An efficient method for collecting IoT data based on active sampling

Abstract

This invention provides an efficient method for collecting IoT data based on active sampling. The method includes: determining the minimum required sampling cost as r+1; mining deep relationships and structures between grids using a spatiotemporal fusion module to obtain an augmented grid graph; and sampling the selected sampling grids to obtain a sampling vector h. (T+1) and it is coupled with the sensing matrix X (T) Combined, the initial T+1 time slot sensing matrix [X] is formed. (T) ,h (T+1) The augmented mesh diagram and the initial sensing matrix of time slot T+1 are input into the spatiotemporal fusion module to obtain a spatiotemporal representation, and two initial factor matrices are derived through neural network training; the final factor matrix U is then obtained. (T+1) and V (T+1) Using the final factor matrix U (T+1) and V (T+1) The data at unsampled locations is calculated, and combined with the sampled data, the complete grid data is obtained. This invention not only significantly reduces the cost of data collection but also ensures the accuracy and reliability of the inference results, thereby providing better services for applications such as environmental monitoring and smart cities in the Internet of Things.

Description

Technical Field

[0001] This invention relates to the field of Internet of Things (IoT) data collection technology, and specifically to an efficient method for collecting IoT data based on active sampling. Background Technology

[0002] In today's rapidly developing Internet of Things (IoT) technology landscape, data collection, as the foundation for various intelligent services, is undeniably crucial. Traditional data collection strategies primarily revolve around densely deploying various IoT devices, such as sensors and intelligent monitoring devices, within a target area to ensure the acquisition of detailed and comprehensive data, thereby providing solid data support for high-quality IoT services. However, this strategy has encountered multiple challenges in practical applications, severely hindering the further popularization and optimization of IoT technology.

[0003] First, from an economic cost perspective, with the rapid increase in the number of IoT devices, not only has the purchase cost of these devices become a significant expense, but subsequent maintenance costs are also continuously rising. Especially in large-scale deployment scenarios, the high cost often becomes an insurmountable obstacle, limiting the widespread application of IoT technology.

[0004] Secondly, even with sufficient economic support for large-scale device deployment, environmental factors and privacy requirements present numerous challenges to data collection. Environmental instability can lead to device malfunctions or data distortion, while strict privacy protections in certain areas can hinder comprehensive data collection. These factors combined make comprehensive data coverage exceptionally difficult, thereby impacting the overall quality and effectiveness of IoT services.

[0005] Coverage, as a key indicator for measuring the quality of IoT services, directly reflects the completeness and effectiveness of data collection. However, in large-scale and fine-grained IoT applications, due to various limitations in device deployment, the collected data often exhibits incompleteness and sparseness. This data sparsity severely weakens the ability of upper-layer applications to make accurate decisions, thus making it difficult to provide truly optimized services.

[0006] To address the challenges of high data collection costs and incomplete coverage, the industry has begun exploring methods to infer unsampled data from already collected data. The feasibility of this approach lies in the continuity of the IoT environment and the strong spatiotemporal correlation of sensor data, characteristics mathematically manifested as low-rank data. Matrix imputation techniques can be used to effectively infer and fill in missing data, thereby achieving efficient data collection.

[0007] While some research has attempted to apply matrix filling techniques to data collection and achieved certain results, most of these studies have focused on optimizing the matrix filling algorithm itself to improve the accuracy of inference results. However, this passive optimization strategy neglects the importance of the sampling point location and the amount of information it carries. In reality, data from different locations differ significantly in terms of information content. If the sampling points are not selected properly, even with further algorithm optimization, it is difficult to avoid serious inference biases.

[0008] Therefore, existing methods have significant shortcomings in their passive sampling strategies when faced with uneven information content at different locations, making it difficult to ensure the accuracy and reliability of inference results. This has become a bottleneck restricting the further development of IoT data collection technology, and new technical solutions are urgently needed to overcome this limitation. Summary of the Invention

[0009] To address the high costs and incomplete coverage issues inherent in traditional IoT data collection methods, this invention aims to provide an efficient IoT data collection method based on active sampling. This method proactively selects information-rich sampling locations and combines them with matrix filling techniques to accurately infer unsampled data from sparse data. This approach not only significantly reduces data collection costs but also ensures the accuracy and reliability of the inference results, thereby providing higher-quality services for IoT applications such as environmental monitoring and smart cities.

[0010] The present invention achieves the above objectives through the following technical solutions:

[0011] An efficient method for collecting IoT data based on active sampling includes the following steps:

[0012] The target area is divided into N grids, and sensor data from each grid within T historical time slots are acquired to form a sensor matrix X of size N×T. (T) Among them, according to the sensing matrix X (T) Given the rank r, the minimum sampling cost required to determine the next time slot T+1 is r+1;

[0013] The mesh graph is augmented by using a spatiotemporal fusion module to mine the deep relationships and structures between meshes to obtain an augmented mesh graph.

[0014] The augmented grid graph is divided into r+1 clusters using spectral clustering, and at least one sampling grid is selected from each cluster.

[0015] The selected sampling grid is sampled to obtain the sampling vector h. (T+1) and it is coupled with the sensing matrix X (T) Combined, the initial T+1 time slot sensing matrix [X] is formed. (T) ,h (T+1) ];

[0016] The augmented mesh diagram and the initial sensing matrix of the T+1 time slot are input into the spatiotemporal fusion module to obtain the spatiotemporal representation, and two initial factor matrices are derived through neural network training.

[0017] The two initial factor matrices are iteratively updated to obtain the final factor matrix U. (T+1) and V (T+1) ;

[0018] Using the final factor matrix U (T+1) and V (T+1) The data at the unsampled locations are calculated, and combined with the sampled data, all the collected grid data are obtained.

[0019] According to the present invention, an efficient IoT data collection method based on active sampling is provided, wherein the historical sensor matrix X is known when determining the minimum sampling cost. (T) Assuming its rank is r, X (T+1) (X (T+1) =[X (T) x (T+1) The rank of X is at most r+1, therefore, by the fundamental properties of matrices, the minimum sampling cost is r+1; where X (T+1) The space is spanned by r+1 linearly independent vectors.

[0020] According to the present invention, an efficient IoT data collection method based on active sampling is provided. During augmentation processing, the deep relationships and structures between grids are mined based on historical grid data. Specifically, the grid graph G = (V, ε) is augmented to obtain an augmented grid graph, where V = {v1, v2, ..., v...}. N} is the set of grids, and ε is the set of edges; the adjacency matrix of the grid graph G is denoted as A, a ij ∈A, if v i v j ∈V, ε ij ∈ε, then a ij =1, otherwise 0.

[0021] The present invention provides an efficient method for collecting IoT data based on active sampling, for grid v i (1≤i≤N), its time representation s across multiple time steps i It can be represented as s i =TC (m) (b i ), where TC represents temporal convolution, and m represents multiple temporal convolutions to aggregate information from all time steps. As an intermediate product of the spatiotemporal fusion module, it is expressed by the following formula:

[0022] TC(X(T) → B (T)

[0023] TC(SC(B (T) ,A))→Y (T)

[0024] Where TC represents temporal convolution and SC represents spatial convolution. and These represent different stages of representation, where D is the representation dimension, and T′ and T″ are the time dimensions after convolution. After stacking multiple blocks, the final representation of the grid can be obtained.

[0025] According to the present invention, an efficient IoT data collection method based on active sampling is provided, which uses time-represented cosine distance to measure the similarity between two grids, grid v i and grid v j The similarity between (1≤j≤N) can be expressed by the following formula:

[0026]

[0027] A similarity matrix can be obtained using the formula. All diagonal elements are equal to 1, w ij The larger the value, the more similar the data patterns between grids, and vice versa.

[0028] According to the present invention, an efficient IoT data collection method based on active sampling re-evaluates the adjacency relationship between grids based on a similarity matrix W, where grid v i and grid v j The edge ε between ij The probability of adding or deleting follows a Bernoulli distribution with probability p. ij It can be expressed as the following formula:

[0029]

[0030] Where max(W·(1-I)) represents the maximum value in matrix W excluding the diagonal elements. This represents their average value.

[0031] According to the present invention, an efficient IoT data collection method based on active sampling is provided, if grid v i and grid v j Physically adjacent, with probability ρ ij Delete edge ε ij , ρ ij With similarity w ij The value decreases as the grid value increases; if the grid value v iand grid v j If the physical locations are not adjacent, then use 1-ρ ij The probability of adding an edge between the two is related to the similarity w. ij The trend remains consistent;

[0032] Obtain augmented mesh diagram

[0033] According to the present invention, an efficient IoT data collection method based on active sampling is provided. When using spectral clustering to divide the augmented mesh graph, the division is based on the Laplacian matrix L, which is derived from the similarity matrix W, i.e., L = DW, where D is obtained by the following formula:

[0034]

[0035] After obtaining the Laplacian matrix L, its eigenvalues ​​are first decomposed to obtain a new matrix composed of its eigenvectors; then the K-Means algorithm is used to divide the grid into r+1 clusters based on the new matrix.

[0036] According to the present invention, an efficient IoT data collection method based on active sampling is provided, wherein the following steps are performed for each cluster to select the cluster center as the sampling grid:

[0037] Calculate node degree: For each node in the cluster, calculate its degree, that is, count the number of edges directly connected to the node, and use this as a measure of node degree centrality.

[0038] Sorting nodes: Based on the calculated node degree, all nodes in the cluster are sorted in descending order. Nodes with higher degrees are listed first, indicating that they have stronger connectivity and higher importance in the cluster.

[0039] Cluster center selection: From the sorted list of nodes, select one or more nodes with the highest degree as the cluster centers of the cluster, and use them as representative points of the sampling grid;

[0040] Forming a sampling grid: The selected cluster centers in each cluster are combined to form a sampling grid for the entire dataset. This sampling grid can reflect the structural characteristics of the dataset and can be used for subsequent data analysis, sampling, or visualization of clustering results.

[0041] According to the present invention, an efficient method for collecting IoT data based on active sampling is provided, which augments the mesh graph. and the initial sensing matrix [X (T) ,h (T+1) Input spatiotemporal fusion module, output spatiotemporal representation

[0042] Through neural network training, spatiotemporal representations Derive two initial factor matrices and

[0043] The final factor matrix is ​​obtained by training two initial factor matrices, and this process is expressed by the following formula:

[0044]

[0045] in,‖‖ F Let F-norm, Z (T+1) [1,1,…,1,z] (T+1) The simplest expression for ], z (T+1) This indicates whether the grid in time slot T+1 was sampled; if sampled, it is marked as 1, otherwise it is marked as 0.

[0046] After obtaining the final factor matrix U (T+1) and V (T+1) Then, via U (T+1) V (T+1)T The data at the unsampled locations is deduced, and combined with the sampled data, this yields all the collected grid data.

[0047] Therefore, compared to existing IoT applications, efficient data collection is crucial for scenarios such as environmental monitoring and smart cities. However, traditional data collection methods face challenges such as high costs and incomplete data coverage. To address these issues, this invention proposes an efficient IoT data collection method based on active sampling. This method actively selects information-rich areas for sampling and combines them with a matrix filling algorithm to accurately infer the perceived data of unsampled areas from sparse samples. This technique not only ensures data accuracy but also significantly reduces the cost of IoT data collection. Therefore, this invention has the following advantages:

[0048] Beneficial effects:

[0049] 1. Lowest data collection cost: This invention achieves the lowest data collection cost by conducting in-depth analysis of historical data to determine the minimum sampling requirements needed for accurate inference in the next time slot, thereby reducing unnecessary sampling work.

[0050] 2. Improve the accuracy of data reasoning: Within the sampling cost range, this invention actively selects sampling locations, fully considers the information differences in different regions, and avoids reasoning deviations caused by insufficient information at sampling points, thereby significantly improving the accuracy and reliability of data reasoning.

[0051] 3. Flexible response to complex environments: The active sampling method of this invention has high flexibility and can dynamically adjust the sampling strategy according to changes in the actual environment. It is highly adaptable and can maintain efficient data collection capabilities even in complex and dynamic IoT environments.

[0052] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0053] Figure 1 This is a flowchart of an embodiment of an efficient IoT data collection method based on active sampling according to the present invention.

[0054] Figure 2 This is a schematic diagram of an embodiment of an efficient IoT data collection method based on active sampling according to the present invention.

[0055] Figure 3 This is a schematic diagram illustrating the application principle of the spatiotemporal fusion module in an embodiment of an efficient IoT data collection method based on active sampling according to the present invention.

[0056] Figure 4 This is a schematic diagram of the factor matrix acquisition steps in an embodiment of an efficient IoT data collection method based on active sampling according to the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0058] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0059] See Figure 1 and Figure 2 This embodiment provides a method for efficient collection of IoT data based on active sampling, which includes the following steps:

[0060] Step S1: Divide the target area into N grids and acquire the sensing data of each grid within T historical time slots to form a sensing matrix X of size N×T. (T) ;

[0061] Step S2, based on the sensing matrix X (T) Given the rank r, the minimum sampling cost required to determine the next time slot T+1 is r+1;

[0062] Step S3: Augment the mesh graph by using the spatiotemporal fusion module to mine the deep relationships and structures between meshes to obtain an augmented mesh graph.

[0063] Step S4: Use spectral clustering to divide the augmented grid map into r+1 clusters, and select at least one sampling grid from each cluster;

[0064] Step S5: Sample the selected sampling grid to obtain the sampling vector h. (T+1) and it is coupled with the sensing matrix X (T) Combined, the initial T+1 time slot sensing matrix [X] is formed. (T) ,h (T+1) ];

[0065] Step S6: Input the augmented mesh map and the initial sensing matrix of time slot T+1 into the spatiotemporal fusion module to obtain the spatiotemporal representation, and derive two initial factor matrices through neural network training;

[0066] Step S7: Iteratively update the two initial factor matrices to obtain the final factor matrix U. (T+1) and V (T+1) ;

[0067] Step S8, using the final factor matrix U (T+1) and V (T+1) The data at the unsampled locations are calculated, and combined with the sampled data, all the collected grid data are obtained.

[0068] In this embodiment, for a given target area, it can be divided into N grids, and the sensing data of the N grids over T historical time slots can be represented as a sensing matrix X of size N×T. (T) ={x (1) ,x (2) ,…,x (T)}, where x (1) ,x (2) ,…,x (T) These represent the sensor data collected across N grids in time slots 1, 2, ..., T. For the future time slot T+1, the goal is to select a small number of grids for sampling, utilizing the sensor matrix X. (T) By accurately inferring the sensor data from other unsampled locations using a small amount of sampled data, the sensor matrix x in time slot T+1 can be obtained. (T+1) .

[0069] As can be seen, this embodiment provides an efficient IoT data collection method based on active sampling, which mainly includes three parts: 1) determining the minimum sampling cost that can guarantee accurate inference; 2) selecting key grids for sampling without exceeding the sampling cost; and 3) using matrix filling to infer data from other unsampled locations.

[0070] In step S1 above, when determining the minimum sampling cost, the historical sensing matrix X is known. (T) Assuming its rank is r, X (T+1) (X (T+1) =[X (T) x (T+1) The rank of X is at most r+1, therefore, by the fundamental properties of matrices, the minimum sampling cost is r+1; where X (T+1) The space is spanned by r+1 linearly independent vectors.

[0071] In this embodiment, when selecting key grids for sampling, the deep relationships and structures between grids are mined based on the historical data of the grids. That is, the grid graph G=(V,ε) is augmented to obtain an augmented grid graph, where V={v1,v2,…,v N} is the set of grids, and ε is the set of edges; the adjacency matrix of the grid graph G is denoted as A, a ij ∈A, if v i v j ∈V, ε ij ∈ε, then a ij =1, otherwise 0.

[0072] For grid v i (1≤i≤N), its time representation s across multiple time steps i It can be represented as s i =TC (m) (b i ), where TC represents temporal convolution, and m represents multiple temporal convolutions to aggregate information from all time steps. As an intermediate product of the spatiotemporal fusion module, the complete process is as follows: Figure 3 As shown, it can be expressed as the following formula:

[0073] TC(X (T) → B (T)

[0074] TC(SC(B (T) ,A))→Y (T)

[0075] Where TC represents temporal convolution and SC represents spatial convolution. and These represent different stages of representation, where D is the representation dimension, and T′ and T″ are the time dimensions after convolution. After stacking multiple blocks, the final representation of the grid can be obtained.

[0076] The similarity between two grids is measured using a time-represented cosine distance, grid v i and grid v j The similarity between (1≤j≤N) can be expressed by the following formula:

[0077]

[0078] Therefore, a similarity matrix can be obtained. All diagonal elements are equal to 1, w ij The larger the value, the more similar the data patterns between grids, and vice versa. The adjacency relationships between grids are reassessed based on the similarity matrix W. Specifically, grid v... i and grid v j The edge ε between ij The probability of adding or deleting follows a Bernoulli distribution with probability p. ij It can be expressed as the following formula:

[0079]

[0080] Where max(W·(1-I)) represents the maximum value in matrix W excluding the diagonal elements (where 1 represents an N×N matrix with all elements equal to 1, and I represents an identity matrix of the same size). This represents their average value. If the grid v i and grid v j Physically adjacent, this embodiment uses probability ρ ij Delete edge ε ij , ρ ij With similarity w ij The value decreases as the grid value increases; if the grid value v i and grid v j If the physical locations are not adjacent, then use 1-ρ ij The probability of adding an edge between the two is related to the similarity w. ij The trend remains consistent. After the above augmentation process, an augmented mesh diagram can be obtained.

[0081] The above process yields an augmented graph where grids with similar data patterns are closer together, making them more likely to be grouped into the same cluster. When partitioning the augmented grid using spectral clustering, the partitioning is based on the Laplacian matrix L, derived from the similarity matrix W, i.e., L = DW, where D is obtained from the following formula:

[0082]

[0083] After obtaining the Laplacian matrix L, its eigenvalues ​​are first decomposed to obtain a new matrix composed of its eigenvectors. Then, the K-Means algorithm is used to divide the grid into r+1 clusters based on the new matrix. Compared with other methods, spectral clustering provides an effective clustering solution by reducing computational complexity and better adapting to data distribution characteristics. For each cluster, several simple and effective methods can be used to select the sampling grid (i.e., cluster centers), such as degree centrality and eigenvector centrality. This embodiment mainly uses degree centrality to achieve this purpose. Degree centrality is one of the simplest centrality measures, which evaluates the importance of a node by calculating its degree (i.e., the number of edges directly connected to it).

[0084] Preferably, this embodiment performs the following steps for each cluster to select the cluster center as the sampling grid, which may include the following steps:

[0085] Calculate node degree: For each node in a cluster, calculate its degree, which is the number of edges directly connected to that node. This is used as a measure of node degree centrality. Sort nodes: Based on the calculated node degree, sort all nodes in the cluster in descending order. Nodes with higher degrees are listed first, indicating stronger connectivity and greater importance within the cluster. Select cluster centers: From the sorted list of nodes, select one or more nodes with the highest degree as the cluster centers of that cluster, serving as representative points for the sampling grid. Form the sampling grid: Combine the selected cluster centers from each cluster to form the sampling grid for the entire dataset. This sampling grid reflects the structural characteristics of the dataset and is used for subsequent data analysis, sampling, or visualization of clustering results.

[0086] After completing the preceding process, the sampling vector h can be obtained. (T+1) This vector corresponds one-to-one with N grids. Unsampled grids are initialized to 0 in the sampling vector. Thus, in this embodiment, the initial sensing matrix [X] of time slot T+1 can be obtained. (T) ,h (T +1) In the matrix filling inference process, matrix factorization is used to extract two factor matrices closely related to the spatiotemporal features of the grid. To accurately derive these factor matrices, the initial spatiotemporal representation of the T+1 time slot grid is first obtained, and the spatiotemporal representation is used for training to output two initial factor matrices. Specific steps are as follows: Figure 4 As shown.

[0087] First, augment the grid diagram and the initial sensing matrix [X (T) ,h (T+1) Input spatiotemporal fusion module, output spatiotemporal representation Then, through neural network training, from spatiotemporal representation Derive two initial factor matrices and Next, the two initial factor matrices are trained to obtain the final factor matrix, which is expressed by the following formula:

[0088]

[0089] in,‖‖ F Let F-norm, Z (T+1) [1,1,…,1,z] (T+1) The simplest expression for ], z (T+1) This indicates whether the grid in time slot T+1 was sampled; if sampled, it is marked as 1, otherwise it is marked as 0.

[0090] After obtaining the final factor matrix U (T+1) and V (T+1) Then, via U (T+1) V (T+1)T The data at the unsampled locations is deduced, and combined with the sampled data, this yields all the collected grid data.

[0091] In practical applications, assume there is a grid map G and its historical sensing matrix X collected over T time slots. (T) To obtain data from the T+1 time slot with high accuracy, the sensor matrix X is first determined. (T) The rank of the lattice graph G is assumed to be r; then the sensing matrix X of the lattice graph G is... (T) The input is processed by the spatiotemporal fusion module to obtain representation B. (T) Then use B (T) Execution graph augmentation can refine the mesh graph G into an augmented mesh graph. Subsequently, the augmented grid diagram was analyzed. Perform spectral clustering to obtain r+1 clusters, and select the grid with the highest degree in each cluster as the sampling grid. After sampling, the sensing matrix X... (T) and sampling vector h (T+1) The spatiotemporal representation is obtained by inputting the spatiotemporal fusion module. Spatiotemporal representations obtained through neural network training Obtain two initial factor matrices and Their update process is shown in Algorithm 1:

[0092]

[0093]

[0094] The final factor matrix U is obtained. (T+1) and V (T+1)Then, calculate U (T+1) V (T+1)T This result approximates the perception matrix X. (T +1) The last column contains the inferred sensing data for the T+1 time slot, x (T+1) byU (T+1) V (T+1)T The T+1 column and sampling vector h (T +1) constitute.

[0095] In summary, this embodiment proposes an innovative and efficient method for collecting IoT data. This method transforms the traditional data collection process into an active sampling optimization problem to achieve low-cost and high-precision data collection. This method combines a matrix filling algorithm with an optimized sampling strategy to ensure information is obtained from the most critical locations, thereby reducing unnecessary sampling costs.

[0096] Furthermore, this embodiment integrates grid diagrams and time-series data, utilizing a spatiotemporal fusion module to uncover deep spatiotemporal correlations between grids. This method helps in selecting more critical sampling locations, thereby improving the accuracy of data inference.

[0097] Furthermore, this embodiment performs clustering based on the similarity of grid data patterns and uses the cluster centers as sampling locations. This strategy effectively covers global spatiotemporal information, reduces redundant information in data acquisition, and improves the representativeness and efficiency of data sampling.

[0098] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0099] The above embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of protection of the present invention. Any non-substantial changes and substitutions made by those skilled in the art based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A method for efficient collection of IoT data based on active sampling, characterized in that, Includes the following steps: The target area is divided into N grids, and sensor data for each grid within T historical time slots are acquired to form a sensor matrix of size N×T. X (T) Among them, according to the sensing matrix X (T) Given the rank r, the minimum sampling cost required to determine the next time slot T+1 is r+1; The mesh graph is augmented by using a spatiotemporal fusion module to mine the deep relationships and structures between meshes to obtain an augmented mesh graph. The augmented grid graph is divided into r+1 clusters using spectral clustering, and at least one sampling grid is selected from each cluster. The selected sampling grid is sampled to obtain the sampling vector. h (T+1) and combine it with the sensing matrix X (T) Combined, an initial T+1 time slot sensing matrix is ​​formed. X (T) , h (T+1) ]; The augmented mesh diagram and the initial sensing matrix of the T+1 time slot are input into the spatiotemporal fusion module to obtain the spatiotemporal representation, and two initial factor matrices are derived through neural network training. The two initial factor matrices are iteratively updated to obtain the final factor matrix. U (T+1) and V (T+1) ; Using the final factor matrix U (T+1) and V (T+1) The data at the unsampled locations are calculated, and combined with the sampled data, all the collected grid data are obtained.

2. The method according to claim 1, characterized in that: When determining the minimum sampling cost, the historical sensing matrix is ​​known. X (T) Assume its rank is r , X (T+1) The rank is at most r +1, X (T+1) =[ X (T) , x (T+1) Therefore, based on the fundamental properties of matrices, the minimum sampling cost is... r +1; in, X (T+1) The space is made of r Spanned by +1 linearly independent vectors.

3. The method according to claim 1, characterized in that: During augmentation, deep relationships and structures between grids are mined based on historical grid data, i.e., the grid graph is analyzed. Augmentation is performed to obtain an augmented mesh graph, in which V ={ v 1, v 2,…, v N } is a collection of grids. It is the set of edges; the adjacency matrix of the mesh graph G is denoted as . , a ij ∈ A ,like v i , v j ∈ V , ,but a ij =1, otherwise 0.

4. The method according to claim 3, characterized in that: For grid v i Its time representation across multiple time steps s i It can be represented as s i =TC (m) ( b i ), where TC represents temporal convolution, m This indicates multiple temporal convolutions to aggregate information from all time steps. As an intermediate product of the spatiotemporal fusion module, it is expressed by the following formula: Where, 1≤ i ≤ N TC represents temporal convolution, and SC represents spatial convolution. These represent different stages of representation. D It is a representation dimension. and The time dimension is the result of convolution. After stacking multiple blocks, the final representation of the grid can be obtained. .

5. The method according to claim 4, characterized in that: The similarity between two grids is measured using a time-represented cosine distance. v i and grid v j The similarity between them is expressed by the following formula: Where, 1≤ j ≤ N A similarity matrix can be obtained using the formula. All diagonal elements are equal to 1. w ij The larger the value, the more similar the data patterns between grids, and vice versa.

6. The method according to claim 5, characterized in that: Based on the similarity matrix W Reassess the adjacency relationships between grids, grid v i and grid v j The edge between ε ij The probability of adding or deleting follows a Bernoulli distribution with probability . p ij It can be expressed as the following formula: in, Representation matrix W The maximum value excluding the diagonal elements. This represents their average value.

7. The method according to claim 6, characterized in that: If grid v i and grid v j Physically adjacent, by probability ρ ij Delete edge ε ij , ρ ij With similarity w ij The value decreases as the grid increases; v i and grid v j If the physical locations are not adjacent, then use 1- ρ ij The probability of adding an edge between the two is related to the similarity. w ij The trend remains consistent; Obtain augmented mesh diagram .

8. The method according to any one of claims 1 to 7, characterized in that: When using spectral clustering to partition augmented mesh graphs, the partitioning is based on the Laplacian matrix. L From the similarity matrix W It is derived that, , D It is obtained from the following formula: Obtain the Laplace matrix L Then, its eigenvalues ​​are first decomposed to obtain its eigenvectors. A new matrix is ​​formed; then the K-Means algorithm is used to divide the grid according to the new matrix. r +1 cluster.

9. The method according to any one of claims 1 to 7, characterized in that: For each cluster, perform the following steps to select cluster centers as the sampling grid: Calculate node degree: For each node in the cluster, calculate its degree, that is, count the number of edges directly connected to the node, and use this as a measure of node degree centrality. Sorting nodes: Based on the calculated node degree, all nodes in the cluster are sorted in descending order. Nodes with higher degrees are listed first, indicating that they have stronger connectivity and higher importance in the cluster. Cluster center selection: From the sorted list of nodes, select one or more nodes with the highest degree as the cluster centers of the cluster, and use them as representative points of the sampling grid; Forming a sampling grid: The selected cluster centers in each cluster are combined to form a sampling grid for the entire dataset. This sampling grid can reflect the structural characteristics of the dataset and can be used for subsequent data analysis, sampling, or visualization of clustering results.

10. The method according to claim 7, characterized in that: Expand the grid diagram and the initial sensing matrix [ X (T) , h (T+1) Input spatiotemporal fusion module, output spatiotemporal representation ; Through neural network training, spatiotemporal representations Derive two initial factor matrices and ; The final factor matrix is ​​obtained by training two initial factor matrices, and this process is expressed by the following formula: in, Denotes the F-norm, Z (T+1) [1,1,…,1, z (T+1) A simple expression of ] z (T+1) Instructions are given in T If the +1 time slot grid is sampled, mark it as 1; otherwise mark it as 0. After obtaining the final factor matrix U (T+1) and V (T+1) Afterwards, through The data at the unsampled locations is deduced, and combined with the sampled data, this yields all the collected grid data.

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