

[0068]

[0069] Among them, b i,j,k For convolutional feature map B i The value in the j-th row and k-th column, a i,j,k Original feature map A in two-dimensional coordinates i The value in the j-th row and k-th column, NK u,v Let be the value of the normalized convolution kernel NK in the u-th row and v-th column, where 1 ≤ u, v ≤ 3.

[0070] (2c) such as Figure 3 As shown, for the set of convolutional feature maps B = {B1, B2, ..., B} n Each feature map B in} i Select a 2×2 pooling window with a stride of 2, and place the initial position of the pooling window on convolutional feature map B. i The top left corner, i.e., B i In the first 2×2 region, the maximum value within the region is selected and placed into the corresponding position c of the pooled feature map. i,j,k where 1≤j≤2 θ-1 ,1≤k≤2 θ-1 Sliding pooling window until B is traversed i, to obtain the corresponding pooling feature map, which can be expressed as follows:

[0071]

[0072] wherein 1≤j≤2 θ-1 ,1≤k≤2 θ-1 , c i,j,k is the value of the jth row and kth column of the pooling feature map C i , b i,j,k is the value of the jth row and kth column of the convolution feature map B i , and the quarter region at the upper left corner of the pooling window covers the j0th row and k0th column of B i . Finally, a set of pooling feature maps C = {C1, C2, …, C n} corresponding to each spatial data set in D is obtained.

[0073] The similarity calculation stage includes the following steps:

[0074] (3a) For a given query sample data set D e , the sample pooling feature map C e is generated according to the method of generating the pooling feature map described in the convolution and pooling stage.

[0075] (3b) For C e and each pooling feature map C n ∈ C in the set of pooling feature maps C = {C1, C2, …, C i}, they are respectively flattened into feature vectors v e and v i , which can be expressed as follows:

[0076]

[0077]

[0078] (3c) Normalize the feature vectors, and calculate the similarity between v e and v i , denoted as the similarity between the corresponding data sets D i and D e , which can be expressed as follows:

[0079]

[0080] wherein θ is a division parameter, v e,t is the tth element of the vector v e , and v i,t is the tth element of the vector v i .

[0081] Figure 2The process of generating the original feature map of a spatial data set is shown, the minimum circumscribed rectangle is determined by the four maximum values of the x-axis and y-axis directions in the data set, and is extended into the minimum circumscribed square, and then the grid coordinate system is generated according to the division parameter, the number of two-dimensional coordinates falling into each grid is counted, and the original feature map is obtained.

[0082] Figure 3 The process of generating a convolution feature map and a pooling feature map from an original feature map is shown, and the Gaussian smoothing convolution kernel can effectively reduce the influence of outliers in the data set on the data distribution structure, so that the main features are extracted by convolution, and the data size is reduced by pooling, so that accuracy and efficiency are considered for subsequent similarity calculation.

[0083] Therefore, in the application, the convolution and pooling algorithm is innovatively applied to the similarity calculation of the spatial data set, a new method framework is proposed, and the limitations of the traditional method in processing complex spatial data sets are effectively overcome. In the convolution and pooling stage, the Gaussian smoothing convolution kernel is selected, which can smooth the feature map and retain the main structural features of the spatial data set, improving the accuracy and robustness of feature extraction. By generating a pooling feature map, the data size is further reduced while retaining the key features, providing an efficient data basis for subsequent similarity calculation. In the similarity calculation stage, the relative cosine similarity is used to measure the similarity between data sets, and the normalized feature vector ensures the balance and comparability between different spatial data set features. Through the three stages designed with care, the application realizes efficient processing of spatial data sets with complex structures. Not only reduces the calculation scale, but also improves the search efficiency, meets the demand of large-scale spatial data processing. Compared with the traditional method, the application can better reflect the complexity and diversity of the spatial data set, and provide strong technical support for the fields of urban planning and smart city construction.

[0084] The above only describes the embodiments of the application and is not used to limit the application. For those skilled in the art, the application can have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the scope of the claims of the application.

Claims

1. A method for similarity computation of spatial datasets based on convolution and pooling, characterized in that: The convolution and pooling-based spatial dataset similarity calculation method includes three steps: Step 1, dataset feature map generation stage: to the spatial dataset warehouse Establish a grid coordinate system , count the number of two-dimensional coordinates to generate a two-dimensional coordinate original feature map ; Step 2, convolution and pooling stage: smooth the two-dimensional coordinate original feature map with a Gaussian smoothing convolution kernel , extract the two-dimensional coordinate original feature map Structural features, and then generate a pooling feature map by selecting the maximum value through a pooling window ; Step 3, similarity calculation stage: the pooled feature maps and the example pooled feature maps generated according to the example data set are flattened into feature vectors and normalized, the relative cosine similarity is calculated, and the similarity between the data sets is obtained, wherein, Step 1 specifically includes the following steps: Step 1.

1. Given a spatial dataset repository , for a two-dimensional coordinate spatial dataset, where, , find all two-dimensional coordinate axis and axis minimum and maximum values, respectively, denoted as ; Step 1.2, establish a rectangular region with and as the diagonals, then extend the width of the rectangle equally to both ends to expand the rectangular region into a square, and then divide the square region into equal grids according to the division parameter to establish a grid coordinate system ; Step 1.3, for each spatial data set in the spatial data set warehouse ​​​​​​​​​​​​​ Step 2 specifically includes the following steps: Step 2.1, select a window as , the standard deviation of the Gaussian smoothing kernel is , which is used to smooth the two-dimensional coordinate original feature map in the subsequent feature extraction, retaining the structural characteristics of the spatial data set; Step 2.2: For the original set of two-dimensional coordinate feature maps The original feature map of each two-dimensional coordinate. Perform "zero padding" and then place the Gaussian smoothed convolution kernel on the original 2D coordinate feature map after "zero padding". The top left corner, that is The first after "zero padding" The region is then processed by sliding a Gaussian smoothing convolution kernel and locally weighted summation until the original two-dimensional coordinate feature map has been traversed. Generate convolutional feature maps Obtain the spatial dataset repository The set of convolutional feature maps corresponding to each spatial dataset. ; Step 2.3: For the set of convolutional feature maps Each convolutional feature map in Select one The pooling window, with a stride set to ,in, The initial position of the pooling window is placed on the convolutional feature map. The top left corner, that is The first For each region, the maximum value within that region is placed into the corresponding position of the pooled feature map. ,in The sliding pooling window continues until all convolutional feature maps have been traversed. The corresponding pooling feature map is obtained. Ultimately, a spatial dataset repository was obtained. The pooling feature map set corresponding to each spatial dataset. The formula is expressed as follows: ， in, , Pooling feature map The Line 1 Column values, Convolutional feature maps The Line 1 The column values ​​represent the top-left quarter of the pooling window, which covers the convolutional feature map. The Line 1 List. 2.The method of claim 1, wherein: A Gaussian smoothing kernel with a window of and a standard deviation of is selected in step 2.1 and comprises the following steps: Step 2.1.1, calculate each value of the convolution kernel: ， wherein, is the coordinate relative to the center of the convolution kernel, is the standard deviation, , take , calculate for all possible values of the convolution kernel is represented as follows:​ ， Step 2.1.2, calculate the sum of all elements of the convolution kernel Each element is then normalized by dividing by the sum to obtain the normalized convolution kernel is represented as follows: ， ， wherein is a convolution kernel the first row the column value, .

3. The method of claim 1, wherein: The two-dimensional coordinate raw feature map in step 2.2 Performing "zero padding" and sliding the convolution kernel and locally weighted summing, including the following steps: Step 2.2.1, add a row of 0 above the first row and below the last row, and add a column of 0 left of the first column and right of the last column of the two-dimensional coordinate original feature map , that is , so that the size of the two-dimensional coordinate original feature map is changed from to to ensure that the feature map size after convolution is unchanged; Step 2.2.2: Apply the Gaussian smoothed convolution kernel to the original feature map in two-dimensional coordinates. Slide upwards, step size is Each location corresponds to a local region, or receptive field. Within the local region covered by the Gaussian smoothed convolution kernel, the Gaussian smoothed convolution kernel is compared with the original two-dimensional coordinate feature map. The corresponding positions are multiplied element-wise, and then all products are summed to obtain an element value of the convolutional feature map. ,in This process is repeated until all convolutional kernels have been traversed. Generate the corresponding convolutional feature map This yields the original feature map set with two-dimensional coordinates. The set of convolutional feature maps corresponding to each feature map in the middle , is represented as: ， wherein is a normalized convolution kernel first row column .

4. The method of claim 1, wherein: Step 3 specifically includes the following steps: Step 3.1, for a given query example dataset , establish a coordinate system according to the minimum and maximum values of the x-axis and y-axis of all two-dimensional coordinates in the query example dataset , count the number of two-dimensional coordinates to generate an example two-dimensional coordinate original feature map , then smooth the example two-dimensional coordinate original feature map using a Gaussian smoothing convolution kernel to obtain an example convolution feature map ;​​​​​ Step 3.2, for the sample pool, the feature maps are flattened into feature vectors and the set of pooled feature maps are flattened into feature vectors , respectively and : ， ； Step 3.3, normalize the feature vector, compute and the similarity of the two-dimensional coordinate space data sets and the query example data set is given by the formula: ， wherein is a division parameter, is a vector of the th element, .

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