Multivariate time series missing value interpolation method and system based on dynamic graph learning

Abstract

The present invention relates to the field of artificial intelligence technology, and specifically discloses a method and system for interpolating missing values ​​of a multivariate time series based on dynamic graph learning, the method comprising: obtaining multivariate time series data with missing values; constructing a graph structure, adjusting the adjacency matrix of the graph structure through a graph neural network, and calculating an adaptive graph structure; the adaptive graph structure calculates forward interpolation values, backward interpolation values, and node embedding representations through an encoder and a decoder; using a multilayer perceptron aggregation to calculate predicted missing values; combining the predicted missing values ​​with the multivariate time series data with missing values ​​to obtain interpolated multivariate time series data. The present invention uses dynamic graph structure learning to model the correlation between variables at different time steps, and simultaneously learns the temporal dependency between variable correlation and time series, and effectively improves the accuracy of missing value interpolation by performing two-stage interpolation calculations on missing data using the learned representation.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a multivariate time series missing value interpolation method and system based on dynamic graph learning. Background Art

[0002] Electronic health records (EHR), as an important source of medical data, play a key role in clinical decision-making, disease monitoring, and health management. However, the missing EHR data is a common challenge, which is mainly caused by equipment failure, data collection difficulties, and different sampling rates. To solve this problem, researchers have proposed a variety of missing value interpolation methods. Traditional methods include filling with fixed values, such as the mean or zero of the variable, weighted average interpolation based on K nearest neighbors, and the widely used statistical method MICE multiple interpolation method for interpolation. In addition, there is matrix decomposition technology, which recovers missing data by decomposing the data matrix into a low-rank matrix.

[0003] With the development of deep learning technology, methods based on recurrent neural networks have begun to be used for missing value interpolation in EHR. These methods can better simulate the time series characteristics of EHR data. For example, BRITS uses a bidirectional RNN model, GRU-D performs multivariate time series interpolation based on gated recurrent units (GRU), and ImputeRNN combines medical knowledge and proposes a dual RNN model to simultaneously learn missing patterns and missing values. In addition, there are studies that interpolate missing values ​​by generating adversarial network frameworks.

[0004] In addition to deep learning methods, graph representation learning has also been introduced into the missing value imputation of EHR. For example, the GRAPE method regards variables and samples as nodes in the graph and observations as edges, transforming the missing value imputation problem into a link prediction problem in the graph. Graph structure learning (GSL), as a powerful tool for modeling real-world objects and their relationships, has been widely used in the research of graph neural networks (GNNs). The goal of GSL is to learn the optimal graph structure to improve the analysis of graph data. Existing GSL methods can be divided into metric-based methods, neural network-based methods, and adaptive methods, among which adaptive methods provide greater flexibility by treating the adjacency matrix as a free parameter.

[0005] In the field of time series forecasting, GSL is used to learn dependencies between variables to improve the accuracy of forecasts. The researchers demonstrated the powerful ability of GSL in capturing variable correlations by learning probability graphs, parameterizing graphs in a differentiable way, and extracting correlations between variables through graph learning modules.

[0006] In summary, although traditional EHR missing value interpolation methods are still effective in some cases, they often ignore the time dependency of the data and the complex correlation between variables, and the interpolation accuracy is not ideal. Summary of the invention

[0007] The present invention aims to solve the problem that the interpolation accuracy of missing values ​​in multivariate time series is not ideal. To this end, the present invention provides a multivariate time series missing value interpolation method and system based on dynamic graph learning, which uses dynamic graph structure learning to model the correlation between variables at different time steps, and simultaneously learns the temporal dependency between variable correlation and time series. The missing data is interpolated in two stages by using the representation learned in the above manner. The first stage calculates the bidirectional interpolation value, and the second stage calculates the predicted missing value, which effectively improves the accuracy of missing value interpolation.

[0008] The present invention provides a multivariate time series missing value interpolation method based on dynamic graph learning, and the technical scheme adopted is as follows: comprising:

[0009] Get multivariate time series data with missing values;

[0010] According to the multivariate time series data with missing values, a graph structure is constructed, an adjacency matrix of the graph structure is adjusted through a graph neural network, and an adaptive graph structure is calculated;

[0011] The adaptive graph structure is calculated by an encoder and a decoder to obtain a forward interpolation value, a backward interpolation value and a node embedding representation, and the encoder adopts a bidirectional gated recurrent unit to perform forward encoding and backward encoding on the adaptive graph structure respectively;

[0012] Aggregating the forward interpolation value, the backward interpolation value and the node embedding representation using a multi-layer perceptron to calculate the predicted missing value;

[0013] The predicted missing values ​​are combined with the multivariate time series data with missing values ​​to obtain interpolated multivariate time series data.

[0014] Furthermore, the graph structure includes nodes and edges, the nodes are variables of the multivariate time series data with missing values, and the weights of the edges are the similarity levels between the variables.

[0015] Furthermore, the adjacency matrix of the graph structure is adjusted by the graph neural network, and the process of calculating the adaptive graph structure is as follows:

[0016] Defining parameterized graph learning models ,in, The adjacency matrix representing the graph structure, represents the model parameters, Contains one or more graph neural network layers;

[0017] The graph neural network layer is expressed by the formula:

[0018]

[0019]

[0020] in, Indicates The nodes of the graph structure of time steps The embedding vector of Indicates The nodes of the graph structure of time steps The embedding vector of Representation Node The neighbor node set of , AGGREGATE represents the aggregation function, Indicates The aggregate of time steps from nodes The embedding vector of the neighbor node of , UPDATE represents the update function;

[0021] The graph structure learning model is used to learn and obtain an adaptive adjacency matrix ,

[0022]

[0023] in, The dimension of the data is ,

[0024] The adjacency matrix in the graph structure Adjust to adaptive adjacency matrix , and obtain an adaptive graph structure.

[0025] Furthermore, the gating mechanism of the bidirectional gated recurrent unit MPGRU is implemented by the message passing neural network MPNN, and the calculation formula is:

[0026]

[0027] in, Indicates The time step Layer Node The vector of represents the adaptive adjacency matrix, MPNN() represents the message passing neural network, is the number of layers of MPNN.

[0028] Furthermore, the message passing neural network MPNN adopts a multi-layer perceptron MLP, the number of layers of the MPNN is two, and the calculation formula is:

[0029]

[0030] in, Indicates The time step Layer Node The vector of Is a node The set of neighbor nodes, MLP() represents the multi-layer perceptron.

[0031] Furthermore, the encoder performs forward encoding and backward encoding on the adaptive graph structure respectively, and the calculation formula is:

[0032]

[0033]

[0034] in, () indicates passing through the forward MPGRU encoder, () indicates passing through the backward MPGRU encoder, represents the first The set of hidden state vectors of all nodes in time steps, represents the backward MPGRU encoder The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The node attribute matrix of time steps, Indicates The node attribute matrix of time steps, Represents the adaptive adjacency matrix.

[0035] Furthermore, the forward interpolation value is calculated as follows:

[0036]

[0037] in, Indicates The forward interpolation values ​​of all nodes in the time step, Indicates The mask of time steps, represents the complement of the mask, represents the weight matrix, represents the bias vector, represents the first The set of hidden state vectors of all nodes in time steps, represents element-wise product, Indicates The node attribute matrix of time steps;

[0038] The calculation formula for the backward interpolation value is:

[0039]

[0040] in, Indicates Backward interpolation values ​​of all nodes at time steps, represents the backward MPGRU encoder The set of hidden state vectors of all nodes at time steps.

[0041] Furthermore, the calculation formula of the decoding process of the decoder is:

[0042]

[0043]

[0044] in, represents the forward spatial decoder Nodes of time steps The node embedding representation of Represents the backward spatial decoder Nodes of time steps The node embedding representation of represents the first Nodes of time steps The hidden state vector of represents the backward MPGRU encoder Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of represents the backward MPGRU encoder Nodes of time steps The hidden state vector of Indicates Time step nodes The forward interpolation value of Indicates Time step nodes The backward interpolation value of , ‖ represents the union.

[0045] Furthermore, the calculation formula for predicting missing values ​​is:

[0046]

[0047] in, Indicates Nodes of time steps The predicted missing values.

[0048] The present invention also provides a multivariate time series missing value interpolation system based on dynamic graph learning, and the technical scheme adopted is as follows: comprising: a data acquisition module, a graph structure generation module, a coding and decoding module, a missing value prediction module and a data combination module connected in sequence,

[0049] The data acquisition module is used to acquire multivariate time series data with missing values;

[0050] The graph structure generation module is used to construct a graph structure according to the multivariate time series data with missing values, adjust the adjacency matrix of the graph structure through a graph neural network, and calculate an adaptive graph structure;

[0051] The encoding and decoding module is used for the adaptive graph structure to calculate forward interpolation values, backward interpolation values ​​and node embedding representation through an encoder and a decoder, and the encoder adopts a bidirectional gated recurrent unit to perform forward encoding and backward encoding on the adaptive graph structure respectively;

[0052] The predicted missing value module is used to aggregate the forward interpolation value, the backward interpolation value and the node embedding representation using a multi-layer perceptron to calculate the predicted missing value;

[0053] The data combining module is used to combine the predicted missing values ​​with the multivariate time series data with missing values ​​to obtain interpolated multivariate time series data.

[0054] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0055] 1. The present invention uses graph neural networks to adjust and optimize graph structures, and uses message passing neural networks and bidirectional gating mechanisms to learn node embedding representations, which can more accurately capture the complex relationships in multivariate time series that change over time, thereby improving the accuracy of missing value interpolation, and has higher precision and reliability when processing multivariate time series data with complex relationships.

[0056] 2. The present invention can optimize the relevant graph structure and node embedding representation, has higher efficiency and flexibility when processing data sets with complex structures, and provides an effective solution for processing complex data in multivariate time series.

[0057] 3. The present invention can make full use of existing information in the prediction process, and calculate the final predicted missing value based on the forward interpolation value, the backward interpolation value and the node embedding representation, thereby improving the accuracy and stability of the prediction.

[0058] 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

[0059] 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.

[0060] Figure 1 It is a flow chart of the method provided by the present invention.

[0061] Figure 2 This is the performance comparison result of the interpolation model under different missing rates provided by the present invention DETAILED DESCRIPTION

[0062] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. 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.

[0063] 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 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 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.

[0064] Combine the following Figure 1 to Figure 2 The present invention is further described in detail, and a multivariate time series missing value interpolation method and system based on dynamic graph learning are described as follows:

[0065] In this embodiment, Figure 1 As shown, a multivariate time series missing value interpolation method based on dynamic graph learning is provided, comprising the following steps:

[0066] Step 1: Obtain multivariate time series data with missing values. The multivariate time series data includes multiple variables.

[0067] Step 2: Based on the multivariate time series data with missing values, a graph structure is constructed, and the adjacency matrix of the graph structure is adjusted through a graph neural network to calculate an adaptive graph structure.

[0068] The goal of this step is to create a preliminary graph structure and then adjust the initial adjacency matrix through the graph neural network to learn the optimal graph structure for each time step. This process allows the graph structure to be optimized and adjusted, removes possible noise, and reflects the dynamic characteristics of the graph structure.

[0069] Step 2.1: Data preprocessing: The observed values ​​of each variable in the time series of the multivariate time series data with missing values ​​are normalized to eliminate the influence of different dimensions and magnitudes to ensure the comparability between different variables.

[0070] Step 2.2: Constructing a graph structure: Use a thresholded Gaussian kernel function to calculate the degree of similarity between normalized variables, assign weights based on the degree of similarity between variables, and thus provide a basis for constructing the edges of the graph structure. The Gaussian kernel function assigns weights based on the Euclidean distance or cosine similarity between observations. Using the values ​​of different variables in the multivariate time series data with missing values ​​at each time step as attribute values, the similarity measure between the variables is calculated to construct a graph structure.

[0071] The graph structure includes nodes and edges, wherein the nodes are variables of the multivariate time series data with missing values, and the weights of the edges are the similarity between the variables. In the graph structure, each node represents a variable, for example, Indicates The node attribute matrix of a time step contains the observed values ​​of the variables at that time step. , The dimension of the data is ; The weights of all edges connecting the nodes are calculated using the adjacency matrix express, , The dimension of the data is . Adjacency Matrix Reflects the initial graph structure, which describes the initial relationship between variables and is used to initialize the entire graph structure sequence of the multivariate time series data with missing values All adjacency matrices in .

[0072] The initial graph structure not only captures the static relationship between variables, but also provides an initial graph for subsequent graph structure optimization. The adjacency matrix of the initial graph structure will be used as the initialization input of the optimization process in graph structure learning, and then adjusted and optimized by the learning algorithm to reveal deeper and more dynamic correlations between variables.

[0073] Step 2.3: Optimize the graph structure: After building the graph structure, use a graph neural network (GNN) to adjust and optimize the graph structure. This way, you can mine the complex relationships between variables and dynamically adjust the topological structure of the graph. , the present invention defines a parameterized graph structure learning model ,in, are model parameters. The corresponding neural layer is responsible for learning the graph structure. It usually contains one or more graph neural network layers, each of which is responsible for processing the information of nodes and edges in the graph and updating the adjacency matrix.

[0074] In GNN, each node has a corresponding embedding vector, which contains the feature information of the node. By learning these embedding vectors, GNN can capture the semantic similarities and differences between nodes. The embedding vector of can be expressed as .

[0075] GNN updates the state of nodes through a message passing mechanism. During this process, each node aggregates information from its neighboring nodes and updates its own embedding vector based on this information and its current state. This process can be expressed by the following formula:

[0076]

[0077]

[0078] in, Indicates Nodes of time steps The embedding vector of Indicates The nodes of the graph structure of time steps The embedding vector of Representation Node The neighbor node set of AGGREGATE represents the aggregation function, which can be average, sum or maximum pooling, etc. The aggregation function in this embodiment adopts the average calculation function. Indicates The aggregate of time steps from nodes The embedding vector of the neighbor node, UPDATE represents the update function, which is used to combine the old embedding vector and the aggregated message to generate a new embedding vector.

[0079] Using graph structure learning model to learn adaptive adjacency matrix , It is updated dynamically and corresponds to different values ​​at each time step. The formula is as follows:

[0080] ,

[0081] In particular,

[0082]

[0083] use To optimize the graph structure, this process is iterative. In each iteration, GNN will update the graph structure based on the new adjacency matrix and node embedding vector. As the training progresses, the graph structure will gradually be optimized to better reflect the potential relationships in the data. represents the activation function, Represents a learnable weight matrix, which can make full use of the feature information of the initial graph structure and update To further optimize and adjust the graph structure, we can obtain an adaptive graph structure. In this way, we can remove the noise that may exist in the original data and capture the dynamic characteristics of the graph structure, so as to learn a more accurate and useful optimal graph structure.

[0084] Step 3: The adaptive graph structure is passed through an encoder and a decoder to calculate a forward interpolation value, a backward interpolation value and a node embedding representation. The encoder uses a bidirectional gated recurrent unit to perform forward encoding and backward encoding on the adaptive graph structure respectively.

[0085] Encoding process: In order to capture the complex dependencies in multivariate time series data, the present invention uses a bidirectional gated recurrent unit (MPGRU) as an encoder. MPGRU is a gated recurrent neural network in which the gating mechanism is implemented through a message passing neural network (MPNN), which enables the present invention to consider both temporal and spatial correlations.

[0086] Specifically, for each time step in the time series, the present invention first uses MPNN to learn the spatial relationship between variables. Assume that Adaptive graph structure with time steps middle, Indicates Nodes of time steps The MPNN formula can be expressed as:

[0087]

[0088] Among them, MPNN() represents the message passing neural network, MLP() represents the multi-layer perceptron, Indicates The time step Layer Node The vector of Indicates The time step Layer Node The vector of Indicates The time step Layer Node The vector of Is a node The set of neighbor nodes of is the number of layers of the MPNN. In this embodiment, a multi-layer perceptron (MLP) is used for aggregation and MPNN is set =2 layers.

[0089] Forward and backward coding: In MPGRU, the present invention uses a gating mechanism to control the flow of information, which can combine spatial and temporal dependencies. Specifically, the present invention uses MPNN as the gating of GRU to combine spatial and temporal dependencies. The modified GRU is called MPGRU. The definition of MPGRU is:

[0090]

[0091] in, It is Nodes of time steps The hidden state vector of It is calculated by MPNN.

[0092] In order to capture the forward and backward time dependencies of multivariate time series, the present invention uses bidirectional MPGRU as an encoder to encode the adaptive graph structure sequence from the forward and backward directions respectively, which can capture the forward and backward dependencies of each variable in the time series and provide comprehensive context information for subsequent interpolation tasks. The forward and backward MPGRU are defined as:

[0093]

[0094]

[0095] in, () indicates passing through the forward MPGRU encoder, () indicates passing through the backward MPGRU encoder, represents the first The set of hidden state vectors of all nodes in time steps, represents the backward MPGRU encoder The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The node attribute matrix of time steps, Indicates The node attribute matrix for each time step.

[0096] After calculating the hidden state vector set, the linear output can be used as the forward interpolation value and the backward interpolation value. The forward interpolation value is calculated as:

[0097]

[0098] in, Indicates The forward interpolation values ​​of all nodes in the time step, Indicates The mask of time steps, represents the complement of the mask, represents the weight matrix, represents the bias vector, represents the first The set of hidden state vectors of all nodes in time steps, Represents element-wise product.

[0099] Similarly, the backward interpolation value is calculated as:

[0100]

[0101] in, Indicates Backward interpolation values ​​of all nodes at time steps, represents the backward MPGRU encoder The set of hidden state vectors of all nodes at time steps.

[0102] The present invention encodes the graph structure sequence from both the forward and backward directions, and can capture the forward and backward dependencies of each variable in the time series, providing comprehensive context information for subsequent interpolation tasks. In this way, the present invention can simultaneously utilize the temporal information in the time series data and the spatial relationship between variables to provide accurate predictions for the interpolation of missing data.

[0103] Decoding process: After obtaining the hidden state vector of the encoder, the present invention designs a spatial decoder to re-extract the dependencies between variables hidden in the adaptive graph structure and obtain the node embedding representation. The decoder uses the complete graph structure information obtained from the MPGRU to re-extract node features through a multi-layer perceptron (MLP) to obtain a more accurate node embedding representation. This step enhances the understanding of the variable relationship in the graph structure and provides additional information for accurate interpolation. The calculation formula of the decoding process is as follows:

[0104]

[0105]

[0106] in, represents the forward spatial decoder Nodes of time steps The node embedding representation of Represents the backward spatial decoder Nodes of time steps The node embedding representation of represents the first Nodes of time steps The hidden state vector of represents the backward MPGRU encoder Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of represents the backward MPGRU encoder Nodes of time steps The hidden state vector of Indicates Time step nodes The forward interpolation value of Indicates Time step nodes The backward interpolation value of , ‖ represents the union (common meaning).

[0107] Step 4: Utilize a multi-layer perceptron to aggregate the forward interpolation values, backward interpolation values, and node embedding representations to calculate the predicted missing values.

[0108] The present invention uses a multi-layer perceptron to aggregate the forward interpolation values, backward interpolation values, and node embedding representations obtained by the encoder and decoder. MLP predicts the missing value of each time step by integrating information from different directions (forward and backward) and different time steps. Specifically, the prediction formula is as follows:

[0109]

[0110] in, Indicates Nodes of time steps The predicted missing values.

[0111] Step 5: Combine the predicted missing values ​​with the multivariate time series data with missing values ​​to obtain interpolated multivariate time series data.

[0112] For The calculation formula for multivariate time series data of time steps is expressed as:

[0113]

[0114] in, Indicates The multivariate time series data after interpolation of time steps, Indicates The set of predicted missing values ​​for time steps.

[0115] The goal of this invention is to minimize the reconstruction error, that is, to minimize the difference between the predicted missing values ​​and the actual observed values. To achieve:

[0116]

[0117] in, Indicates The mask of time steps, Indicates The multivariate time series data after interpolation of time steps, Indicates The node attribute matrix of time steps, represents the absolute value of the Euclidean distance, Indicates the maximum value of the time step.

[0118] The present invention can not only utilize existing observation data, but also predict missing values ​​through learned spatiotemporal dependencies and graph structure relationships, thereby achieving accurate interpolation of multivariate time series data; and optimize its parameters by minimizing reconstruction errors to improve the accuracy of interpolation.

[0119] The following verifies the effectiveness of this method:

[0120] This embodiment uses a public real data set: MIMIC-III (Medical Information Marking in Intensive Care) data set as multivariate time series data with missing values. The MIMIC-III clinical database is a large free public database that contains health data of inpatients at Beth Israel Deaconess Medical Center from 2001 to 2012. MIMIC-III contains observation data with missing values ​​for 20 different variables within 48 hours, with 8760 samples with a time step of 1 hour as time series data, and each time series data is first covered with a partial proportion of artificial mask as test data. The statistical data of the data set are shown in Table 1.

[0121] Table 1 Dataset overview

[0122]

[0123] The present invention compares GSLImpute (this method) with 9 machine learning and deep learning methods, 6 of which are existing advanced machine learning and deep learning methods, namely Mean, MICE, VAR, KNN, BRITS and rGAIN, and the other three are partial models of the present invention, namely MPGRU, BiMPGRU and GRIN.

[0124] Mean: Mean filling, missing values ​​are replaced by the global mean of each variable.

[0125] MICE: Multiple imputation, imputing each missing value under a specific missing mechanism by chained equations.

[0126] VAR: Vector Autoregression, captures the correlation between multiple time series and fills in missing values ​​through regression prediction.

[0127] KNN: K nearest neighbor, uses the KNN algorithm to query the K samples most similar to the missing variable and take their weighted average for interpolation.

[0128] BRITS: Bidirectional Recurrent Neural Networks,Estimate missing values ​​using bidirectional recurrent neural networks.

[0129] rGAIN: Generative Adversarial Networks,Generate missing values ​​in time series using unsupervised generative adversarial networks.

[0130] MPGRU: Message Passing Neural Network with Gated Recurrent Unit,MPGRU combines message passing neural network and gated recurrent unit to predict missing values.

[0131] BiMPGRU: Bidirectional Gated Recurrent Unit, BiMPGRU uses bidirectional GRU instead of unidirectional GRU in MPGRU.

[0132] GRIN: An encoder-decoder architecture based on BiMPGRU and GNN. The difference from this method is that no graph neural network is used to adjust and optimize the graph structure.

[0133] In the interpolation model training for handling missing data, this embodiment considers two settings: internal interpolation and external interpolation. Internal imputation uses all available data for training, except those that are missing and used to evaluate the interpolation performance. This method uses as much information as possible to train the model, hoping to improve the model's ability to interpolate unknown data. External imputation uses only data from the training set for training. This means that the model will not be exposed to data in the test set or other validation sets, which helps simulate the situation in real applications, that is, the model must interpolate on data that has not been seen. By default, in point-missing experiments, only external interpolation scenarios are considered. This means that the training and testing of the model are separated, ensuring that the performance evaluation of the model is more rigorous and realistic, reflecting the interpolation ability of the model in real applications. In summary, the main difference between internal and external interpolation is that they use different ranges of data. Internal interpolation uses a wider range of data (including training sets and additional available data), while external interpolation only uses data from the training set.

[0134] This example uses mean absolute error (MAE), mean relative error (MRE), and mean square error (MSE) as experimental evaluation indicators on the test data set. The formulas are as follows:

[0135]

[0136]

[0137]

[0138] in, represents the predicted value, Indicates the actual value, Indicates quantity.

[0139] The interpolation performance comparison results of this method and 9 machine learning and deep learning methods are shown in Tables 2 and 3. It can be seen that whether it is extrapolation or interpolation, this method is significantly better than other baseline methods.

[0140] Table 2 Comparison of interpolation performance of extrapolation models

[0141]

[0142] Table 3 Comparison results of interpolation performance of interpolation models

[0143]

[0144] In addition, this embodiment also sets up a comparison of interpolation errors (MAE, MRE and MSE) under different missing rates. The missing rates are 10%, 15%, 20%, 25% and 30%. The interpolation errors of different methods for different missing rates are compared respectively. It can be observed that the error of this method is lower than that of other baseline methods at each missing rate. The results are as follows: Figure 2 As shown in (a)-(c) in the figure.

[0145] The present invention has been extensively experimentally compared on the public medical dataset MIMIC-III, demonstrating that the performance of the present invention in interpolating missing values ​​of multivariate time series exceeds that of other existing advanced baseline methods, proving the effectiveness of the present invention in accurately modeling the dynamic correlation of time series variables and data interpolation.

[0146] This embodiment also provides a multivariate time series missing value interpolation system based on dynamic graph learning, and the technical solution adopted is as follows: comprising: a data acquisition module, a graph structure generation module, a coding and decoding module, a missing value prediction module and a data combination module connected in sequence,

[0147] The data acquisition module is used to acquire multivariate time series data with missing values;

[0148] The graph structure generation module is used to construct a graph structure according to the multivariate time series data with missing values, adjust the adjacency matrix of the graph structure through a graph neural network, and calculate an adaptive graph structure;

[0149] The encoding and decoding module is used for the adaptive graph structure to calculate forward interpolation values, backward interpolation values ​​and node embedding representation through an encoder and a decoder, and the encoder adopts a bidirectional gated recurrent unit to perform forward encoding and backward encoding on the adaptive graph structure respectively;

[0150] The predicted missing value module is used to aggregate the forward interpolation value, the backward interpolation value and the node embedding representation using a multi-layer perceptron to calculate the predicted missing value;

[0151] The data combining module is used to combine the predicted missing values ​​with the multivariate time series data with missing values ​​to obtain interpolated multivariate time series data.

[0152] 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 multivariate time series missing value interpolation method based on dynamic graph learning, characterized in that: include: Get multivariate time series data with missing values; According to the multivariate time series data with missing values, a graph structure is constructed, an adjacency matrix of the graph structure is adjusted through a graph neural network, and an adaptive graph structure is calculated; The adaptive graph structure is calculated by an encoder and a decoder to obtain a forward interpolation value, a backward interpolation value and a node embedding representation, and the encoder adopts a bidirectional gated recurrent unit to perform forward encoding and backward encoding on the adaptive graph structure respectively; The encoder performs forward encoding and backward encoding on the adaptive graph structure respectively, and the calculation formula is: in, () indicates passing through the forward MPGRU encoder, () indicates passing through the backward MPGRU encoder, represents the first The set of hidden state vectors of all nodes in time steps, represents the first The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The node attribute matrix of time steps, Indicates The node attribute matrix of time steps, represents the adaptive adjacency matrix; in, The dimension of the data is , The adjacency matrix representing the graph structure, represents the model parameters, Contains one or more graph neural network layers; The forward interpolation value is calculated as: in, Indicates The forward interpolation values ​​of all nodes in the time step, Indicates The mask of time steps, represents the complement of the mask, represents the weight matrix, represents the bias vector, represents the first The set of hidden state vectors of all nodes in time steps, Indicates The node attribute matrix of time steps, represents element-wise product; The calculation formula for the backward interpolation value is: in, Indicates Backward interpolation values ​​of all nodes at time steps, represents the first The set of hidden state vectors of all nodes at time steps; The calculation formula of the decoder's decoding process is: in, represents the forward spatial decoder Nodes of time steps The node embedding representation of Represents the backward spatial decoder Nodes of time steps The node embedding representation of represents the first Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of Indicates Time step nodes The forward interpolation value of Indicates Time step nodes The backward interpolation value of , ‖ represents the union; Aggregating the forward interpolation value, the backward interpolation value and the node embedding representation using a multi-layer perceptron to calculate the predicted missing value; The predicted missing values ​​are combined with the multivariate time series data with missing values ​​to obtain interpolated multivariate time series data.

2. The method for interpolating missing values ​​of multivariate time series based on dynamic graph learning as claimed in claim 1, characterized in that: The graph structure includes nodes and edges, the nodes are variables of the multivariate time series data with missing values, and the weights of the edges are the similarity levels between the variables.

3. The multivariate time series missing value interpolation method based on dynamic graph learning as claimed in claim 1 or 2, characterized in that: The process of adjusting the adjacency matrix of the graph structure through the graph neural network and calculating the adaptive graph structure is as follows: Defining parameterized graph learning models , The graph neural network layer is expressed by the formula: in, Indicates The nodes of the graph structure of time steps The embedding vector of Indicates The nodes of the graph structure of time steps The embedding vector of Representation Node The neighbor node set of , AGGREGATE represents the aggregation function, Indicates The aggregate of time steps from nodes The embedding vector of the neighbor node of , UPDATE represents the update function; The graph structure learning model is used to learn and obtain an adaptive adjacency matrix , The adjacency matrix in the graph structure Adjust to adaptive adjacency matrix , and obtain an adaptive graph structure.

4. The method for interpolating missing values ​​of multivariate time series based on dynamic graph learning as claimed in claim 1, characterized in that: The gating mechanism of the bidirectional gated recurrent unit MPGRU is implemented through the message passing neural network MPNN, and the calculation formula is: in, Indicates The time step Layer Node The vector of represents the adaptive adjacency matrix, MPNN() represents the message passing neural network, is the number of layers of MPNN.

5. The method for interpolating missing values ​​of multivariate time series based on dynamic graph learning as claimed in claim 4, characterized in that: The message passing neural network MPNN adopts a multi-layer perceptron MLP. The number of layers of MPNN is two, and the calculation formula is: in, Indicates The time step Layer Node The vector of Is a node The set of neighbor nodes, MLP() represents the multi-layer perceptron.

6. The method for interpolating missing values ​​of multivariate time series based on dynamic graph learning as claimed in claim 1, characterized in that: The formula for predicting missing values ​​is: in, Indicates Nodes of time steps The predicted missing values.

7. A multivariate time series missing value interpolation system based on dynamic graph learning, characterized in that: The method for interpolating missing values ​​of a multivariate time series based on dynamic graph learning according to any one of claims 1 to 6 comprises: a data acquisition module, a graph structure generation module, a coding and decoding module, a missing value prediction module and a data combination module connected in sequence, The data acquisition module is used to acquire multivariate time series data with missing values; The graph structure generation module is used to construct a graph structure according to the multivariate time series data with missing values, adjust the adjacency matrix of the graph structure through a graph neural network, and calculate an adaptive graph structure; The encoding and decoding module is used for the adaptive graph structure to calculate forward interpolation values, backward interpolation values ​​and node embedding representation through an encoder and a decoder, and the encoder adopts a bidirectional gated recurrent unit to perform forward encoding and backward encoding on the adaptive graph structure respectively; The encoder performs forward encoding and backward encoding on the adaptive graph structure respectively, and the calculation formula is: in, () indicates passing through the forward MPGRU encoder, () indicates passing through the backward MPGRU encoder, represents the first The set of hidden state vectors of all nodes in time steps, represents the first The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The set of hidden state vectors of all nodes in time steps, Indicates The node attribute matrix of time steps, Indicates The node attribute matrix of time steps, represents the adaptive adjacency matrix; in, The dimension of the data is , The adjacency matrix representing the graph structure, represents the model parameters, Contains one or more graph neural network layers; The forward interpolation value is calculated as: in, Indicates The forward interpolation values ​​of all nodes in the time step, Indicates The mask of time steps, Represents the complement of the mask, represents the weight matrix, represents the bias vector, represents the first The set of hidden state vectors of all nodes in time steps, Indicates The node attribute matrix of time steps, represents element-wise product; The calculation formula for the backward interpolation value is: in, Indicates Backward interpolation values ​​of all nodes at time steps, represents the first The set of hidden state vectors of all nodes at time steps; The calculation formula of the decoder's decoding process is: in, represents the forward spatial decoder Nodes of time steps The node embedding representation of Represents the backward spatial decoder Nodes of time steps The node embedding representation of represents the first Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of represents the first Nodes of time steps The hidden state vector of Indicates Time step nodes The forward interpolation value of Indicates Time step nodes The backward interpolation value of , ‖ represents the union; The predicted missing value module is used to aggregate the forward interpolation value, the backward interpolation value and the node embedding representation using a multi-layer perceptron to calculate the predicted missing value; The data combining module is used to combine the predicted missing values ​​with the multivariate time series data with missing values ​​to obtain interpolated multivariate time series data.

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