Multivariable time sequence prediction method based on collaborative graph

Abstract

The invention discloses a multivariable time sequence prediction method based on a collaborative graph, and belongs to the technical field of time sequence analysis. The method mainly comprises the following steps that firstly, a multivariate time sequence is processed through a multi-scale feature extraction network, and feature representation matrixes under different scales are generated; secondly, capturing a multi-level relation mode between variables by utilizing a collaborative graph structure and a hypergraph structure, and generating an adjacent matrix and an incidence matrix which represent a multi-scale graph structure and the hypergraph structure; and then, learning a dependency relationship in space and time through the graph convolutional network and the hypergraph convolutional network to obtain multi-scale space-time dependency. And finally, fusing the feature dependence matrixes under each scale, and generating a final prediction result through a multi-layer perceptron and a convolutional neural network. According to the method, the multi-scale spatial relationship and the space-time dependency relationship are effectively combined, the multivariate time series can be predicted more accurately, and the prediction precision is improved.

Description

Technical Field

[0001] The present invention belongs to the field of multivariate time series analysis, and in particular relates to a multivariate time series prediction method based on a collaboration graph. Background Art

[0002] Modern society benefits from a wide range of sensors to record changes in temperature, prices, traffic speeds, electricity usage, and many other forms of data. The recorded time series from different sensors can form multivariate time series data and can be related to each other. For example, an increase in daily temperature may lead to an increase in electricity usage. In order to capture the systematic trends of a set of dynamically changing variables, the problem of multivariate time series forecasting has been studied for at least six decades. It sees great applications in the fields of economics, finance, bioinformatics, and traffic.

[0003] Time series forecasting involves inferring future trends and patterns by analyzing past observational data. Accurately forecasting time series plays a vital role in decision-making and planning in various social fields. Multivariate time series forecasting is an important subtask in time series forecasting, which focuses on the evolution and interrelationships of multiple variables over time, which makes predicting future trends more challenging.

[0004] In the early days, traditional statistical methods (such as vector autoregression and Gaussian process) were widely used in multivariate time series tasks. These methods rely on predefined assumptions to capture linear dependencies between time points. However, these methods are insufficient in dealing with nonlinear and non-stationary dependencies. With the development of deep neural networks, models such as convolutional neural networks (CNN), recurrent neural networks (RNN), and Transformer models based on global attention mechanisms have begun to be applied to multivariate time series prediction tasks. These models perform well in identifying long-term dependencies, but often ignore the impact of spatial information on prediction results.

[0005] Recently, graph neural networks (GNNs) have attracted extensive attention in multivariate time series tasks due to their ability to model spatial relations among multiple variables. Existing methods usually rely on predefined or adaptively learned adjacency matrices to capture spatial dependencies. Although these methods have addressed the problem of multiple relational patterns to some extent, they still have limitations in modeling complex spatial dependencies. In particular, traditional graph structures mainly focus on the relations between pairwise variables, ignoring higher-level abstract relational patterns. In addition, existing graph convolutional networks either only propagate low-order point-to-point correlations between nodes or only use high-order information, ignoring the interactions between different levels. To address this issue, this paper proposes a collaborative graph-based approach that uses graph and hypergraph networks to capture both low-order and high-order relations, and uses an attribute-enhanced hypergraph convolutional network to fully learn the interactivity of multi-order spatial relations. Summary of the invention

[0006] To overcome this problem, we propose a synergy graph-based multivariate time series forecasting method that models and learns multi-order spatial relationships of multivariate time series data.

[0007] First, the multivariate time series is processed through a multi-scale feature extraction network to generate feature representation matrices at different scales. Secondly, the collaborative graph structure and hypergraph structure are used to capture the multi-level relationship patterns between variables, and multi-scale graph structure and hypergraph structure representations are generated. Then, the spatial and temporal dependencies are learned through the graph convolutional network (GCN) and the hypergraph convolutional network (HGCN) to obtain multi-scale spatiotemporal dependencies. Finally, the feature dependency matrices at each scale are fused, and the final prediction results are generated through multi-layer perceptron and convolutional neural network.

[0008] Experimental results on four benchmark datasets demonstrate that our proposed model achieves state-of-the-art performance. In addition, ablation experiments show that the use of collaborative graphs and hypergraphs improves the ability of multivariate time series feature mining and the robustness of the performance improvement.

[0009] The present invention provides a multivariate time series prediction method based on a collaboration graph, comprising the following steps:

[0010] Step 1. Initialize the multi-scale feature representation of MTS, perform convolution operation on the input MTS data in the time dimension, use two convolutional networks to extract the feature representation of each scale, and finally add the output features of the two networks to obtain the multi-scale feature representation matrix of each scale. MTS is a multivariate time series.

[0011] Step 2. Input the multi-scale feature representation matrix obtained in step 1 into the collaborative relationship construction module, capture the multi-level relationship patterns between variables through graph structure and hypergraph structure, and construct low-order point-to-point relationships between variables based on static and dynamic adjacency matrices; generate a multi-scale association matrix using a randomly initialized hyperedge embedding matrix to capture high-order non-point-to-point relationship patterns, and obtain multi-scale graph structure and hypergraph structure representations;

[0012] Step 3. Input the multi-scale graph structure and hypergraph structure representation obtained in step 2 into the collaborative relationship learning module, and learn the spatial and temporal dependencies through the graph convolutional network and hypergraph convolutional network;

[0013] First, a bidirectional graph convolutional network is used to learn the incoming and outgoing information of nodes and obtain spatial dependencies.

[0014] Then, a two-layer attribute-enhanced hypergraph convolutional network is designed to achieve interactive learning between the node and attribute layers and enhance the multi-level spatial dependency feature association;

[0015] Finally, the outputs of the graph convolutional network and the hypergraph convolutional network are added together and combined with the temporal convolutional network to learn the spatiotemporal dependencies and obtain the spatiotemporal feature representation at multiple scales.

[0016] Step 4. Fuse and output the multi-scale spatiotemporal feature representation obtained in step 3, and use a multi-layer perceptron and convolutional neural network to convert it into the required output dimension to generate the final prediction result.

[0017] In the above technical solution, the specific process of step 1 is:

[0018] Step 1-1. Given a series of observed time series signals X = {x1, x2, ..., x T},in It represents the value at the time step t, and N represents the number of variables at this moment;

[0019] First, the original multivariate time series input undergoes a sequential graph convolutional network operation in the time dimension, and each layer generates feature representations of multiple scales. The feature representation of the kth scale is defined as N represents the number of variables at this moment, is the length of the sequence in the kth dimension, F k is the feature dimension of the kth scale;

[0020] Step 1-2. Use two parallel convolutional networks to add scale features.

[0021] One of the networks uses kernel sizes 1x7, 1x6, and 1x3 in each layer, with stride set to 2;

[0022] The other network uses a kernel size of 1x1 and a 1x2 pooling layer. are different convolution kernels, , is the bias term, which is formally:

[0023]

[0024]

[0025] Step 1-3. Finally, add the output features of the two networks to obtain the multi-scale feature representation matrix X for each scale k :

[0026]

[0027] In the above technical solution, the specific process of step 2 is:

[0028] Step 2-1. Represent the multi-scale feature matrix X of each scale obtained in step 1 k Input into the graph structure building module to obtain a multi-scale adjacency matrix representing the multi-scale graph structure.

[0029] First, a static graph learned in a parameter-driven manner is used to obtain the distance relationship between nodes. The formula is as follows:

[0030]

[0031]

[0032] in, represents the randomly initialized node embedding at the kth scale, and They are all training parameters, tanh and ReLU are activation functions, static representation and To get the adjacency matrix This matrix represents the static low-order point-to-point relationships at the kth scale;

[0033] Then, a data-driven strategy is used to learn dynamic low-order point-to-point relationships, treating the data itself as dynamic features at each time step and using a multi-layer perceptron to transform the raw MTS data into Mapping into dynamic features Will U k With dynamic representation and Merge to learn a dynamic adjacency matrix at the kth scale

[0034]

[0035]

[0036]

[0037] Finally, by combining the static and dynamic adjacency matrices, the final adjacency matrix A at the kth scale is derived k , effectively capturing the static and dynamic point-to-point relationship patterns, and obtaining a multi-scale adjacency matrix set

[0038] Step 2-2. Represent the multi-scale feature matrix X of each scale obtained in step 1 kInput into the hypergraph structure, construct the module, and obtain a multi-scale association matrix representing the multi-scale hypergraph structure;

[0039] First, randomly initialize the hyperedge of the kth scale and with the parameter Multiply to get the hyperedge embedding of the kth scale Then, the parameters and The k-th scale correlation matrix is ​​obtained by multiplying the transpose of Where N represents the number of variables and K represents the number of hyperedges. The association matrix of the kth scale can be expressed as:

[0040]

[0041]

[0042] in, and is a trainable parameter,

[0043] Finally, the incidence matrix set Contains the set of all association matrices that express higher-order, non-pairwise relationships between variables at multiple scales.

[0044] Step 2-3. Set the multi-scale adjacency matrix and the incidence matrix set Sent to the subsequent collaborative relationship learning module to learn spatiotemporal dependencies.

[0045] In the above technical solution, the specific process of step 3 is:

[0046] Step 3-1. The multi-scale adjacency matrix set obtained from step 2 and the incidence matrix set We use collaborative graphs and hypergraph convolutional networks to promote the interaction of spatial dependencies at multiple levels, while using temporal convolutional networks to capture more comprehensive spatiotemporal dependencies.

[0047] In the spatial dependency learning phase, first, a bidirectional graph convolutional network is used to learn the incoming and outgoing information of nodes.

[0048]

[0049] in and Incoming and outgoing parameters, is the spatial feature from the bidirectional graph convolution, Represents a bidirectional graph convolutional neural network.

[0050] Step 3-2. To obtain the hyperedge embedding matrix S k , multiplying the incident matrix with the input embedding at the kth scale and adding an additional adjacency learnable matrix To extract the high-level spatial dependencies of the attribute layers between hyperedges, the formula is expressed as:

[0051]

[0052] in represents the embedding representation of K hyperedges, each with dimensions F, I k is the k-th scale incidence matrix, X k is the embedding representation at the kth scale;

[0053] These hyperedges are also aggregated to generate the original node embedding at the kth scale The formula is expressed as:

[0054]

[0055] in Represents the activation function

[0056] Step 3-3. Add the two types of spatial features together to get a more comprehensive spatial representation relationship. β is a hyperparameter:

[0057]

[0058] Step 3-4. After learning the spatial dependencies, a temporal convolutional network is provided to capture the temporal dependencies and the H obtained in the previous layer is k Input temporal convolutional layer to obtain spatiotemporal representation at each scale

[0059]

[0060] In the time dimension Perform convolution operation, Represents different convolution kernels at different scales.

[0061] In the above technical solution, the specific process of step 4 is:

[0062] First, the feature representations of multiple scales are concatenated to obtain

[0063] Then, average pooling is performed on the scale dimension to obtain

[0064] Finally, Pooling(H) is transformed to the required prediction dimension using an MLP layer with a kernel size of 1xF and a CNN with a kernel size of 1x1.

[0065]

[0066]

[0067] That is the predicted value for the next H moments.

[0068] Because the present invention adopts the above technical solution, it has the following beneficial effects:

[0069] The present invention solves the technical problem of modeling complex relationships between variables and achieves higher prediction accuracy and model performance by proposing a new multivariate time series prediction framework: including a collaborative graph mechanism and a novel spatial learning strategy. Specifically, the collaborative graph mechanism seamlessly integrates dynamic graphs and hypergraphs to adaptively capture multi-level relationships between variables; while the spatial learning strategy combines collaborative graphs and hypergraph convolutional networks to effectively promote interactions across multi-level spatial dependencies, while using temporal convolutional networks to learn comprehensive spatiotemporal dependencies. By integrating the functions of hypergraphs and graphs, the experimental results of the present invention on baseline datasets show significant superiority, providing valuable insights for modeling complex relationships in future multivariate time series tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a simplified flow chart;

[0071] Figure 2 It is the overall model of the network;

[0072] Figure 3 It is a combination of data-driven strategy and parameter-driven strategy;

[0073] Figure 4 It is a double-layer attribute-enhanced hypergraph convolutional network. DETAILED DESCRIPTION

[0074] The following is a detailed description of the embodiments of the present invention. Although the present invention will be described and illustrated in conjunction with some specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, modifications or equivalent substitutions made to the present invention should all be included in the scope of the claims of the present invention.

[0075] In addition, in order to better illustrate the present invention, numerous specific details are given in the following specific embodiments. It will be understood by those skilled in the art that the present invention can also be implemented without these specific details.

[0076] The present invention provides a multivariate time series prediction method based on a collaboration graph, which is characterized by comprising the following steps:

[0077] Step 1. Initialize the multi-scale feature representation of the multivariate time series (MTS) and perform a convolution operation on the input MTS data in the time dimension. Use two convolutional networks to extract the feature representation of each scale, and finally add the output features of the two networks to obtain the multi-scale feature representation matrix of each scale;

[0078] Step 2. Input the multi-scale feature representation matrix obtained in step 1 into the collaborative relationship construction module to capture the multi-level relationship patterns between variables through graph structure and hypergraph structure. Based on static and dynamic adjacency matrices, low-order point-to-point relationships between variables are constructed; multi-scale association matrices are generated using randomly initialized hyperedge embedding matrices to capture high-order non-point-to-point relationship patterns, and obtain multi-scale graph structure and hypergraph structure representations;

[0079] Step 3. Input the multi-scale graph structure and hypergraph structure representation obtained in step 2 into the collaborative relationship learning module, and learn the spatial and temporal dependencies through the graph convolutional network (GCN) and the hypergraph convolutional network (HGCN). First, use the bidirectional graph convolutional network to learn the incoming and outgoing information of the nodes to obtain the spatial dependencies. Then, design a two-layer attribute-enhanced hypergraph convolutional network to realize interactive learning between the node and attribute layers and enhance the multi-level spatial dependency feature association. Finally, add the outputs of GCN and HGCN, and combine them with the temporal convolutional network (TCN) to learn the spatiotemporal dependencies and obtain the spatiotemporal feature representation at multiple scales;

[0080] Step 4. Fuse and output the multi-scale spatiotemporal feature representation obtained in step 3, and use a multi-layer perceptron (MLP) and a convolutional neural network (CNN) to convert it into the required output dimension to generate the final prediction result.

[0081] In the above technical solution, the specific process of step 1 is:

[0082] Step 1-1. Given a series of observed time series signals X = {x1, x2, ..., x T},in It represents the value at the time step t, and N represents the number of variables at this moment;

[0083] First, the original multivariate time series input undergoes a sequential graph convolutional network operation in the time dimension, and each layer generates feature representations of multiple scales. The feature representation of the kth scale is defined as N represents the number of variables at this moment, is the length of the sequence in the kth dimension, F k is the feature dimension of the kth scale;

[0084] Step 1-2. Use two parallel convolutional networks to add scale features.

[0085] One of the networks uses kernel sizes 1x7, 1x6, and 1x3 in each layer, with stride set to 2;

[0086] The other network uses a kernel size of 1x1 and a 1x2 pooling layer. are different convolution kernels, is the bias term, which is in the form:

[0087]

[0088]

[0089] Step 1-3. Finally, add the output features of the two networks to obtain the multi-scale feature representation matrix X for each scale k :

[0090]

[0091] In the above technical solution, the specific process of step 2 is:

[0092] Step 2-1. Represent the multi-scale feature matrix X of each scale obtained in step 1 k Input into the graph structure building module to obtain a multi-scale adjacency matrix representing the multi-scale graph structure.

[0093] First, a static graph learned in a parameter-driven manner is used to obtain the distance relationship between nodes. The formula is as follows:

[0094]

[0095]

[0096] in, represents the randomly initialized node embedding at the kth scale, and They are all training parameters, tanh and ReLU are activation functions, static representation and To get the adjacency matrix This matrix represents the static low-order point-to-point relationships at the kth scale;

[0097] Then, a data-driven strategy is used to learn dynamic low-order point-to-point relationships, treating the data itself as dynamic features at each time step and using a multi-layer perceptron to transform the raw MTS data into Mapping into dynamic features , will U k With dynamic representation and Merge to learn a dynamic adjacency matrix at the kth scale

[0098]

[0099]

[0100]

[0101] Finally, by combining the static and dynamic adjacency matrices, the final adjacency matrix A at the kth scale is derived k , effectively capturing the static and dynamic point-to-point relationship patterns, and obtaining a multi-scale adjacency matrix set

[0102] Step 2-2. Represent the multi-scale feature matrix X of each scale obtained in step 1 k Input into the hypergraph structure, construct the module, and obtain a multi-scale association matrix representing the multi-scale hypergraph structure;

[0103] First, randomly initialize the hyperedge of the kth scale and with the parameter Multiply to get the hyperedge embedding of the kth scale Then, the parameters and The k-th scale correlation matrix is ​​obtained by multiplying the transpose of Where N represents the number of variables and K represents the number of hyperedges. The association matrix of the kth scale can be expressed as:

[0104]

[0105]

[0106] in, and is a trainable parameter,

[0107] Finally, the incidence matrix set Contains the set of all association matrices that express higher-order, non-pairwise relationships between variables at multiple scales.

[0108] Step 2-3. Set the multi-scale adjacency matrix and the incidence matrix set Sent to the subsequent collaborative relationship learning module to learn spatiotemporal dependencies.

[0109] In the above technical solution, the specific process of step 3 is:

[0110] Step 3-1. The multi-scale adjacency matrix set obtained from step 2 and the incidence matrix set We use collaborative graphs and hypergraph convolutional networks to promote the interaction of spatial dependencies at multiple levels, while using temporal convolutional networks to capture more comprehensive spatiotemporal dependencies.

[0111] In the spatial dependency learning phase, first, a bidirectional graph convolutional network is used to learn the incoming and outgoing information of nodes.

[0112]

[0113] in and Incoming and outgoing parameters, is the spatial feature from the bidirectional graph convolution, Represents a graph convolutional neural network.

[0114] Step 3-2. To obtain the hyperedge embedding matrix S k , multiplying the incident matrix with the input embedding at the kth scale and adding an additional adjacency learnable matrix To extract the high-level spatial dependencies of the attribute layers between hyperedges, the formula is expressed as:

[0115]

[0116] in represents the embedding representation of K hyperedges, each with dimensions F, I k is the k-th scale incidence matrix, X k is the embedding representation at the kth scale;

[0117] These hyperedges are also aggregated to generate the original node embedding at the kth scale The formula is expressed as:

[0118]

[0119] Step 3-3. Add the two types of spatial features together to get a more comprehensive spatial representation relationship. β is a hyperparameter:

[0120]

[0121] Step 3-4. After learning the spatial dependencies, a temporal convolutional network is provided to capture the temporal dependencies and the H obtained in the previous layer is k Input temporal convolutional layer to obtain spatiotemporal representation at each scale

[0122]

[0123] In the time dimension Perform convolution operation, Represents different convolution kernels at different scales.

[0124] In the above technical solution, the specific process of step 4 is:

[0125] First, the feature representations of multiple scales are concatenated to obtain

[0126] Then, average pooling is performed on the scale dimension to obtain

[0127] Finally, Pooling(H) is transformed to the required prediction dimensions using an MLP layer with a kernel size of 1xF and a CNN with a kernel size of 1x1.

[0128]

[0129]

[0130] That is the predicted value for the next H moments.

[0131] Because the present invention adopts the above technical solution, it has the following characteristics:

[0132] Through the multi-scale feature extraction network, the present invention solves the problem of feature representation in multivariate time series processing, realizes the generation of feature representation matrices at different scales, and improves the efficiency and diversity of feature extraction. Compared with the traditional single-scale feature extraction method, this multi-scale feature extraction can better capture the detailed information in the time series and enhance the expression ability of the model.

[0133] By using collaborative graph structures and hypergraph structures, the present invention solves the problem of modeling complex relationships between variables in multivariate time series. Through static and dynamic adjacency matrices, as well as hyperedge embedding matrices, low-order and high-order relationship patterns between variables are effectively captured, improving the accuracy and comprehensiveness of relationship modeling. Compared with traditional graph structure modeling, this collaborative graph and hypergraph structure can more comprehensively capture the multi-level relationships between variables.

[0134] Through graph convolutional networks (GCN) and hypergraph convolutional networks (HGCN), the present invention solves the problem of modeling spatial and temporal dependencies. The bidirectional graph convolutional network and the attribute-enhanced hypergraph convolutional network effectively learn spatial and temporal dependencies and improve the model's ability to model complex dependencies. This network structure that combines graph convolution and hypergraph convolution can more comprehensively learn spatial and temporal dependencies between variables compared to a single type of network.

[0135] Finally, through multi-layer perceptron and convolutional neural network, the present invention solves the fusion problem of multi-scale spatiotemporal feature representation. By fusing spatiotemporal features of different scales, the final prediction result is generated, which improves the accuracy and robustness of the prediction. This multi-scale spatiotemporal feature fusion strategy can more accurately predict the future trend of multivariate time series compared with the traditional single-scale prediction method.

Claims

1. A multivariate time series prediction method based on a synergy graph, characterized in that: The following steps are involved: Step 1. Initialize the multi-scale feature representation of MTS, perform convolution operation on the input MTS data in the time dimension, use two convolutional networks to extract the feature representation of each scale, and finally add the output features of the two networks to obtain the multi-scale feature representation matrix of each scale. MTS is a multivariate time series. Step 2. Input the multi-scale feature representation matrix obtained in step 1 into the collaborative relationship construction module, capture the multi-level relationship pattern between variables through graph structure and hypergraph structure, and construct low-order point-to-point relationships between variables based on static and dynamic adjacency matrices; The randomly initialized hyperedge embedding matrix is ​​used to generate multi-scale correlation matrices to capture high-order non-point-to-point relationship patterns and obtain multi-scale graph and hypergraph structure representations. Step 3. Input the multi-scale graph structure and hypergraph structure representation obtained in step 2 into the collaborative relationship learning module, and learn the spatial and temporal dependencies through the graph convolutional network and hypergraph convolutional network; First, a bidirectional graph convolutional network is used to learn the incoming and outgoing information of nodes and obtain spatial dependencies. Then, a two-layer attribute-enhanced hypergraph convolutional network is designed to achieve interactive learning between the node and attribute layers and enhance the multi-level spatial dependency feature association; Finally, the outputs of the graph convolutional network and the hypergraph convolutional network are added together and combined with the temporal convolutional network to learn the spatiotemporal dependencies and obtain the spatiotemporal feature representation at multiple scales. Step 4. Fuse and output the multi-scale spatiotemporal feature representation obtained in step 3, and use a multi-layer perceptron and convolutional neural network to convert it into the required output dimension to generate the final prediction result.

2. The multivariate time series prediction method based on collaborative graph according to claim 1, characterized in that: The specific process of step 1 is: Step 1-1. Given a series of observed time series signals X = {x1, x2, ..., x T },in It represents the value at the time step t, and N represents the number of variables at this moment; First, the original multivariate time series input undergoes sequential graph convolutional network operations in the time dimension, and each layer generates feature representations of multiple scales. The feature representation of the kth scale is defined as N represents the number of variables at this moment, is the length of the sequence in the kth dimension, F k is the feature dimension of the kth scale; Step 1-2. Use two parallel convolutional networks to add scale features. One of the networks uses kernel sizes 1x7, 1x6, and 1x3 in each layer, with stride set to 2; The other network uses a kernel size of 1x1 and a 1x2 pooling layer. are different convolution kernels, is the bias term, which is in the form: Step 1-3. Finally, add the output features of the two networks to obtain the multi-scale feature representation matrix X for each scale k :

3. The multivariate time series prediction method based on collaborative graph according to claim 2 is characterized in that: The specific process of step 2 is: Step 2-1. Represent the multi-scale feature matrix X of each scale obtained in step 1 k Input into the graph structure building module to obtain a multi-scale adjacency matrix representing the multi-scale graph structure. First, a static graph learned in a parameter-driven manner is used to obtain the distance relationship between nodes. The formula is as follows: in, represents the randomly initialized node embedding at the kth scale, and They are all training parameters, tanh and ReLU are activation functions, static representation and To get the adjacency matrix This matrix represents the static low-order point-to-point relationships at the kth scale; Then, a data-driven strategy is used to learn dynamic low-order point-to-point relationships, treating the data itself as dynamic features at each time step and using a multi-layer perceptron to transform the raw MTS data into Mapping into dynamic features , will U k With dynamic representation and Merge to learn a dynamic adjacency matrix at the kth scale Finally, by combining the static and dynamic adjacency matrices, the final adjacency matrix A at the kth scale is derived k , effectively capturing the static and dynamic point-to-point relationship patterns, and obtaining a multi-scale adjacency matrix set Step 2-2. Represent the multi-scale feature matrix X of each scale obtained in step 1 k Input into the hypergraph structure, construct the module, and obtain a multi-scale association matrix representing the multi-scale hypergraph structure; First, randomly initialize the hyperedge of the kth scale and with the parameter Multiply to get the hyperedge embedding of the kth scale Then, the parameters and The k-th scale correlation matrix is ​​obtained by multiplying the transpose of N represents the number of variables, K represents the number of hyperedges, and the k-th scale association matrix can be expressed as: in, and is a trainable parameter, Finally, the incidence matrix set Contains the set of all association matrices that express higher-order, non-pairwise relationships between variables at multiple scales. Step 2-3. Set the multi-scale adjacency matrix and the incidence matrix set Sent to the subsequent collaborative relationship learning module to learn spatiotemporal dependencies.

4. The multivariate time series prediction method based on collaborative graph according to claim 3 is characterized in that: The specific process of step 3 is: Step 3-1. The multi-scale adjacency matrix set obtained from step 2 and the incidence matrix set We use collaborative graphs and hypergraph convolutional networks to promote the interaction of spatial dependencies at multiple levels, while using temporal convolutional networks to capture more comprehensive spatiotemporal dependencies. In the spatial dependency learning phase, first, a bidirectional graph convolutional network is used to learn the incoming and outgoing information of nodes. Its reason and Incoming and outgoing parameters, is the spatial feature from the bidirectional graph convolution, Represents a graph convolutional neural network using node-incoming directions and node-outgoing directions. Step 3-2. To obtain the hyperedge embedding matrix S k , multiplying the incident matrix with the input embedding at the kth scale and adding an additional adjacency learnable matrix To extract the high-level spatial dependencies of the attribute layers between hyperedges, the formula is expressed as: in represents the embedding representation of K hyperedges, each with dimensions F, I k is the k-th scale incidence matrix, X k is the embedding representation at the kth scale; These hyperedges are also aggregated to generate the original node embedding at the kth scale The formula is expressed as: in represents the embedding of K hyperedges, represents the activation function, I represents the association matrix; Step 3-3. Add the two types of spatial features together to get a more comprehensive spatial representation relationship. β is a hyperparameter: Step 3-4. After learning the spatial dependencies, a temporal convolutional network is provided to capture the temporal dependencies and the H obtained in the previous layer is k Input temporal convolutional layer to obtain spatiotemporal representation at each scale In the time dimension Perform convolution operation, Represents different convolution kernels at different scales.

5. The multivariate time series prediction method based on collaborative graph according to claim 1, characterized in that: The specific process of step 4 is: First, the feature representations of multiple scales are concatenated to obtain Then, average pooling is performed on the scale dimension to obtain Finally, Pooling(H) is transformed to the required prediction dimensions using an MLP layer with a kernel size of 1xF and a CNN with a kernel size of 1x1. That is the predicted value for the next H moments.

Images