A spatiotemporal sequence interpolation method and device for heterogeneous missing

Abstract

This invention discloses a spatiotemporal sequence interpolation method and apparatus for heterogeneous missing data, belonging to the field of spatiotemporal data processing technology. Addressing the random or continuous missing data in sensor networks due to faults or communication interruptions, this method sets up static spatial experts, dynamic spatial experts, short-term time experts, and long-term periodic experts in parallel within the same framework to capture fixed geographical adjacency, time-varying spatial correlation, local continuous trends, and long-term periodic patterns, respectively. Spatial features are extracted through high-order diffusion graph convolution and bidirectional gated loops, while temporal features are extracted using multi-layer spatiotemporal attention. A memory attention gating network is introduced to dynamically weight and fuse the outputs of each expert based on reconstruction errors, achieving adaptive interpolation at the node and time step levels. Experiments show that this method significantly improves accuracy and robustness compared to existing technologies in various real-world datasets and heterogeneous missing data scenarios, and can be widely applied to scenarios requiring high-completeness spatiotemporal data, such as intelligent transportation, air quality monitoring, and the energy Internet of Things.

Description

Technical Field

[0001] This invention relates to the field of spatiotemporal sequence data processing technology, and in particular to a spatiotemporal sequence interpolation method and apparatus for heterogeneous missing data. Background Technology

[0002] In emerging infrastructure such as smart cities, dual-carbon monitoring, and smart grids, numerous sensor nodes continuously collect observational data with geographical locations and timestamps, forming so-called "spatiotemporal sequence data." This data is widely used in fields such as intelligent transportation, air quality monitoring, meteorological observation, and the Internet of Things for energy, supporting critical tasks such as urban management, environmental monitoring, and resource allocation. Each spatiotemporal sequence not only records the dynamic process of a location changing over time but also implies the spatial correlation between different locations. However, due to factors such as sensor failure, communication interruptions, and environmental interference, the actual spatiotemporal data collected often contains a large number of missing values.

[0003] These missing data are not random or follow a single pattern, but rather exhibit high heterogeneity. In the temporal dimension, there are both brief, random missing data points and long-term, continuous missing data points; in the spatial dimension, there may be local anomalies at individual nodes, or regional missing data where multiple nodes are simultaneously offline. This complex and varied missing data pattern poses a significant challenge to data integrity and subsequent analysis, prediction, and decision-making. Therefore, how to accurately and robustly recover missing data has become one of the core issues in spatiotemporal data processing.

[0004] To address this problem, researchers have conducted extensive studies on "spatiotemporal dependency structures," attempting to infer the true values ​​at missing locations by modeling spatial correlations and temporal evolution patterns. Spatial dependency refers to the tendency for adjacent or structurally similar nodes to exhibit similar observations at the same time point; temporal dependency refers to the trend or periodic evolutionary patterns that exist between the same node at different time steps. Based on these two types of dependencies, existing spatiotemporal sequence interpolation methods can be broadly categorized into three types:

[0005] The first category is imputation methods that only model time dependencies. These methods treat each spatial node as an independent one-dimensional time series, using historical observation data to model its temporal evolution. Common techniques include autoregressive models (such as ARIMA), exponential smoothing, Kalman filters, and recurrent neural networks (such as LSTM and GRU). These methods perform well in capturing short-term trends and periodicity, and are suitable for scenarios with low missing proportions and strong temporal continuity. However, they ignore spatial correlations and cannot utilize information from neighboring nodes, leading to imputation results that are prone to bias when facing large-scale missing data or the spread of sudden events, and even performing poorly in areas with sparse node distribution.

[0006] The second category is interpolation methods that only model spatial dependencies. These methods assume that nodes that are spatially close or structurally similar at the same time point have similar observations. They often use spatial interpolation algorithms (such as inverse distance weighting and kriging) or graph-based learning methods (such as graph convolutional networks, GCNs) for modeling. They can effectively utilize local spatial structures and have good recovery capabilities for short-term missing data in densely populated node regions. However, these methods usually ignore the dynamic evolution in the temporal dimension and cannot capture the historical trends and periodic changes of the nodes themselves, resulting in a lack of temporal consistency in the interpolation results. This is especially true when there are long-term missing data or when the system state evolves, leading to poor recovery performance.

[0007] The third category is interpolation methods that jointly model spatiotemporal dependencies. In recent years, with the development of deep learning, researchers have proposed various modeling frameworks that integrate spatiotemporal information, such as ST-GCN, ASTGCN, and STGAT. These methods attempt to simultaneously capture the dependencies between spatial and temporal dimensions by combining spatial convolution of graph structures with time-series modeling modules (such as RNNs, TCNs, and Transformers), thereby improving the accuracy and robustness of interpolation. In addition, there are methods based on tensor decomposition (such as HaLRTC and BTTF) and Transformer models based on attention mechanisms (such as ImputeFormer), which further explore the latent structure of spatiotemporal data through low-rank reconstruction or cross-dimensional attention mechanisms. Summary of the Invention

[0008] This invention proposes a method and apparatus for spatiotemporal sequence interpolation addressing heterogeneous missing sequences. This method explicitly decouples and models the implicit spatiotemporal dependencies of spatiotemporal sequences through structured expert partitioning. The specific technical solution is as follows:

[0009] A spatiotemporal sequence imputation method for heterogeneous missing sequences includes the following steps:

[0010] The original spatiotemporal sequences acquired by the sensor network are standardized, and the observation tensor is synchronized with the missing mask based on the mask tensor;

[0011] The static spatial expert and dynamic spatial expert submodules are launched in parallel. The static spatial expert submodule uses a fixed geographic adjacency matrix to drive graph convolution to generate hidden states and spatial interpolation results. The dynamic spatial expert submodule fuses historical observations, node embeddings and periodic time embeddings at each time step and generates a time-varying adjacency matrix through self-attention. Then, it obtains a multi-order support set through high-order diffusion. The hidden states are extracted using the support set. The hidden states are fused through structure-aware decoding and gating to output the spatial interpolation results.

[0012] The short-term time expert and long-term period expert submodules are launched in parallel. Both submodules include: fusing the input observations and the mask, and then using a multilayer perceptron to uniformly map the original channels to the hidden dimensions to obtain a preliminary representation. The design recovers the initial representation by learningable mask vectors, projects periodic temporal embeddings into the hidden space and broadcasts them in the node dimension. Then, fixed positional codes are superimposed in the temporal dimension to obtain a representation with positional codes. The model is then performed by stacked spatiotemporal attention to finally obtain the hidden state and temporal interpolation results.

[0013] The observation tensor, missing mask, and hidden states of each expert are concatenated to form a query embedding. The query embedding is refined by memory attention and its cosine similarity to the states of each expert after self-attention transformation is calculated to generate normalized expert weights. The imputation features of each expert are weighted and summed according to the weights to obtain the final imputation result. The best choice and worst avoidance labels are dynamically calculated based on the reconstruction error of each expert.

[0014] A spatiotemporal sequence interpolation device for heterogeneous missing sequences includes the following steps:

[0015] The sequence acquisition module standardizes the raw spatiotemporal sequence acquired by the sensor network and synchronizes the observation tensor with the missing mask based on the mask tensor.

[0016] The spatial dependency modeling module starts static and dynamic spatial expert sub-modules in parallel. The static spatial expert sub-module uses a fixed geographic adjacency matrix to drive graph convolution to generate hidden states and spatial interpolation results. The dynamic spatial expert sub-module fuses historical observations, node embeddings and periodic time embeddings at each time step and generates a time-varying adjacency matrix through self-attention. Then, it obtains a multi-order support set through high-order diffusion. The hidden state is extracted using the support set. The hidden state is then fused with structure-aware decoding and gating to output the spatial interpolation result.

[0017] The time-dependent modeling module initiates short-term time expert and long-term period expert submodules in parallel. Both submodules involve fusing input observations and masks, and then using a multilayer perceptron to uniformly map the original channels to the hidden dimensions to obtain a preliminary representation. The design recovers the initial representation by learningable mask vectors, projects periodic temporal embeddings into the hidden space and broadcasts them in the node dimension. Then, fixed positional codes are superimposed in the temporal dimension to obtain a representation with positional codes. The model is then performed by stacked spatiotemporal attention to finally obtain the hidden state and temporal interpolation results.

[0018] The output module concatenates the observation tensor, missing mask, and hidden states of each expert into a query embedding. After the query embedding is refined by memory attention, the cosine similarity between the query embedding and the state after the self-attention transformation of each expert is calculated to generate normalized expert weights. The imputation features of each expert are weighted and summed according to the weights to obtain the final imputation result. The best choice and worst avoidance labels are dynamically calculated based on the reconstruction error of each expert.

[0019] An electronic device includes: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.

[0020] A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.

[0021] The present invention has the following beneficial effects:

[0022] This invention explicitly decouples spatiotemporal dependencies through four types of structured experts. Static spatial experts (SE), dynamic spatial experts (DE), short-term time experts (RTE), and long-term time experts (LTE) are set up in parallel within the same interpolation framework. Expert weights are generated at the node and time step levels by a gating network, and the expert outputs are adaptively weighted and fused to obtain the interpolation result.

[0023] This invention is based on dynamic graph construction (DE) based on "prior × attention". At each time step, the dynamic spatial expert fuses historical observations, temporal embeddings, and node embeddings to calculate attention relevance; and multiplies it element-wise with the prior similarity matrix obtained from node embeddings / geography / relevance to form a time-varying adjacency matrix, which is used for subsequent graph convolution / recursive propagation.

[0024] This invention employs memory attention gating with dynamic supervision based on expert error. The gating network uses memory attention to generate query representations, matches and scores four expert hidden representations, and introduces gating supervision labels (best choice and worst avoidance) to explicitly constrain the route distribution, improving selection stability and interpretability.

[0025] This invention proposes a structured expert hybrid framework that enables dynamic adaptive modeling of complex dependency structures in spatiotemporal sequence imputation tasks. By explicitly dividing and coordinating four types of expert modules, it can capture multi-level spatiotemporal dependencies, including static space, dynamic space, short-term time, and long-term periodicity, and achieves structural adaptation to heterogeneous missing patterns through a gating mechanism. System experiments conducted on multiple real-world public datasets and various missing scenarios demonstrate that the proposed solution significantly outperforms existing mainstream methods in terms of accuracy, robustness, and generalization ability. Attached Figure Description

[0026] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0028] like Figure 1 As shown, a spatiotemporal sequence interpolation method for heterogeneous missing sequences according to the present invention includes the following steps:

[0029] Step 1: Data preprocessing. The data acquired by the sensor network is converted into an observation tensor, and the observation tensor is recovered based on the mask tensor.

[0030] Data from a source Acquisition is obtained from a sensor network consisting of spatial nodes, with each node continuously... Data collected at each time step Dimensional observations form an observation tensor. However, due to sensor malfunctions, transmission delays, or other external factors, some values ​​are missing in the tensor.

[0031] Introduce a mask tensor of the same shape. ,in Indicates the location The observation tensor on Observations on the tensor are available if they are not, otherwise they are missing. The goal is to use the existing observation tensor... and mask tensor Learn an interpolation function To recover the complete observation tensor and make The model aims to approximate the true value as closely as possible to the missing values. The input observation tensor of the model... It has been standardized by standard deviation for the purpose of gradient stabilization.

[0032] Step 2, spatial dependency modeling, introduces static spatial expert submodule and dynamic spatial expert submodule, and models the two types of spatial dependency structures respectively.

[0033] This invention introduces two types of structured spatial expert modules: static spatial expert submodules and dynamic spatial expert submodules. These submodules model static and dynamic spatial dependency structures respectively, enhancing the model's adaptability and discriminative ability against different types of spatial dependency patterns. The two types of experts are essentially identical in structure, except for the adjacency matrix design.

[0034] In the Static Spatial Expert (SE) submodule, a priori given static adjacency matrix is ​​used as the basis for spatial structure information. In this invention, this static adjacency matrix is ​​calculated using the distances between sensors. In the actual model, all graph-related operations (such as higher-order graph convolution, gated recurrent units, etc.) in the Static Spatial Expert (SE) submodule are based on this fixed adjacency matrix.

[0035] In contrast, spatial dependency structures in the real world are often not constant but dynamically change with factors such as environment and time period. To characterize these time-varying spatial relationships, the dynamic spatial expert submodule (DE) adaptively learns the adjacency matrix at each time step. The main process is as follows:

[0036] At each time step This method integrates historical node observations, temporal context, and semantic information to dynamically model spatial structure. The specific steps are as follows:

[0037] First, extract the historical observation sequence for each node. ,in For the length of the history window, For the number of nodes, The number of channels. After stitching together observations from different channels, the data is passed through two layers of nonlinear fully connected networks. Basic dynamic features are obtained. Temporal embedding is also introduced. (representing intraday and weekly cycles respectively), and two sets of node embedding matrices. , where the embedding matrix The embedding matrix is ​​used to represent the embedding of each node during the outward propagation of information. This is used to represent the embedding representation of each node during the information inward reception process. Based on this, the forward and reverse node dynamic feature matrices are constructed respectively:

[0038] ;

[0039] ;

[0040] in, This represents the stitching together of historical observations for each node across all channels, where This represents a splicing operation on the channel dimension C. It is the observation data of historical observation sequence X on channel C.

[0041] Subsequently, the dynamic correlation between node pairs is modeled using a self-attention mechanism, specifically:

[0042] ;

[0043] ;

[0044] in, These are the static prior adjacency matrices, calculated from node embedding similarity. For self-attention parameters, This represents the Hadamard product (element-wise multiplication), with the Softmax operation normalizing each row. For the final feature dimension, , These are obtained by calculating the node embedding similarity, which represents the static prior adjacency matrix, and correspond to the static graph structure priors in the upstream and downstream directions, respectively. , These represent the dynamic adjacency matrix learned at time t, the dynamic correlation between node pairs calculated using a self-attention mechanism, and then compared with the static prior adjacency matrix. , We obtain it by multiplying element by element.

[0045] final, and Each as a time The forward and reverse dynamic adjacency matrices, where The forward dynamic adjacency matrix (upstream) at time t is used to model the dependency of information flowing from upstream nodes to downstream nodes; The downstream dynamic adjacency matrix at time t is used to model the dependency of information feedback from downstream nodes to upstream nodes. These two types of matrices differ in directionality and are used for information propagation in subsequent dynamic graph convolutions and recursive structures, enabling adaptive modeling of time-varying spatial dependencies.

[0046] To more comprehensively capture the multi-level spatial dependencies between nodes, this invention introduces a higher-order diffusion support set when constructing the graph structure. Specifically, for any time t, regardless of whether a static adjacency matrix is ​​used... Or a dynamic graph adjacency matrix All of them generate multi-order support matrices through high-order matrix multiplication. Each support matrix is ​​defined as follows:

[0047] ;

[0048] in, Let represent the adjacency matrix at time t, k represent the diffusion order, and K represent the maximum diffusion order, i.e., the highest order in the set of support matrices considered. Let represent the k-th support matrix at time t, obtained through exponentiation of the adjacency matrix. This higher-order diffusion mechanism significantly enhances the model's ability to model long-distance spatial dependencies and higher-order structural relationships, enabling nodes to perceive a wider neighborhood range when aggregating information. Finally, the resulting support set... It will be used in subsequent spatial dependency modeling modules to achieve richer and more flexible spatial feature interactions.

[0049] To fully model the complex spatial topology in spatiotemporal sequences, this invention proposes an interpolation method with a bidirectional graph convolutional recurrent network as its backbone. This module not only integrates forward and backward spatiotemporal contexts but also achieves adaptive interpolation for heterogeneous missing distributions and spatial relationships through a structure-aware spatial decoding and gating fusion mechanism.

[0050] At each time step t, observe the node. As input, it combines the hidden state from the previous time step with the current spatial support matrix. The spatiotemporal hidden state of nodes is updated recursively through a graph convolutional gated recurrent unit (GCGRU). Specifically, this includes:

[0051] Forward Pass: Recursively generates forward hidden states based on prior observations and historical states. ;

[0052] Backward Pass: Recursively generates backward hidden states based on subsequent observations. .

[0053] Bidirectional recursive design can explicitly utilize historical and future information, mitigating the problem of accumulated interpolation errors in long missing segments caused by unidirectional inference.

[0054] Obtaining the forward and reverse hidden states and After representing the forward and reverse hidden states respectively, a structure-aware spatial decoder is further designed to refine the interpolation results. For each time t, the observations are... Missing mask Node embedding and hidden states , The concatenation process, followed by multi-stage spatial convolution and spatial attention mechanisms, extracts high-order neighbor features and structural context information. The spatial decoder outputs bidirectional refined interpolated values. and refined interpolation result characterization This effectively improves the robustness of interpolation under complex spatial relationships. Node embedding It refers to and The average.

[0055] To adapt to node heterogeneity and spatial dependency diversity, the model introduces a gated fusion network to adaptively weight the structural representations from different directions and expert branches. Specifically, the forward and reverse spatial representation vectors are weighted... With node embedding Missing mask splicing, as a hidden state of the interpolation output results of the corresponding spatial expert submodule. Missing mask This refers to the missing mask of this historical sequence. The splicing result is fed into a multilayer perceptron (MLP) to obtain the final interpolated output. :

[0056] ;

[0057] Step 3: Time-dependent modeling. Two parallel sub-modules, short-term time experts and long-term cycle experts, are introduced to model local continuity and global cycle trends.

[0058] Temporal dependency structures play an indispensable role in multivariate spatiotemporal sequence imputation. To address the temporal characteristics at different scales, this invention introduces two parallel sub-modules: a Recent Temporal Expert and a Long Temporal Expert, to fully model local continuity and global periodic trends, thereby improving the accuracy and generalization ability of missing value recovery.

[0059] Both types of experts maintain a consistent model structure, differing only in their inputs. Specifically, the short-term expert submodule focuses on modeling the dependencies between adjacent time steps in the observation sequence, concentrating on the information flow within the local context. Its core idea is to leverage the strong correlations between consecutive time steps in the sequence to efficiently imput missing data within a short window. Therefore, the input to the short-term expert includes observations within the current time window. Time embedding The inputs are the time embedding and the missing mask m of the current window, where the time embedding is... It is calculated using a time index; specifically, the input time index sequence is... , where T is the time step. Let the set of periodic units be . For any unit Its standard period length is defined as Where: the standard cycle length of a day is 24 hours, and the standard cycle length of a week is 7 hours. 24 hours. Then, the timestamp t is converted to a uniform nanosecond count. Calculate the phase angle: Then, for each periodic unit u, sine and cosine embeddings are generated using sine and cosine functions respectively. The sine and cosine embeddings of each u are then concatenated to obtain the final time embedding. .

[0060] To capture broader global trends, long-term dependencies, and cyclical patterns, the long-term cycle expert submodule takes extended historical windows and cycle auxiliary features as inputs. Cycle auxiliary features refer to the features of the same window spanning seven days before and after the extended historical window, serving as auxiliary features for daily and weekly cycles, focusing on modeling long-term time dependencies across cycles and seasons. The long-term cycle expert submodule can effectively fill in global gaps and long-segment breaks that are difficult to imputate with local information.

[0061] The specific sub-module structures for the short-term time expert and long-term cycle expert are as follows: Before entering the Transformer structure, the input observations and masks are first fused, retaining only the true observations:

[0062] ;

[0063] in, To find the Hadamard product;

[0064] Then, a multilayer perceptron is used to uniformly map the original channels to the hidden dimensions to obtain a preliminary representation. ;

[0065] Furthermore, to avoid missing locations lacking representation, a learnable mask vector is designed. Features of the missing parts:

[0066] ;

[0067] Next, the periodic time is embedded. Projected into the hidden space and broadcast along the node dimension to achieve temporal conditionalization:

[0068] ;

[0069] ;

[0070] in, This represents a broadcast operation.

[0071] In addition, to enhance the temporal sequence information, a fixed positional code is superimposed on the time dimension to obtain a representation with positional codes. .

[0072] Subsequently Modeling is performed using L stacked spatiotemporal Transformers. Each layer first performs attention calculations in the temporal dimension, then in the node dimension, and finally maps the result through a feedforward network (FFN) to obtain the final representation of the current Transformer layer. After being stacked through L layers, the final state is hidden. , The final interpolation result is then obtained through a multilayer perceptron. The masking mechanism ensures that the model effectively propagates information based solely on true observations.

[0073] Step 4: With the introduction of a gating mechanism, the expert output is dynamically weighted and combined based on the input context;

[0074] To adaptively select the most suitable expert at each spatial node and time step, this invention proposes a gating network based on memory attention. Unlike the traditional MoE model, the gating mechanism of this invention explicitly utilizes expert error for dynamic supervision, thereby achieving fine-grained, spatiotemporally aware routing decisions.

[0075] Given the original input , mask And the hidden status of each expert First, the input and mask are merged into a unified query embedding:

[0076] ;

[0077] in, It represents a learnable linear transformation matrix for X, used to project input features onto the query space dimension; MLP refers to a multilayer perceptron (MLP) whose input is a mask. The output is the same as Representing patterns with the same dimension serves to perform non-linear encoding of missing patterns. These are learnable fusion weights. Subsequently, the learned memory units are utilized. Refine the attention of the query:

[0078] ;

[0079] Apply a self-attention transformation to the hidden state of each expert:

[0080] ;

[0081] , , The query projection matrix corresponding to the e-th expert is used to represent the hidden state. Mapping to the query, key, and value vector space, experts gating probability Calculated using cosine similarity:

[0082] ;

[0083] And select the expert with the highest probability, that is The final interpolation result is a combination of expert results for each node at each time step.

[0084] To dynamically guide gating selection, two types of supervision labels are defined for each expert based on their reconstruction error. and The details are as follows:

[0085] If experts error Exceeding the high quantile threshold Then let ;otherwise .

[0086] If experts error Below the lower quantile threshold And the corresponding actual value exceeds the threshold. Then let ;otherwise .

[0087] These dynamically generated labels drive the gating network to favor selecting more accurate experts and suppressing poorly performing ones. Formally, the gating loss is defined as:

[0088] ;

[0089] in, Control the relative strength of the "best choice" incentives and the "worst avoidance" penalties.

[0090] Another aspect of the present invention provides a spatiotemporal sequence interpolation device for heterogeneous missing sequences, comprising the following steps:

[0091] The sequence acquisition module standardizes the raw spatiotemporal sequence acquired by the sensor network and synchronizes the observation tensor with the missing mask based on the mask tensor.

[0092] The spatial dependency modeling module starts static and dynamic spatial expert sub-modules in parallel. The static spatial expert sub-module uses a fixed geographic adjacency matrix to drive graph convolution to generate hidden states and spatial interpolation results. The dynamic spatial expert sub-module fuses historical observations, node embeddings and periodic time embeddings at each time step and generates a time-varying adjacency matrix through self-attention. Then, it obtains a multi-order support set through high-order diffusion. The hidden state is extracted using the support set. The hidden state is then fused with structure-aware decoding and gating to output the spatial interpolation result.

[0093] The time-dependent modeling module initiates short-term time expert and long-term period expert sub-modules in parallel. Both sub-modules involve fusing input observations and masks, and then using a multilayer perceptron to uniformly map the original channels to the hidden dimensions to obtain a preliminary representation. The design recovers the initial representation by learningable mask vectors, projects periodic temporal embeddings into the hidden space and broadcasts them in the node dimension. Then, fixed positional codes are superimposed in the temporal dimension to obtain a representation with positional codes. The model is then performed by stacked spatiotemporal attention to finally obtain the hidden state and temporal interpolation results.

[0094] The output module concatenates the observation tensor, missing mask, and hidden states of each expert into a query embedding. After the query embedding is refined by memory attention, the cosine similarity between the query embedding and the state after the self-attention transformation of each expert is calculated to generate normalized expert weights. The imputation features of each expert are weighted and summed according to the weights to obtain the final imputation result. The best choice and worst avoidance labels are dynamically calculated based on the reconstruction error of each expert.

[0095] Another aspect of the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.

[0096] Another aspect of the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.

[0097] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0098] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0099] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0100] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0101] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0102] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A spatiotemporal sequence interpolation method for heterogeneous missing sequences, characterized in that, Includes the following steps: The raw spatiotemporal sequences acquired by the sensor network are standardized, and the observation tensor is synchronized with the missing mask based on the mask tensor; specifically: by A sensor network composed of spatial nodes acquires data, with each node continuously... Data collected at each time step Dimensional observations form an observation tensor. To address the issue of missing values ​​in the tensor, a mask tensor of the same shape is introduced. ,in Indicates the location The observation tensor on The observations are considered available if they are not, otherwise they are considered missing. The goal is to use the existing observation tensor as a basis for analysis. and mask tensor Learn an interpolation function To recover the complete observation tensor and make Approximate the true value at the missing location; The static spatial expert submodule and the dynamic spatial expert submodule are launched in parallel. The static spatial expert submodule uses a fixed geographic adjacency matrix to drive graph convolution to generate hidden states and spatial interpolation results. The dynamic spatial expert submodule fuses historical observations, node embeddings and periodic time embeddings at each time step and generates a time-varying adjacency matrix through self-attention. Then, it obtains a multi-order support set through high-order diffusion. The hidden state is extracted using the support set. The hidden state is then fused with structure-aware decoding and gating to output the spatial interpolation result. The short-term and long-term expert submodules are launched in parallel. Both the short-term and long-term expert submodules include: fusing the input observations and the mask, and then using a multilayer perceptron to uniformly map the original channels to the hidden dimensions to obtain a preliminary representation. The design recovers the initial representation by learningable mask vectors, projects periodic temporal embeddings into the hidden space and broadcasts them in the node dimension. Then, fixed positional codes are superimposed in the temporal dimension to obtain a representation with positional codes. The model is then performed by stacked spatiotemporal attention to finally obtain the hidden state and temporal interpolation results. The observation tensor, missing mask, and hidden states of each expert are concatenated to form a query embedding. The query embedding is refined by memory attention and its cosine similarity to the states of each expert after self-attention transformation is calculated to generate normalized expert weights. The imputation features of each expert are weighted and summed according to the weights to obtain the final imputation result. The best choice and worst avoidance labels are dynamically calculated based on the reconstruction error of each expert.

2. The method according to claim 1, characterized in that, The dynamic spatial expert submodule concatenates intraday phase embeddings and intraweek phase embeddings of upstream and downstream nodes, and then obtains the query and key through linear mapping. After Softmax normalization, it is multiplied element-wise with the static prior adjacency matrix to form a bidirectional time-varying adjacency matrix that simultaneously reflects prior geographical correlation and real-time data correlation.

3. The method according to claim 1, characterized in that, Higher-order diffusion generates a set of support matrices covering first-order to multi-order neighbors by continuously exponentially expanding the adjacency matrix to a preset maximum order.

4. The method according to claim 1, characterized in that, The short-term expert submodule takes observations from the most recent historical window as input, while the long-term period expert submodule takes observations from the same window extended to seven days before and after as input.

5. The method according to claim 1, characterized in that, The learnable mask vector replaces the all-zero vector at the masked position with the same dimension in the input layer, and is then broadcast and added to the real observation vector to generate the restored initial representation.

6. The method according to claim 1, characterized in that, Memory attention is specifically calculated by taking a scaled dot product of the learnable memory unit matrix and the query embedding, and then summing the results with weights.

7. The method according to claim 1 or 6, characterized in that, Dynamic supervision sets the best choice label to 1 only when the actual observed value is higher than the preset threshold and the expert error is in the low quantile. At the same time, when the high error exceeds the high quantile, the worst avoidance label is set to 0.

5. Adaptive reward and punishment for expert routing is achieved through backpropagation of gating loss.

8. A spatiotemporal sequence interpolation device for heterogeneous missing sequences, which implements the method of claim 1, characterized in that, Includes the following steps: The sequence acquisition module standardizes the raw spatiotemporal sequence acquired by the sensor network and synchronizes the observation tensor with the missing mask based on the mask tensor. The spatial dependency modeling module starts the static spatial expert submodule and the dynamic spatial expert submodule in parallel. The static spatial expert submodule uses a fixed geographic adjacency matrix to drive graph convolution to generate hidden states and spatial interpolation results. The dynamic spatial expert submodule fuses historical observations, node embeddings and periodic time embeddings at each time step and generates a time-varying adjacency matrix through self-attention. Then, it obtains a multi-order support set through high-order diffusion. The hidden state is extracted using the support set. The hidden state is then fused with structure-aware decoding and gating to output the spatial interpolation result. The time-dependent modeling module initiates short-term time expert submodules and long-term period expert submodules in parallel. Both the short-term time expert submodule and the long-term period expert submodule include: fusing input observations and masks, and then using a multilayer perceptron to uniformly map the original channels to the hidden dimensions to obtain a preliminary representation. The design recovers the initial representation by learningable mask vectors, projects periodic temporal embeddings into the hidden space and broadcasts them in the node dimension. Then, fixed positional codes are superimposed in the temporal dimension to obtain a representation with positional codes. The model is then performed by stacked spatiotemporal attention to finally obtain the hidden state and temporal interpolation results. The output module concatenates the observation tensor, missing mask, and hidden states of each expert into a query embedding. After the query embedding is refined by memory attention, the cosine similarity between the query embedding and the state after the self-attention transformation of each expert is calculated to generate normalized expert weights. The imputation features of each expert are weighted and summed according to the weights to obtain the final imputation result. The best choice and worst avoidance labels are dynamically calculated based on the reconstruction error of each expert.

9. An electronic device, characterized in that, include: One or more processors; A memory for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to perform the method described in any one of claims 1 to 7.

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