Fusion method for dependency between variables of multivariable time sequence based on overlapping grouping

Abstract

The invention relates to an overlapping grouping-based multi-variable time sequence inter-variable dependency fusion method, and aims to solve the problems that in the prior art, an implementation strategy considering an inter-variable dependency relationship is easy to introduce an irrelevant or unnecessary inter-variable dependency relationship; and the technical problem that the same variable possibly has a relatively strong dependency relationship with multiple groups of different variables is easily ignored. Comprising the following steps: modeling a long-term dependency relationship among variables of a multivariable time sequence by adopting an overlapping grouping method to obtain an overlapping variable grouping list, then obtaining feature representation vectors respectively corresponding to single-variable time subsequences in multivariable time subsequences, constructing a feature representation matrix, and constructing a feature representation matrix on the basis of the overlapping variable grouping list; and fusing long-term and short-term dependency relationships among variables into the feature representation matrix by adopting a mask multi-head attention mechanism so as to complete the fusion of the dependency among the variables of the multivariable time sequence.

Description

Technical Field

[0001] This invention relates to time series data, and more specifically to a fusion method for inter-variable dependencies in multivariate time series data based on overlapping grouping. Background Technology

[0002] With the continuous development of data acquisition technology, people are collecting more and more time-series data from social production and daily life processes. Time-series data is the observation result of a process or system. Its values ​​are usually measured and collected at uniform time intervals or a given sampling frequency, and can be represented as a matrix. ,in These represent the number of observations and the number of observed variables, respectively. Represents real numbers, For matrix The elements in Representing the Variables in The observations at each time point represent the observations of a variable at different times in each column of the matrix, while each row represents the observations of multiple variables at the same time point. If... This is called a univariate time series; if 2. This is called a multivariate time series. In multivariate time series, there are often complex dependencies between variables, and these dependencies have a significant impact on the analysis of multivariate time series data.

[0003] In existing methods for analyzing multivariate time series data, attention mechanisms are often used to consider dependencies between variables. Specifically, there are two types of implementation strategies: one is the global modeling strategy, which considers all potential dependencies between variables at the same time. However, this strategy is prone to introducing irrelevant or unnecessary dependencies between variables (which can be regarded as noise); the other is the non-overlapping grouping modeling strategy, which groups variables into non-overlapping groups (a variable belongs to only one group) and considers the dependencies between variables only within the group. However, this strategy is prone to ignoring the situation where the same variable may have strong dependencies with multiple different groups of variables (some variables in these different groups of variables do not have substantial dependencies). Summary of the Invention

[0004] To address the technical problems that existing implementation strategies that consider inter-variable dependencies easily introduce irrelevant or unnecessary inter-variable dependencies, and easily overlook the fact that the same variable may have strong dependencies on multiple different groups of variables, this invention provides a fusion method for inter-variable time series variables based on overlapping grouping.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A fusion method for multivariate time series variables based on overlapping grouping, characterized by the following steps: S1. Decompose the multivariate time series into A univariate time series, wherein, ; S2. Based on the univariate time series correlation measurement method, perform iterative calculations. The long-term correlation score is used to determine the correlation between any two univariate time series within a given univariate time series dataset. Based on this long-term correlation score, and according to a set filtering threshold, a long-term correlation matrix is ​​constructed. ; S3. Based on the long-term correlation matrix of variables Construct a long-term correlation plot of variables; S4. Use the graph maxima detection algorithm on the long-term correlation graph of variables to find overlapping groups of serial variables and obtain a list of overlapping variable groups; S5. Construct and train a deep neural network model employing a channel-independent strategy. Using a multivariate time subsequence as input, output based on the deep neural network model. The feature representation vectors corresponding to each univariate time subsequence are used to construct a feature representation matrix; the multivariate time subsequences are taken from the multivariate time series generated by the underlying process or model that governs the generation of multivariate time series without any changes. S6. Based on the overlapping variable grouping list, a masked multi-head attention mechanism is adopted to incorporate long-term and short-term dependencies between variables into the feature representation matrix, thereby obtaining the variable feature representation after dependency fusion and completing the fusion of dependencies between variables in multivariate time series.

[0006] Furthermore, step S4 specifically includes: S4.1 Define the overlapping variable grouping list as follows Set it to an empty list and set the node tag. ; S4.2 Extract node markers from the long-term correlation plot of variables. The corresponding node The subgraph is formed by all one-step neighbor nodes and the edges connecting them; the subgraph does not include nodes. and its edges connected to its 1-step neighbor nodes; S4.3 Find all the maximal cliques on the subgraph; S4.4, Combine the nodes contained in each maximal clique with the nodes mentioned above. Form a candidate group and add the candidate group to the list of overlapping variable groups. middle; S4.5, Settings ,judge If the condition is met, return to step S4.2; otherwise, proceed to step S4.6. S4.6 Merging overlapping variable grouping lists Candidate grouping, i.e., removing duplicate groups and groups contained in other groups, and sorting the variables in each group according to their... The variables are sorted in ascending order to obtain the final list of overlapping variable groups. ,in, Indicates the number of groups. .

[0007] Furthermore, step S6 specifically includes: S6.1 Define the list of characteristics for grouping variables as follows: Set it to an empty list and set a grouping flag. Given the current time The length is Multivariate time subsequence Split into A single-variable time subsequence; S6.2. Based on the univariate time series correlation measurement method, perform iterative calculations. The correlation score between any two univariate time series in a given univariate time series is used to construct a local correlation matrix of variables based on the correlation score. S6.3 Calculate the grouping in the overlapping variable grouping list The grouped mask matrix, where ; S6.4 Calculate the grouping based on the grouping mask matrix. The local correlation matrix of the variables is obtained, and then the grouping is calculated based on the local correlation matrix of the variables. Bernoulli sampling probability matrix; S6.5. Based on the Bernoulli sampling probability matrix, construct grouping using reparameterization techniques. Variable correlation mask matrix; S6.6. Based on the feature representation matrix constructed in step S5 and the variable correlation mask matrix constructed in step S6.5, a masked multi-head attention mechanism is used to calculate the variable feature representations that fuse the long-term and short-term dependencies between variables. And add it to the list of grouping variable feature representations. ; S6.7, Settings ,judge If the condition is not met, proceed to step S6.8; otherwise, return to step S6.3. S6.8 List the characteristics of the grouping variables Variable feature representation in according to By concatenating in ascending order and row-wise, we obtain the concatenated matrix. ; S6.9 Construct a two-layer linear neural network and connect the resulting matrix. Mapping to a multivariate sequence feature representation that incorporates dependencies between variables Based on multivariate sequence feature representation This yields the variable feature representations after dependency fusion, thus completing the fusion of dependencies between variables in a multivariate time series.

[0008] Furthermore, in step S2, based on the long-term correlation score and according to the set filtering threshold, a long-term correlation matrix of the variables is constructed. The process is as follows: Set filter threshold If the long-term correlation score Then Set to 0 if the long-term correlation score Then keep The value remains unchanged, based on the filtered long-term relevance score. Construct a long-term correlation matrix of variables ,in, Indicates the first The univariate time series and the first Long-term correlation scores between univariate time series.

[0009] Furthermore, in step S3, the long-term correlation plot of the variables is as follows: ,in, Represents the set of nodes in a graph. The set of edges representing a node; The solution process is as follows: traverse the long-term correlation matrix of the variables. An upper triangular or lower triangular matrix, without diagonals, if Then at node and nodes Add an edge between ,node Indicates the first A sequence variable of a univariate time series. ,node Indicates the first A sequence variable of a univariate time series. .

[0010] Furthermore, in step S5, the process of constructing a deep neural network model using a channel-independent strategy is as follows: Construct an initial deep neural network model using a channel-independent strategy, with multivariate time subsequence... As input, the feature representation vector corresponding to the univariate time subsequence is used as output. A loss function is constructed based on the objective of the multivariate time series analysis task with the feature representation vector as input. The deep neural network model adopting the channel-independent strategy is trained to obtain the trained deep neural network model, thus completing the construction of the deep neural network model adopting the channel-independent strategy.

[0011] Further, in step S6.3, the group mask matrix is ​​calculated. The formula is: ; In the formula, , Indicates belonging to a group The label of the variable, .

[0012] Furthermore, in step S6.4, grouping Local correlation matrix of variables The calculation formula is: ; In the formula, Represents the local correlation matrix of variables. This represents the matrix dot product operation. In step S6.4, grouping Bernoulli sampling probability matrix The calculation formula is: ; In the formula, , , Indicates belonging to a group The label of the variable, .

[0013] The beneficial effects of this invention are: 1. This invention provides a fusion method for multivariate time series variable dependencies based on overlapping grouping. By modeling the long-term dependencies between multivariate time series variables using an overlapping grouping method, it better reflects the actual situation of long-term dependencies between multivariate time series variables. At the same time, it considers the local (short-term dependencies) between variables, which can more accurately characterize the complex dependency structure between variables, thereby helping to learn higher-quality variable feature representations. This solves the technical problems of existing implementation strategies that consider the dependencies between variables, which easily introduce irrelevant or unnecessary variable dependencies, and easily ignore the fact that the same variable may have strong dependencies with multiple different groups of variables.

[0014] 2. The present invention provides a fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping, which can learn higher quality feature representations for each variable sequence in a multivariate time series. It can be used as a module in multivariate time series analysis methods (such as prediction, classification, clustering, etc.) based on variable feature representations to improve the performance of the analysis methods. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating an embodiment of a fusion method for multivariate time series variables based on overlapping grouping according to the present invention. Figure 2 This is a flowchart illustrating the process of finding overlapping variable groups in step S4 of an embodiment of a fusion method for multivariate time series variables based on overlapping grouping according to the present invention. Figure 3 This is a schematic diagram of the process of learning the variable feature representation of the fusion variable dependency in step S6 of an embodiment of the fusion method for multivariate time series variables based on overlapping grouping of the present invention. Figure 4 This is step S3 of an embodiment of the fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping of the present invention, which is a long-term correlation graph of the variables in the multivariate time series ILI. Detailed Implementation

[0016] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] The fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping, provided in this embodiment, is applied to the improved multivariate time series prediction model PatchTST to verify the effectiveness of the method in this embodiment.

[0018] Specifically, after PatchTST employs a variable independence strategy to learn feature representations for each input variable sequence, the method in this embodiment incorporates the dependencies between variables into the feature representations before predicting the variables. The multivariate time series used in this embodiment is the ILI multivariate time series from the UCI dataset, which has 7 variables and a sequence length of 966. This sequence is divided into training and test sets of lengths 772 and 194, respectively. The training set is used to calculate long-term dependencies between variables and train the improved PatchTST model. The test set is used to verify the predictive performance of the improved PatchTST model. The main parameter settings of the PatchTST model are as follows: the length of the input historical subsequence is... The prediction length is 24; the patch length is 16; the sliding step size is 8; the PatchTST model dimension is 256; the feature representation dimension is 256; the PatchTST model has 4 attention layers, 2 attention heads, 2 variable dependency attention layers, and 2 attention heads.

[0019] The process of applying the fusion method based on overlapping grouping of multivariate time series variables in this embodiment to the improved multivariate time series prediction model PatchTST is as follows: Fusion of inter-variable dependencies in ILI multivariate time series, such as... Figure 1 As shown, it includes the following steps: S1. For a given ILI multivariate time series Break it down into A single variable time series ,in, , This indicates the number of observations; in this embodiment, the ILI multivariate time series contains 7 series, namely... The ILI multivariate time series dataset is the training set. .

[0020] S2. Based on univariate time series correlation measurement methods (such as Spearman correlation coefficient, Cosine similarity coefficient, negative Euclidean distance, negative dynamic time warping (DTW) distance, etc., the specific method can be selected according to the attributes of the time series), iterate and calculate... Construct a long-term correlation matrix by calculating the long-term correlation scores between any two univariate time series from a given set of univariate time series. ,in, Indicates the first The univariate time series and the first The correlation score between two univariate time series is a key indicator; a higher value indicates a stronger dependency between the two variables. It is a symmetric matrix, with the diagonal representing the long-term correlation between the variable and itself, and has the highest correlation score of 1; based on the set filtering threshold... Filter the correlation matrix If Then Setting it to 0 indicates that the long-term dependency between the two variables is not considered; if Then keep The values ​​remain unchanged, and after filtering, the final long-term correlation matrix of the variables is constructed. In this embodiment, the Spearman correlation coefficient is used to calculate the long-term correlation between two univariate time series. The Spearman correlation coefficient can be used to measure the correlation of non-stationary series. The Spearman correlation score matrix of the seven variables of the ILI multivariate time series is as follows: Take threshold After filtering, the final long-term correlation matrix of the variables is constructed as follows: .

[0021] S3. Based on the long-term correlation matrix of variables Construct a long-term correlation plot of variables ;in, Represents the set of nodes in a graph, nodes Represents sequence variables , , Represents the set of edges between nodes; The solution process is as follows: traverse the long-term correlation matrix of the variables. An upper triangular or lower triangular matrix, without diagonals, if Then at node and nodes Add an edge between ,node Indicates the first A sequence variable of a univariate time series. ,node Indicates the first A sequence variable of a univariate time series. In this embodiment, the constructed long-term correlation plot of the ILI sequence variables is as follows: Figure 4 As shown, the sequence variable nodes are represented by 1, 2, 3, 4, 5, 6, and 7 respectively.

[0022] S4. In the long-term correlation diagram of variables The algorithm above uses a graph clique detection algorithm to find overlapping groups of sequence variables and obtain a list of overlapping variable groups; for example... Figure 2 As shown, the specific steps are as follows: S4.1 Define the overlapping variable grouping list as follows Set it to an empty list and set the node tag. ; S4.2 Extract node markers from the long-term correlation plot of variables. The corresponding node The subgraph formed by all one-step neighbor nodes and the edges connecting the neighbor nodes. The subgraph Nodes not included and its edges connected to its 1-step neighbor nodes; S4.3, in the subgraph Find all maximal cliques on the graph; maximal cliques are subgraphs. A set of nodes and the edges connecting them form a complete graph, meaning that any two nodes are connected by an edge, and the subgraph... Adding any of the remaining nodes and their edges to the graph does not form a complete graph; S4.4, Combine the nodes contained in each maximal clique with the nodes mentioned above. Form a candidate group and add the candidate group to the list of overlapping variable groups. middle; S4.5, Settings ,judge If the condition is met, return to step S4.2; otherwise, proceed to step S4.6. S4.6 Merging overlapping variable grouping lists Candidate grouping, i.e., removing duplicate groups and groups contained in other groups, and sorting the variables in each group according to their... The variables are sorted in ascending order to obtain the final list of overlapping variable groups. ,in, Indicates the number of groups. In this embodiment, the variable overlap grouping of the multivariate time series ILI is as follows: ; Right now .

[0023] S5. Construct and train a deep neural network model employing a channel-independent strategy (e.g., a linear neural network-based model, a recurrent neural network-based model, a convolutional neural network-based model, a Transformer-based model, etc.) to learn a feature representation vector for each variable in the multivariate time series. The deep neural network model is used for multivariate time series... For input, used for output The feature representation vectors corresponding to the univariate time subsequences are denoted as follows: ,in It is the dimension of feature representation. Each column is a feature representation vector of the corresponding variable sequence. Based on the feature representation vectors, a feature representation matrix is ​​constructed. The process of constructing a deep neural network model using a channel-independent strategy is as follows: An initial deep neural network model using a channel-independent strategy is constructed, with multivariate time subsequence... As input, the feature representation vectors corresponding to univariate time series are used as output. A loss function is constructed based on the objective of the multivariate time series analysis task, using the feature representation vectors as input. This loss function is then used to train a deep neural network model employing a channel-independent strategy, resulting in a trained deep neural network model. This model is used for output. The feature representation vectors corresponding to each univariate time series are used. In this embodiment, the Transformer-based model PatchTST (excluding the final prediction mapping linear network) is used to learn the feature representations of the multivariate time series, and the loss function is MAE (Mean Absolute Error).

[0024] S6. Grouping list based on overlapping variables It employs a masked multi-head attention mechanism in the feature representation matrix. By incorporating long-term and short-term dependencies between variables, we obtain a variable feature representation after dependency fusion. ;like Figure 3 As shown, the specific steps are as follows: S6.1 Define the list of characteristics for grouping variables as follows: Set it to an empty list and set a grouping flag. , will be given at the current time The length is Multivariate time subsequence Split into univariate time subsequences , and Both are taken from the same multivariate time series; S6.2. Based on univariate time series correlation measurement methods (such as Cosine similarity coefficient, negative Euclidean distance, negative dynamic time warping (DTW) distance, etc.), iterate and calculate... The correlation score between any two univariate time series in a given univariate time series is used to construct a local (short-term) correlation matrix of the variables based on the correlation score. ;in Indicates the first The sequence of variables and the first variable sequence The correlation score of a series of variables indicates the higher the dependence between the two variables. It is a symmetric matrix, with the diagonal representing the local correlation between the variable and itself, and has the highest correlation score of 1. This reflects the local (short-term) dependencies between variable sequences; in this embodiment, the Cosine similarity coefficient is used as the method for measuring the correlation between univariate time series. S6.3, Calculate Grouping Group mask matrix ,in The calculation formula is: ; In the formula, , Indicates belonging to a group The label of the variable, ; S6.4 Calculate the grouping based on the grouping mask matrix. The local correlation matrix of the variables is obtained, and then the grouping is calculated based on the local correlation matrix of the variables. Bernoulli sampling probability matrix; Among them, grouping Local correlation matrix of variables The calculation formula is: ; In the formula, This represents the local correlation matrix of variables; that is, it only considers the local correlation of variables that are strongly correlated on a long-term scale. This represents the matrix dot product operation. Among them, grouping Bernoulli sampling probability matrix The calculation formula is: ; In the formula, , , Indicates belonging to a group The label of the variable, Soon Normalized to probability matrix , ; S6.5. Based on the Bernoulli sampling probability matrix, construct groupings using the reparameterization trick. Variable correlation mask matrix ; The value of is determined through Bernoulli sampling, that is, by probability. It takes the value 1, and is determined by probability. If the value is 0, then It contains information on long-term and short-term dependencies between variables in the input multivariate sequence; S6.6 Feature representation matrix constructed based on step S5 The variable correlation mask matrix constructed in step S6.5 A masked multi-head attention mechanism is used to compute variable feature representations of long-term and short-term dependencies between fused variables. and will Add a list of features for grouping variables ; S6.7, Settings ,judge If the condition is not met, proceed to step S6.8; otherwise, return to step S6.3. S6.8 List the characteristics of the grouping variables All variable characteristics , ,according to By concatenating in ascending order and row-wise, we obtain the concatenated matrix. , of which Arriving at the Behavior No. Variable feature representation for each group ; S6.9 Construct a two-layer linear neural network, that is, a two-layer linear neural network with only an input layer and an output layer, and no activation function in the nodes. Connect the resulting matrix. Mapping to a multivariate sequence feature representation that incorporates dependencies between variables Soon Each column in the map is mapped to a The feature representation of dimension, then It is a multivariate sequence feature representation that incorporates the dependencies between variables, based on multivariate sequence feature representation. This yields the variable feature representations after dependency fusion, thus completing the fusion of dependencies between variables in a multivariate time series.

[0025] Finally, the predictive mapping linear network of the PatchTST model is applied to... Given input, predict The Future Step sequence value In this embodiment .

[0026] In this embodiment, a multivariate time series is used. The training data is used to train steps S5 and S6, as well as the overall deep neural network consisting of the two linear neural networks used for prediction in the PatchTST model. The loss function used is MAE (Mean Absolute Error).

[0027] Assuming that the underlying processes or models governing the generation of multivariate time series remain unchanged, i.e., the long-term dependencies between variables in the multivariate time series remain unchanged, then this overall deep neural network can be used to predict time points. The Future Step sequence value.

[0028] In this embodiment, a pre-trained deep neural network is run on a test set to predict the future. The mean square error (MSE) and mean absolute error (MAE) of the step sequence values ​​were 1.881 and 0.804, respectively. In comparison, the average MSE and MAE of the PatchTST model were 2.010 and 0.891, respectively. This indicates that incorporating inter-variable dependencies into the feature representation of multivariate time series can improve the quality of variable sequence feature representation and thus effectively enhance the performance of multivariate time series prediction algorithms.

[0029] Compared with the PatchTST model, which adopts a global modeling strategy to improve the model by considering the dependencies between all variables, the average MSE and MAE values ​​are 2.346 and 1.050, respectively. It can be seen that the predictive performance of the model has decreased significantly. This shows that introducing irrelevant or unnecessary dependencies between variables will degrade the quality of variable feature representation, thereby reducing the performance of multivariate time series prediction algorithms.

[0030] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping, characterized in that, Includes the following steps: S1. Decompose the multivariate time series into... A univariate time series, wherein, ; S2. Based on the univariate time series correlation measurement method, perform iterative calculations. The long-term correlation score is used to determine the correlation between any two univariate time series within a given univariate time series dataset. Based on this long-term correlation score, and according to a set filtering threshold, a long-term correlation matrix is ​​constructed. ; S3. Based on the long-term correlation matrix of variables Construct a long-term correlation plot of variables; S4. Use the graph maxima detection algorithm on the long-term correlation graph of variables to find overlapping groups of serial variables and obtain a list of overlapping variable groups; S5. Construct and train a deep neural network model employing a channel-independent strategy. Using a multivariate time subsequence as input, output based on the deep neural network model. The feature representation vectors corresponding to each univariate time subsequence are used to construct a feature representation matrix. The multivariate time series is taken from the multivariate time series generated by the underlying process or model that governs the generation of multivariate time series, which has not changed; S6. Based on the overlapping variable grouping list, a masked multi-head attention mechanism is adopted to incorporate long-term and short-term dependencies between variables into the feature representation matrix, thereby obtaining the variable feature representation after dependency fusion and completing the fusion of dependencies between variables in multivariate time series.

2. The fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping according to claim 1, characterized in that, Step S4 is as follows: S4.1 Define the overlapping variable grouping list as follows Set it to an empty list and set the node tag. ; S4.2 Extract node markers from the long-term correlation plot of variables. The corresponding node The subgraph is formed by all one-step neighbor nodes and the edges connecting them; the subgraph does not include nodes. and its edges connected to its 1-step neighbor nodes; S4.3 Find all the maximal cliques on the subgraph; S4.4, Combine the nodes contained in each maximal clique with the nodes mentioned above. Form a candidate group and add the candidate group to the list of overlapping variable groups. middle; S4.5, Settings ,judge If the condition is met, return to step S4.2; otherwise, proceed to step S4.

6. S4.6 Merging overlapping variable grouping lists Candidate grouping, i.e., removing duplicate groups and groups contained in other groups, and sorting the variables in each group according to their... The variables are sorted in ascending order to obtain the final list of overlapping variable groups. ,in, Indicates the number of groups. .

3. The fusion method for multivariate time series variables based on overlapping grouping according to claim 2, characterized in that, Step S6 is as follows: S6.1, Define the list of characteristics for grouping variables as follows: Set it to an empty list and set a grouping flag. Given the current time The length is Multivariate time subsequence Split into A single-variable time subsequence; S6.

2. Based on the univariate time series correlation measurement method, perform iterative calculations. The correlation score between any two univariate time series in a given univariate time series is used to construct a local correlation matrix of variables based on the correlation score. S6.3 Calculate the grouping in the overlapping variable grouping list The group mask matrix, where ; S6.4 Calculate the grouping based on the grouping mask matrix. The local correlation matrix of the variables is obtained, and then the grouping is calculated based on the local correlation matrix of the variables. Bernoulli sampling probability matrix; S6.

5. Based on the Bernoulli sampling probability matrix, construct grouping using reparameterization techniques. Variable correlation mask matrix; S6.

6. Based on the feature representation matrix constructed in step S5 and the variable correlation mask matrix constructed in step S6.5, a masked multi-head attention mechanism is used to calculate the variable feature representations that fuse the long-term and short-term dependencies between variables. And add it to the list of grouping variable feature representations. ; S6.7, Settings ,judge If the condition is not met, proceed to step S6.8; otherwise, return to step S6.

3. S6.8 List the characteristics of the grouping variables Variable feature representation in according to By concatenating in ascending order and row-wise, we obtain the concatenated matrix. ; S6.9 Construct a two-layer linear neural network and connect the resulting matrix. Mapping to a multivariate sequence feature representation that incorporates dependencies between variables Based on multivariate sequence feature representation This yields the variable feature representations after dependency fusion, thus completing the fusion of dependencies between variables in a multivariate time series.

4. The fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping according to claim 3, characterized in that: In step S2, based on the long-term correlation score and according to the set filtering threshold, a long-term correlation matrix of variables is constructed. The process is as follows: Set filter threshold If the long-term correlation score Then Set to 0 if the long-term correlation score Then keep The value remains unchanged, based on the filtered long-term relevance score. Construct a long-term correlation matrix of variables ,in, Indicates the first The univariate time series and the first Long-term correlation scores between univariate time series.

5. The fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping according to claim 4, characterized in that: In step S3, the long-term correlation plot of the variables is as follows: ,in, Represents the set of nodes in a graph. The set of edges representing a node; The solution process is as follows: traverse the long-term correlation matrix of the variables. An upper triangular or lower triangular matrix, without diagonals, if Then at node and nodes Add an edge between ,node Indicates the first A sequence variable of a univariate time series. ,node Indicates the first A sequence variable of a univariate time series. .

6. The fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping according to claim 5, characterized in that: In step S5, the process of constructing a deep neural network model using a channel-independent strategy is as follows: Construct an initial deep neural network model using a channel-independent strategy, with multivariate time subsequence... As input, the feature representation vector corresponding to the univariate time subsequence is used as output. A loss function is constructed based on the objective of the multivariate time series analysis task with the feature representation vector as input. The deep neural network model adopting the channel-independent strategy is trained to obtain the trained deep neural network model, thus completing the construction of the deep neural network model adopting the channel-independent strategy.

7. The fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping according to claim 6, characterized in that: In step S6.3, the block mask matrix is ​​calculated. The formula is: ； In the formula, , Indicates belonging to a group The label of the variable, .

8. The fusion method for inter-variable dependencies in multivariate time series based on overlapping grouping according to claim 7, characterized in that: In step S6.4, grouping Local correlation matrix of variables The calculation formula is: ； In the formula, Represents the local correlation matrix of variables. This represents the matrix dot product operation. In step S6.4, grouping Bernoulli sampling probability matrix The calculation formula is: ； In the formula, , , Indicates belonging to a group The label of the variable, .

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