A method for filling missing values ​​in spatiotemporal data based on graph structure learning

Abstract

The present invention relates to the field of artificial intelligence technology, and provides a method for filling missing values ​​of spatiotemporal data based on graph structure learning. The method decomposes spatiotemporal data with missing values ​​into spatial correlation information and time series signals according to signal categories; constructs training labels and input signals according to time series signals; projects the input signals into a high-dimensional latent space, obtains time series representations through a cross-time representation extraction module; obtains node scale representations through a node scale space learning module; obtains feature scale representations through a feature scale space learning module; obtains reconstructed time series signals through a cross-feature representation learning module; forms a filling framework with modules that process input signals to obtain reconstructed time series signals, and inputs the time series signals into the trained filling framework to obtain complete spatiotemporal data. The present invention is significantly superior to existing methods in terms of filling accuracy indicators, and can significantly improve the performance of downstream spatiotemporal analysis tasks.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a method for filling missing values ​​in spatiotemporal data based on graph structure learning. Background Art

[0002] Spatiotemporal data is a type of data with intrinsic spatial and temporal patterns, which is usually continuously recorded by multiple sensors at sites in different geographical locations. Spatiotemporal data is widely used in tasks such as air quality monitoring, traffic condition forecasting, and weather forecasting. However, due to sensor failure or communication interference, missing values ​​often appear in spatiotemporal data. Effective spatiotemporal data missing value filling technology can not only repair these missing values ​​and ensure the integrity and accuracy of the data set, but also significantly improve the performance of downstream tasks such as traffic forecasting. Therefore, researching and developing efficient methods for filling missing values ​​in spatiotemporal data is crucial for application analysis that relies on accurate and complete data.

[0003] Spatial correlation in spatiotemporal data is usually given in the form of a graph, where nodes represent sites where spatiotemporal data are recorded, and edges reflect the geographic distance or spatial connectivity between each site. Existing methods usually use the given graph structure and graph neural network in spatiotemporal data to capture spatial dependencies, but this approach implicitly assumes that for all features recorded at each site, the global spatial dependencies of the same features recorded by the same type of sensors at different sites fully satisfy the spatial dependencies implied in the given graph structure. However, for different features, their global spatial dependencies may be different, and there may also be dependencies between different features recorded within each site. Using only the given graph structure as a reference for graph neural networks to capture spatial dependencies cannot model the fine-grained global spatial dependencies between different features in reality, nor can it model the spatial dependencies between different features within a site that are common to all sites. Therefore, due to the lack of guidance of fine-grained spatial dependencies, existing methods cannot accurately refer to the observed values ​​of other related features when filling in missing values ​​in spatiotemporal data, which affects the filling effect and thus the performance of subsequent spatiotemporal data analysis. Summary of the invention

[0004] The present invention aims to solve at least one of the technical problems existing in the related art. To this end, the present invention provides a method for filling missing values ​​in spatiotemporal data based on graph structure learning. The present invention effectively utilizes the known inherent spatial correlation in spatiotemporal data and the learned various graph structure information through graph diffusion convolution, and promotes the modeling of spatial dependencies of spatiotemporal data. The present invention is significantly better than the existing methods in filling accuracy indicators in three spatiotemporal data sets with real missing values. When performing downstream analysis on the data set filled by the present invention, the present invention can significantly improve the performance of downstream spatiotemporal analysis tasks.

[0005] The present invention provides a method for filling missing values ​​of spatiotemporal data based on graph structure learning, comprising:

[0006] S1: Obtain spatiotemporal data with missing values ​​for multiple nodes, decompose the spatiotemporal data into spatial correlation information and time series signals according to signal categories, and construct training labels and input signals according to the time series signals;

[0007] Spatiotemporal data refers to data continuously recorded by various sensors at sites in different geographical locations, with nodes representing real sites.

[0008] S2: Project the input signal into a high-dimensional latent space to obtain a latent space representation, and then input the latent space representation into a cross-time representation extraction module to obtain a temporal representation.

[0009] S3: learning the scale global graph structure of different nodes through the node scale space learning module, taking the node scale global graph structure as a reference, inputting the spatial correlation information and temporal representation into the node scale space learning module to obtain the node scale representation;

[0010] S4: learning the common feature scale graph structure between different features of all nodes through the feature scale space learning module, taking the common feature scale graph structure as a reference, inputting the time series representation into the feature scale space learning module to obtain the feature scale representation;

[0011] S5: splicing and projecting the time series representation, node scale representation and feature scale representation, inputting them into the cross-feature representation learning module, and obtaining the reconstructed time series signal after projection;

[0012] S6: The cross-time representation extraction module, the node scale space learning module, the feature scale space learning module and the feature scale space learning module form a filling framework, and the filling framework is trained according to the training labels and the reconstructed time series signal;

[0013] S7: Input the time series signal containing missing values ​​in the spatiotemporal data into the trained filling framework to obtain the output vector, and obtain the complete spatiotemporal data by referring to the output vector.

[0014] According to a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention, the spatial correlation information is composed of a static graph, an adjacency matrix is ​​constructed through the static graph, and the spatial relationship information of the static graph is represented by the adjacency matrix.

[0015] According to a method for filling missing values ​​in spatiotemporal data based on graph structure learning provided by the present invention, the method also includes constructing a first binary mask matrix with the same scale as the time series signal according to the actual existing positions of the missing values ​​of the spatiotemporal data, and initializing all values ​​of the first binary mask matrix with 1; traversing the readings of the features of each node corresponding to the time series signal at each moment, and if the readings are missing, setting the corresponding positions of the first binary mask matrix to 0.

[0016] According to a method for filling missing values ​​in spatiotemporal data based on graph structure learning provided by the present invention, the method also includes randomly selecting observation values ​​in a time series signal as training labels, forming an input signal with observation values ​​other than the training labels, constructing a second binary mask matrix based on the training labels, initializing it with 1, traversing the training labels, and setting the elements corresponding to the missing positions to 0.

[0017] According to a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention, the step S2 includes:

[0018] S21: Project the input signal into a high-dimensional latent space through a linear projection operation to obtain a representation in the latent space. The calculation expression of the representation in the latent space is:

[0019]

[0020] in, is the representation in the latent space, is the input signal, is the projected linear layer;

[0021] S22: The representation in the latent space is divided into all nodes and all features, and the time dependency of each feature on each node after the division is mined through the self-attention mechanism to obtain information about the feature. The output component of is calculated as:

[0022]

[0023]

[0024]

[0025]

[0026] in, Representation in latent space About Features The weight, The characteristics recorded on the node The query vector is The characteristics recorded on the node The key-value vector of The characteristics recorded on the node The value vector of The features that need to be learned The query projection matrix, The features that need to be learned The key-value projection matrix, The features that need to be learned The value of the projection matrix, is the normalized exponential function, is the number of channels, For the characteristics The output component of is transposed;

[0027] S23: The features recorded on each node The output component After splicing, we get the time series representation, and the calculation expression is:

[0028]

[0029] in, For timing representation, is the concatenation function,

[0030] The process of extracting temporal representation from latent space representation is the process of building a cross-temporal representation extraction module.

[0031] According to a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention, the step S3 includes:

[0032] S31: Record node features through sensors, assign source node embedding vectors and target node embedding vectors to each different feature recorded by each sensor, and use the source node embedding vector to obtain the influence corresponding to each node. The calculation expression is:

[0033]

[0034] in, are the features recorded by the sensor, Features The source node embedding vector of is the influence corresponding to the node, is the projected linear layer;

[0035] S32: Use the Hadamard product to combine the influence corresponding to the node and the source node embedding vector so that the edge with the node corresponding to the influence as the source point has the maximum weight. The calculation expression is:

[0036]

[0037] in, is the corrected source node embedding vector,

[0038] S33: Calculate the features The adjacency matrix corresponding to the global node scale metagraph of is calculated as:

[0039]

[0040] in, Features The adjacency matrix corresponding to the global node scale metagraph of is the normalized exponential function, is the linear rectification activation function, is the target node embedding vector, for The transpose of

[0041] S34: Using the spatial correlation information and the learned global node scale meta-graph, the node scale representation of the feature is learned through graph diffusion convolution. The calculation expression is:

[0042]

[0043] in, Features The node scale representation of For timing characterization About Features The weight, is the number of steps of the graph diffusion operation, For the The first graph convolution kernel that needs to be learned in the first step is For the The second graph convolution kernel that needs to be learned in the next step is For the The third graph convolution kernel that needs to be learned in the next step is is the out-degree matrix of the adjacency matrix, for The inverse matrix of is the in-degree matrix of the adjacency matrix, for The inverse matrix of is the adjacency matrix of spatial correlation information, for The transpose of

[0044] S35: The node scale representations of each feature are concatenated to obtain the node scale representation. The calculation expression of the node scale representation is:

[0045]

[0046] in, is the node scale representation, is the splicing function;

[0047] The process of learning the global node scale meta-graph and extracting node scale representation is the process of constructing a node scale space learning module.

[0048] According to a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention, the step S4 includes:

[0049] S41: Assign a source feature embedding vector and a target feature embedding vector to each feature recorded by each sensor, and use the source node source feature embedding vector to obtain the influence corresponding to each feature. The calculation expression is:

[0050]

[0051] in, For each feature, is the source feature embedding vector, is the projected linear layer;

[0052] S42: The influence and source feature embedding vectors are combined using the Hadamard product, so that in the learned feature scale graph structure, the edge whose node corresponding to the influence is the source point has the largest weight.

[0053] The calculation expression is:

[0054]

[0055] in, is the corrected source feature embedding vector,

[0056] S43: Calculate the adjacency matrix corresponding to the characteristic scale metagraph for all nodes. The calculation expression is:

[0057]

[0058] in, is the adjacency matrix corresponding to the characteristic scale metagraph for all nodes, is the target feature embedding vector, for The transpose of is the normalized exponential function, is the linear rectification activation function;

[0059] S44: Arrange the time series representations by features, refer to the learned feature scale meta-graph, learn the feature scale representation through graph diffusion convolution, and the calculation expression is:

[0060]

[0061] in, is the characteristic scale representation, is the number of steps of the graph diffusion operation, For the The graph convolution kernel that needs to be learned in the next step, It is the temporal representation after arrangement;

[0062] The process of learning the feature scale meta-graph and extracting the feature scale representation constitutes the feature scale learning module.

[0063] According to a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention, the step S5 includes:

[0064] S51: The time series representation, node scale representation and feature scale representation are concatenated and projected using a linear layer to obtain a representation. The calculation expression is:

[0065]

[0066] in, To characterize, is the projected linear layer, is the concatenation function, For timing representation, is the node scale representation, Characterize the characteristic scale;

[0067] S52: The representation is divided according to the timestamp, and the self-attention mechanism is used to calculate the corresponding cross-feature representation for the component of each timestamp corresponding to the representation. The calculation expression is:

[0068]

[0069]

[0070]

[0071]

[0072] in, For timestamp The representation of For timestamp The query vector is For timestamp The key-value vector of For timestamp The value vector of is the first parameter matrix to be learned, is the second parameter matrix to be learned, is the third parameter matrix that needs to be learned, is the number of channels, For timestamp The corresponding cross-feature representation, is the normalized exponential function, is transposed;

[0073] S53: Concatenate the cross-feature representations corresponding to all timestamps to form a cross-feature representation. The calculation expression is:

[0074]

[0075] in, For cross-feature representation,

[0076] S54: After projecting the cross-feature representation, a reconstructed time series signal is obtained, and the calculation expression is:

[0077]

[0078] in, is the reconstructed timing signal,

[0079] The process of extracting cross-feature representations from representations constitutes the cross-feature representation learning module.

[0080] According to a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention, the method further includes, in the step S6, training the learnable parameters of each module in the framework, and the objective function to be minimized during training is:

[0081]

[0082] in, is the objective function to be minimized for training, is the expectation about the timing signal, is the square value after L2 regularization, is the training label, is the second binary mask matrix, is the reconstructed timing signal.

[0083] According to a method for filling missing values ​​in spatiotemporal data based on graph structure learning provided by the present invention, the method further includes, in the step S7, setting a time series signal containing missing values ​​in the spatiotemporal data as an input signal, processing it through a trained filling framework to obtain a reconstructed time series signal, using the reconstructed time series signal as an output vector, and obtaining complete spatiotemporal data with reference to the output vector:

[0084]

[0085] in, For complete spatiotemporal data, is the reconstructed timing signal, is the first binary mask matrix, It is a time series signal containing missing values ​​in spatiotemporal data.

[0086] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0087] The present invention provides a method for filling missing values ​​in spatiotemporal data based on graph structure learning, which is significantly superior to existing methods in terms of filling accuracy indicators. When downstream analysis is performed on the data set filled by the present invention, the performance of downstream spatiotemporal analysis tasks can be significantly improved.

[0088] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0090] Figure 1 It is a flow chart of a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention.

[0091] Figure 2 It is a schematic diagram of a filling framework of a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention.

[0092] Figure 3 It is a schematic diagram of a node scale space learning module of a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention.

[0093] Figure 4 It is a schematic diagram of a characteristic scale space learning module of a method for filling missing values ​​of spatiotemporal data based on graph structure learning provided by the present invention.

[0094] Figure 5 This is a performance effect diagram of the application of a method for filling missing values ​​in spatiotemporal data based on graph structure learning and other methods provided by the present invention in downstream analysis tasks. DETAILED DESCRIPTION

[0095] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme in the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0096] In the description of the embodiments of the present invention, it should be noted that the terms “first”, “second” and “third” are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0097] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiment of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0098] Combine the following Figures 1 to 5 The present invention describes a method for filling missing values ​​of spatiotemporal data based on graph structure learning.

[0099] like Figure 1 As shown, a method for filling missing values ​​of spatiotemporal data based on graph structure learning includes:

[0100] S1: Obtain spatiotemporal data with missing values ​​for multiple nodes, decompose the spatiotemporal data into spatial correlation information and time series signals according to signal categories, and construct training labels and input signals according to the time series signals;

[0101] Spatiotemporal data refers to data continuously recorded by various sensors at sites in different geographical locations, with nodes representing real sites.

[0102] The spatial correlation information is composed of a static graph, an adjacency matrix is ​​constructed through the static graph, and the spatial relationship information of the static graph is represented by the adjacency matrix;

[0103] Obtain spatiotemporal data with missing values ​​for multiple sites, use nodes to represent sites in reality, obtain spatiotemporal data with missing values ​​for multiple nodes, and decompose the spatiotemporal data with missing values ​​into spatial correlation information according to signal categories. and timing signals , where spatial correlation information It is composed of static graphs, i.e. ,in, is a set of nodes, each of which represents a site in reality. is a set of edges, each edge represents a known fixed spatial relationship between a pair of nodes; the adjacency matrix Representation diagram Spatial relationship information, adjacency matrix Elements in Reaction Edge Collection The edge The corresponding weights, where the nodes , All belong to the node set .

[0104] According to the actual existence position of the missing values ​​of the spatiotemporal data, the first binary mask matrix with the same scale as the time series signal is constructed, and all values ​​of the first binary mask matrix are initialized with 1; the readings of each feature of each node at each moment of the time series signal are traversed. If the reading is missing, the corresponding position of the first binary mask matrix is ​​set to 0.

[0105] Randomly select some observations in the time series signal as training labels, and use the observations other than the training labels to form the input signal. Construct a second binary mask matrix based on the training labels and initialize it with 1. Traverse the training labels and set the elements corresponding to the missing positions to 0.

[0106] S2: Project the input signal into a high-dimensional latent space to obtain a latent space representation, and then input the latent space representation into a cross-time representation extraction module to obtain a temporal representation.

[0107] S21: Project the input signal into a high-dimensional latent space through a linear projection operation to obtain a representation in the latent space. The calculation expression of the representation in the latent space is:

[0108]

[0109] in, is the representation in the latent space, is the input signal, is the projected linear layer;

[0110] S22: The representation in the latent space is divided into all nodes and all features, and the time dependency of each feature on each node after the division is mined through the self-attention mechanism to obtain information about the feature. The output component of is calculated as:

[0111]

[0112]

[0113]

[0114]

[0115] in, Representation in latent space About Features The weight, The characteristics recorded on the node The query vector is The characteristics recorded on the node The key-value vector of The characteristics recorded on the node The value vector of The features that need to be learned The query projection matrix, The features that need to be learned The key-value projection matrix, The features that need to be learned The value of the projection matrix, is the normalized exponential function, is the number of channels, For the characteristics The output component of is transposed;

[0116] S23: The features recorded on each node The output component After splicing, we get the time series representation, and the calculation expression is:

[0117]

[0118] in, For timing representation, is the concatenation function,

[0119] The process of extracting temporal representation from latent space representation is the process of building a cross-temporal representation extraction module.

[0120] S3: learning the scale global graph structure of different nodes through the node scale space learning module, taking the node scale global graph structure as a reference, inputting the spatial correlation information and temporal representation into the node scale space learning module to obtain the node scale representation;

[0121] S31: Record node features through sensors, assign source node embedding vectors and target node embedding vectors to each different feature recorded by each sensor, and use the source node embedding vector to obtain the influence corresponding to each node. The calculation expression is:

[0122]

[0123] in, are the features recorded by the sensor, Features The source node embedding vector of is the influence corresponding to the node, is the projected linear layer;

[0124] S32: Use the Hadamard product to combine the influence corresponding to the node and the source node embedding vector so that the edge with the node corresponding to the influence as the source point has the maximum weight. The calculation expression is:

[0125]

[0126] in, is the corrected source node embedding vector,

[0127] S33: Calculate the characteristics The adjacency matrix corresponding to the global node scale metagraph of is calculated as:

[0128]

[0129] in, Features The adjacency matrix corresponding to the global node scale metagraph of is the normalized exponential function, is the linear rectification activation function, is the target node embedding vector, for The transpose of

[0130] S34: Using the spatial correlation information and the learned global node scale meta-graph, the node scale representation of the feature is learned through graph diffusion convolution. The calculation expression is:

[0131]

[0132] in, Features The node scale representation of For timing characterization About Features The weight, is the number of steps of the graph diffusion operation, For the The first graph convolution kernel that needs to be learned in the first step is For the The second graph convolution kernel that needs to be learned in the next step is For the The third graph convolution kernel that needs to be learned in the next step is is the out-degree matrix of the adjacency matrix, for The inverse matrix of is the in-degree matrix of the adjacency matrix, for The inverse matrix of is the adjacency matrix of spatial correlation information, for The transpose of

[0133] S35: The node scale representations of each feature are concatenated to obtain the node scale representation. The calculation expression of the node scale representation is:

[0134]

[0135] in, is the node scale representation, is the splicing function;

[0136] The process of learning the global node scale meta-graph and extracting node scale representation is the process of building a node scale space learning module, such as Figure 3 shown.

[0137] S4: learning the common feature scale graph structure between different features of all nodes through the feature scale space learning module, taking the common feature scale graph structure as a reference, inputting the time series representation into the feature scale space learning module to obtain the feature scale representation;

[0138] S41: Assign a source feature embedding vector and a target feature embedding vector to each feature recorded by each sensor, and use the source node source feature embedding vector to obtain the influence corresponding to each feature. The calculation expression is:

[0139]

[0140] in, For each feature, is the source feature embedding vector, is the projected linear layer;

[0141] S42: The influence and source feature embedding vectors are combined using the Hadamard product, so that in the learned feature scale graph structure, the edge whose node corresponding to the influence is the source point has the largest weight.

[0142] The calculation expression is:

[0143]

[0144] in, is the corrected source feature embedding vector,

[0145] S43: Calculate the adjacency matrix corresponding to the characteristic scale metagraph for all nodes. The calculation expression is:

[0146]

[0147] in, is the adjacency matrix corresponding to the characteristic scale metagraph for all nodes, is the target feature embedding vector, for The transpose of is the normalized exponential function, is the linear rectification activation function;

[0148] S44: Arrange the time series representations by features, refer to the learned feature scale meta-graph, learn the feature scale representation through graph diffusion convolution, and the calculation expression is:

[0149]

[0150] in, is the characteristic scale representation, is the number of steps of the graph diffusion operation, For the The graph convolution kernel that needs to be learned in the next step, It is the temporal representation after arrangement;

[0151] The process of learning the feature scale meta-graph and extracting the feature scale representation constitutes the feature scale learning module, e.g. Figure 4 shown.

[0152] S5: splicing and projecting the time series representation, node scale representation and feature scale representation, inputting them into the cross-feature representation learning module, and obtaining the reconstructed time series signal after projection;

[0153] S51: The time series representation, node scale representation and feature scale representation are concatenated and projected using a linear layer to obtain a representation. The calculation expression is:

[0154]

[0155] in, To characterize, is the projected linear layer, is the concatenation function, For timing representation, is the node scale representation, Characterize the characteristic scale;

[0156] S52: The representation is divided according to the timestamp, and the self-attention mechanism is used to calculate the corresponding cross-feature representation for the component of each timestamp corresponding to the representation. The calculation expression is:

[0157]

[0158]

[0159]

[0160]

[0161] in, For timestamp The representation of For timestamp The query vector is For timestamp The key-value vector of For timestamp The value vector of is the first parameter matrix to be learned, is the second parameter matrix to be learned, is the third parameter matrix that needs to be learned, is the number of channels, For timestamp The corresponding cross-feature representation, is the normalized exponential function, is transposed;

[0162] S53: Concatenate the cross-feature representations corresponding to all timestamps to form a cross-feature representation. The calculation expression is:

[0163]

[0164] in, For cross-feature representation,

[0165] S54: After projecting the cross-feature representation, a reconstructed time series signal is obtained, and the calculation expression is:

[0166]

[0167] in, is the reconstructed timing signal,

[0168] The process of extracting cross-feature representations from representations constitutes the cross-feature representation learning module.

[0169] like Figure 2 As shown, S6: the cross-time representation extraction module, the node scale space learning module, the feature scale space learning module and the feature scale space learning module form a filling framework, and the filling framework is trained according to the training labels and the reconstructed time series signal;

[0170] The steps of processing the input signal to obtain the reconstructed time series signal are combined into a filling framework, and the learnable parameters of each module in the framework are trained. The objective function to be minimized during training is:

[0171]

[0172] in, is the objective function to be minimized for training, is the expectation about the timing signal, is the square value after L2 regularization, is the training label, is the second binary mask matrix, is the reconstructed timing signal.

[0173] S7: Input the time series signal containing missing values ​​in the spatiotemporal data into the trained filling framework to obtain the output vector, and obtain the complete spatiotemporal data by referring to the output vector.

[0174] The time series signal containing missing values ​​in the spatiotemporal data is set as the input signal, and the reconstructed time series signal is obtained through the trained filling framework processing. The reconstructed time series signal is used as the output vector, and the complete spatiotemporal data is obtained by referring to the output vector;

[0175]

[0176] For complete spatiotemporal data, is the reconstructed timing signal, is the first binary mask matrix, It is a time series signal containing missing values ​​in spatiotemporal data.

[0177] The filling accuracy of a method for filling missing values ​​of spatiotemporal data based on graph structure learning of the present invention is verified under different missing rates: filling is performed on three spatiotemporal data sets with real missing values, namely Dutch Wind, Beijing Meteorology (BeijingMEO) and London Air Quality (LondonAQ). Two indicators for evaluating filling accuracy, root mean square error (RMSE) and mean absolute error (MAE), are used. Each group of experiments is repeated 5 times, and the average value is reported. Table 1 shows the filling experimental results of the present invention and other methods on the Dutch Wind dataset at different missing rates, Table 2 shows the filling experimental results of the present invention and other methods on the Beijing MEO dataset at different missing rates, and Table 3 shows the filling experimental results of the present invention and other methods on the London AQ dataset at different missing rates.

[0178] Table 1. Experimental results of the present invention and other methods on the DutchWind dataset at different missing rates

[0179]

[0180] Table 2. Experimental results of the present invention and other methods on the BeijingMEO dataset at different missing rates

[0181]

[0182] Table 3. Experimental results of the present invention and other methods on the LondonAQ dataset at different missing rates

[0183]

[0184] It can be seen from Tables 1, 2 and 3 that as the missing rate increases, the filling performance of most methods will decrease, and the existing spatiotemporal filling methods are not significantly better than the multivariate time series filling methods, because the existing spatiotemporal filling methods can only use the given graph structure, which affects the modeling of spatial dependencies. However, the present invention has achieved better performance than other existing methods on different data sets with different missing rates. This is because the present invention accurately models fine-grained spatial dependencies through graph structure learning of nodes and feature scales.

[0185] In this example, the application effect of the method of the present invention on the downstream time series analysis task is verified by filling the missing spatiotemporal data set LondonAQ in the real world. First, the missing values ​​in the LondonAQ data set are filled, and the average PM2.5 concentration of the CD1 station in the next 6 hours is predicted using the Adaboost regressor based on the recorded data of the previous 12 hours, and the analysis effect of the task is evaluated using the RMSE and MAE indicators. Figure 5 Figure (a) shows the RMSE indicator evaluation result. Figure 5 Figure (b) shows the MAE indicator evaluation result. Figure 5 From the comparison of the application performance effects of the downstream analysis tasks on the LondonAQ dataset, it can be found that the present invention can effectively improve the performance of the downstream analysis tasks.

[0186] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for filling missing values ​​in spatiotemporal data based on graph structure learning, characterized in that: include: S1: Obtain spatiotemporal data with missing values ​​for multiple nodes, decompose the spatiotemporal data into spatial correlation information and time series signals according to signal categories, and construct training labels and input signals according to the time series signals; Spatiotemporal data refers to data continuously recorded by various sensors at sites in different geographical locations, with nodes representing real sites. S2: Project the input signal into a high-dimensional latent space to obtain a latent space representation, and then input the latent space representation into a cross-time representation extraction module to obtain a temporal representation. S3: learning the scale global graph structure of different nodes through the node scale space learning module, taking the node scale global graph structure as a reference, inputting the spatial correlation information and temporal representation into the node scale space learning module to obtain the node scale representation; S31: Record node features through sensors, assign source node embedding vectors and target node embedding vectors to each different feature recorded by each sensor, and use the source node embedding vector to obtain the influence corresponding to each node. The calculation expression is: in, are the features recorded by the sensor, Features The source node embedding vector of is the influence corresponding to the node, is the projected linear layer; S32: Use the Hadamard product to combine the influence corresponding to the node and the source node embedding vector so that the edge with the node corresponding to the influence as the source point has the maximum weight. The calculation expression is: in, is the corrected source node embedding vector, S33: Calculate the characteristics The adjacency matrix corresponding to the global node scale metagraph of is calculated as: in, Features The adjacency matrix corresponding to the global node scale metagraph of is the normalized exponential function, is the linear rectification activation function, is the target node embedding vector, for The transpose of S34: Using the spatial correlation information and the learned global node scale meta-graph, the node scale representation of the feature is learned through graph diffusion convolution. The calculation expression is: in, Features The node scale representation of For timing characterization About Features The weight, is the number of steps of the graph diffusion operation, For the The first graph convolution kernel that needs to be learned in the first step is For the The second graph convolution kernel that needs to be learned in the next step is For the The third graph convolution kernel that needs to be learned in the next step is is the out-degree matrix of the adjacency matrix, for The inverse matrix of is the in-degree matrix of the adjacency matrix, for The inverse matrix of is the adjacency matrix of spatial correlation information, for The transpose of S35: The node scale representations of each feature are concatenated to obtain the node scale representation. The calculation expression of the node scale representation is: in, is the node scale representation, is the splicing function; The process of learning the global node scale meta-graph and extracting the node scale representation is the process of constructing the node scale space learning module; S4: learning the common feature scale graph structure between different features of all nodes through the feature scale space learning module, taking the common feature scale graph structure as a reference, inputting the time series representation into the feature scale space learning module to obtain the feature scale representation; S5: splicing and projecting the time series representation, node scale representation and feature scale representation, inputting them into the cross-feature representation learning module, and obtaining the reconstructed time series signal after projection; S6: The cross-time representation extraction module, the node scale space learning module, the feature scale space learning module and the feature scale space learning module form a filling framework, and the filling framework is trained according to the training labels and the reconstructed time series signal; S7: Input the time series signal containing missing values ​​in the spatiotemporal data into the trained filling framework to obtain the output vector, and obtain the complete spatiotemporal data by referring to the output vector.

2. According to claim 1, a method for filling missing values ​​of spatiotemporal data based on graph structure learning is characterized in that: The spatial correlation information is composed of a static graph, an adjacency matrix is ​​constructed through the static graph, and the spatial relationship information of the static graph is represented by the adjacency matrix.

3. According to the method for filling missing values ​​of spatiotemporal data based on graph structure learning according to claim 1, it is characterized in that: According to the actual existence positions of the missing values ​​of the spatiotemporal data, a first binary mask matrix with the same scale as the time series signal is constructed, and all values ​​of the first binary mask matrix are initialized with 1; the readings of the features of each node at each moment corresponding to the time series signal are traversed, and if the readings are missing, the corresponding positions of the first binary mask matrix are set to 0.

4. The method for filling missing values ​​of spatiotemporal data based on graph structure learning according to claim 1, characterized in that: Randomly select observations in the time series signal as training labels, and use the observations other than the training labels to form the input signal. Construct a second binary mask matrix based on the training labels and initialize it with 1. Traverse the training labels and set the elements corresponding to the missing positions to 0.

5. The method for filling missing values ​​of spatiotemporal data based on graph structure learning according to claim 1, characterized in that: The S2 step includes: S21: Project the input signal into a high-dimensional latent space through a linear projection operation to obtain a representation in the latent space. The calculation expression of the representation in the latent space is: in, is the representation in the latent space, is the input signal; S22: The representation in the latent space is divided into all nodes and all features, and the time dependency of each feature on each node after the division is mined through the self-attention mechanism to obtain information about the feature. The output component of is calculated as: in, Representation in latent space About Features The weight, The characteristics recorded on the node The query vector is The characteristics recorded on the node The key-value vector of The characteristics recorded on the node The value vector of The features that need to be learned The query projection matrix, The features that need to be learned The key-value projection matrix, The features that need to be learned The value of the projection matrix, is the number of channels, For the characteristics The output component of is transposed; S23: The features recorded on each node The output component After splicing, we get the time series representation, and the calculation expression is: The process of extracting temporal representation from latent space representation is the process of building a cross-temporal representation extraction module.

6. The method for filling missing values ​​of spatiotemporal data based on graph structure learning according to claim 1, characterized in that: The S4 step includes: S41: Assign a source feature embedding vector and a target feature embedding vector to each feature recorded by each sensor, and use the source node source feature embedding vector to obtain the influence corresponding to each feature. The calculation expression is: in, For each feature, is the source feature embedding vector, S42: The influence and source feature embedding vectors are combined using the Hadamard product, so that in the learned feature scale graph structure, the edge whose node corresponding to the influence is the source point has the largest weight. The calculation expression is: in, is the corrected source feature embedding vector, S43: Calculate the adjacency matrix corresponding to the characteristic scale metagraph for all nodes. The calculation expression is: in, is the adjacency matrix corresponding to the characteristic scale metagraph for all nodes, is the target feature embedding vector, for The transpose of S44: Arrange the time series representations by features, refer to the learned feature scale meta-graph, learn the feature scale representation through graph diffusion convolution, and the calculation expression is: in, is the characteristic scale representation, is the number of steps of the graph diffusion operation, For the The graph convolution kernel that needs to be learned in the next step, It is the temporal representation after arrangement; The process of learning the feature scale meta-graph and extracting the feature scale representation constitutes the feature scale learning module.

7. The method for filling missing values ​​of spatiotemporal data based on graph structure learning according to claim 1, characterized in that: The S5 step includes: S51: The time series representation, node scale representation and feature scale representation are concatenated and projected using a linear layer to obtain a representation. The calculation expression is: in, To characterize, is the node scale representation, Characterize the characteristic scale; S52: The representation is divided according to the timestamp, and the self-attention mechanism is used to calculate the corresponding cross-feature representation for the component of each timestamp corresponding to the representation. The calculation expression is: in, For timestamp The representation of For timestamp The query vector is For timestamp The key-value vector of For timestamp The value vector of is the first parameter matrix to be learned, is the second parameter matrix to be learned, is the third parameter matrix that needs to be learned, is the number of channels, For timestamp The corresponding cross-feature representation, is transposed; S53: Concatenate the cross-feature representations corresponding to all timestamps to form a cross-feature representation. The calculation expression is: in, For cross-feature representation, S54: After projecting the cross-feature representation, a reconstructed time series signal is obtained, and the calculation expression is: in, is the reconstructed timing signal, The process of extracting cross-feature representations from representations constitutes the cross-feature representation learning module.

8. The method for filling missing values ​​of spatiotemporal data based on graph structure learning according to claim 1, characterized in that: In step S6, the learnable parameters of each module in the framework are trained, and the objective function to be minimized during training is: in, is the objective function to be minimized for training, is the expectation about the timing signal, is the square value after L2 regularization, is the training label, is the second binary mask matrix, is the reconstructed timing signal.

9. The method for filling missing values ​​of spatiotemporal data based on graph structure learning according to claim 1, characterized in that: In the step S7, the time series signal containing missing values ​​in the spatiotemporal data is set as the input signal, and the reconstructed time series signal is obtained through the trained filling framework processing, and the reconstructed time series signal is used as the output vector, and the complete spatiotemporal data is obtained by referring to the output vector: in, For complete spatiotemporal data, is the reconstructed timing signal, is the first binary mask matrix, It is a time series signal containing missing values ​​in spatiotemporal data.

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