Information retrieval and analysis-oriented time-varying dependent perception time series data interpolation method

Abstract

The invention relates to the technical field of information retrieval and analysis driven by multivariable time series data, in particular to a time-varying dependent sensing time series data interpolation method oriented to information retrieval and analysis, which comprises the following steps of: constructing a global-local fusion diffusion model of time-varying dependent sensing; the method comprises the following steps: adaptively modeling variable dependence of time sequence change through a window segmentation module based on fast Fourier transform (FFT), and distinguishing positive and negative correlation in combination with a correlation feature extraction module; according to the information retrieval and analysis-oriented time-varying dependent sensing time sequence data interpolation method, experiments on AQI, TEP and Entry data sets show that the interpolation performance of the method is superior to that of a mainstream baseline model, and the method has the advantages that the method is simple in structure, convenient to operate and high in reliability. The global consistency and the local fidelity can be considered, and the data quality is improved to guarantee the information retrieval and analysis efficiency.

Description

Technical Field

[0001] This invention relates to the field of information retrieval and analysis technology driven by multivariate time series data, specifically a time-dependent perceptual time series data interpolation method for information retrieval and analysis. Background Technology

[0002] In information retrieval and analysis tasks driven by multivariate time series data, such as querying and trend analysis of industrial process status, ambient air quality, or power grid energy consumption patterns, complete and high-quality data is a fundamental prerequisite for ensuring the accuracy of retrieval results and the reliability of analytical conclusions. However, in practical applications, data loss caused by factors such as sensor failure and transmission interruption is common, which seriously undermines data integrity. This not only leads to the retrieval system returning incomplete or biased information but also directly reduces the performance of subsequent data analysis tasks (such as prediction and anomaly detection). Therefore, developing time series interpolation techniques capable of accurately reconstructing missing values ​​is crucial. Existing data interpolation methods can be broadly classified into four categories: methods based on recurrent neural networks (RNNs), methods based on variational autoencoders (VAEs), methods based on generative adversarial networks (GANs), and methods based on diffusion models. Early deep learning attempts employed recurrent neural networks (such as M-RNN and BRITS) to capture temporal dependencies through recurrent structures. Subsequently, generative models introduced a new paradigm. VAE-based methods (such as D3VAE and CTA) utilize encoder-decoder architectures to learn compact latent representations of data, while GAN-based methods (including E2GAN and PC-GAIN) use adversarial training to generate realistic interpolation results but are susceptible to problems such as mode collapse. Recently, diffusion models, represented by CSDI, SSSD, and MTSCI, have become a promising new paradigm. They iteratively refine noisy inputs into well-structured representations through learned denoising mechanisms, balancing stability and accurate reconstruction capabilities.

[0003] Despite recent progress, existing time series interpolation methods still face two fundamental challenges. First, existing models struggle to capture the diverse and time-varying dependencies between variables. Most methods rely on single, static inter-series correlations to capture these relationships (e.g., using graph neural networks with fixed graph structures to calculate correlations). However, in real-world applications, multivariate time series often exhibit intricate and dynamically evolving relationships. For example, in a power grid system, electricity demand and renewable energy generation may show a positive correlation under stable weather conditions, but this correlation may reverse during extreme events such as storms. Ignoring such dynamic and context-dependent correlations severely weakens interpolation accuracy and model robustness. Secondly, existing methods struggle to effectively integrate global trend information with local dynamic information, often emphasizing one aspect while neglecting the other, resulting in suboptimal interpolation results. Globally focused models (such as BRITS) can capture overall time patterns but struggle to capture dramatic local fluctuations, while locally focused methods (such as PC-GAIN) can generate realistic, fine-grained dynamics but lack the global consistency necessary for reliable interpolation. This imbalance highlights the inherent limitations of existing frameworks in their architecture. Therefore, in response to the above situation, there is an urgent need to develop time-varying dependency-aware time-series data interpolation methods for information retrieval and analysis to overcome the shortcomings in current practical applications. Summary of the Invention

[0004] The purpose of this invention is to provide a time-varying dependent sensing time-series data interpolation method for information retrieval and analysis, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A time-varying dependent perceptual time-series data interpolation method for information retrieval and analysis includes the following steps:

[0007] Step 1: Perform adaptive window segmentation on the multivariate time series to capture the inherent periodicity of the data;

[0008] Step 2: Extract the correlation features between variables with polar signs, and explicitly distinguish between positive and negative correlations;

[0009] Step 3: Construct a dual-channel diffusion process to capture both the global time trend and local dynamic changes;

[0010] Step 4: Integrate the dual-channel outputs through a dynamic fusion mechanism to obtain complete time-series data interpolation results.

[0011] As a further aspect of the present invention: In step 1, the adaptive window segmentation is implemented based on FFT, specifically including:

[0012] The original time series is mapped to embedded features that include location encoding and periodic timestamp encoding;

[0013] The embedded features are processed by FFT to extract the amplitude vector and filter the time scale corresponding to the dominant frequency;

[0014] The time series is divided into windows of variable length according to the time scale to accommodate the non-stationary nature of the data.

[0015] As a further aspect of the present invention: in step 2, the extraction of signed correlation features specifically includes:

[0016] Calculate the Pearson correlation coefficient between variables within a dynamic window to quantify the strength of the association between variables;

[0017] Based on a preset correlation threshold, positively correlated neighbor sets and negatively correlated neighbor sets are separated to construct a polarity-aware graph.

[0018] Message passing is performed on the polarity-aware graph to aggregate positive and negative correlation neighbor information, and then merge it with the variable's own historical representation. After feature normalization, correlation features with polarity signs are generated.

[0019] As a further aspect of the present invention: in step 3, the dual-channel diffusion process includes a local signal estimation channel and a global signal extraction channel. The local signal estimation channel is used to capture fine-grained short-term changes, and the global signal extraction channel is used to capture long-range time dependencies.

[0020] As a further aspect of the present invention: the implementation process of the local signal estimation channel includes:

[0021] The time series is divided into multiple consecutive windows, and sub-windows are extracted from each window;

[0022] Contextual information is constructed based on the overlapping area of ​​the preceding and subsequent windows, forming a time bridge across windows;

[0023] Using the sub-window and context information as conditions, local noise is estimated through a noise prediction network to ensure the continuity and smooth transition of window boundaries.

[0024] As a further aspect of the present invention: the implementation process of the global signal extraction channel includes:

[0025] The noisy input during the diffusion process is downsampled to obtain a compact representation that maintains the temporal-feature structure ratio;

[0026] The boundary of the compact representation is processed using a mean-filling strategy to reduce boundary artifacts;

[0027] Global noise is estimated using a noise prediction network, conditioned on the compact representation after filling, the non-missing part of the observation data, and the correlation features with polar signs.

[0028] An upsampling operation is performed on the global noise to restore it to the original data dimension.

[0029] As a further aspect of the present invention: in step 4, the dynamic fusion mechanism specifically includes:

[0030] An adjustable scaling factor is introduced to perform weighted fusion of the local noise output from the local signal estimation channel and the global noise output from the global signal extraction channel, balancing global consistency and local fidelity.

[0031] The fused noise is applied to the reverse diffusion process to gradually remove the noise and reconstruct the complete time series data.

[0032] As a further aspect of the present invention, it also includes a model training step, wherein the model training includes local channel training and global channel training, and the model parameters are updated by gradient descent method by minimizing the local noise prediction error and the global noise prediction error, respectively.

[0033] As a further aspect of the present invention: the model training process employs an early stopping rule, terminating training when the loss does not decrease within a consecutive preset period, thereby avoiding model overfitting.

[0034] As a further aspect of the present invention, the preset correlation threshold is in the range of 0.1 to 0.4, which is used to accurately distinguish between positive and negative correlations and optimize the accuracy of dependency modeling between variables.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] The time-varying dependent perception global-local fusion diffusion model (TAGL) proposed in this invention fuses global and local information through a dual-channel architecture and adopts a dynamic fusion mechanism to adaptively balance global consistency and local fidelity, which can generate interpolation results with both accuracy and consistency, effectively reconciling the trade-off between long-range global trends and fine-grained local dynamics.

[0037] The FFT-based window segmentation module can adaptively divide the sequence into frequency-aware segments according to the inherent periodicity of the data. Combined with the correlation feature extraction module, it can explicitly distinguish between positive and negative correlations. The two modules work together to provide a fine-grained and adaptive representation of dynamically evolving intervariate dependencies, effectively solving the problem that existing models are unable to capture diverse and time-varying dependencies between variables.

[0038] Extensive experiments on multiple real-world benchmark datasets (AQI, TEP, Energy) demonstrate that TAGL consistently achieves state-of-the-art (SOTA) performance, significantly outperforming existing baseline models in both mean absolute error (MAE) and root mean square error (RMSE), highlighting its advantages in accuracy and robustness.

[0039] TAGL maintains excellent interpolation accuracy at different data missing rates (10%-90%) and its performance degradation is more stable. It also shows strong robustness even in extremely challenging scenarios with up to 90% data missing, making it suitable for real-world applications where data missing is unpredictable and may be very severe.

[0040] The local signal estimation channel constructs a "time bridge" by fusing localized windows and their contextual information, ensuring continuity and smooth transition at the boundaries of adjacent windows; the global signal extraction module can effectively capture long-range dependencies, further improving the reliability and consistency of the interpolation results. Attached Figure Description

[0041] Figure 1 This is an overall architecture diagram of the time-varying dependency-aware global-local fusion diffusion model in an embodiment of the present invention.

[0042] Figure 2 The figure shows the ablation experiment results of the TAGL model on the AQI, TEP, and Energy datasets in this embodiment of the invention.

[0043] Figure A shows the ablation experiment results on the TEP dataset; Figure B shows the ablation experiment results on the Energy dataset; and Figure C shows the ablation experiment results on the AQI dataset.

[0044] Figure 3 This is a comparison chart of the imputation performance of TAGL and the baseline model under different data missing rates in an embodiment of the present invention;

[0045] Figure A shows the comparison of mean absolute error on the Energy dataset; Figure B shows the comparison of mean absolute error on the TEP dataset; Figure C shows the comparison of mean absolute error on the AQI dataset; Figure D shows the comparison of root mean square error on the Energy dataset; Figure E shows the comparison of root mean square error on the TEP dataset; and Figure F shows the comparison of root mean square error on the AQI dataset.

[0046] Figure 4 In this embodiment of the invention, the TAGL model is used at different correlation thresholds. The graph shows the variation in interpolation performance.

[0047] Figure A shows different signed correlation thresholds. Figure B shows the change in mean absolute error under different signed correlation thresholds; Figure B shows the change in root mean square error under different signed correlation thresholds.

[0048] Figure 5 This is a comparison chart of the missing value imputation results of TAGL, BRITS, and PC-GAIN models on the AQI dataset in this embodiment of the invention;

[0049] Figure A shows the actual value (true value) curve; Figure B shows the reconstructed value curve of the BRITS model; Figure C shows the reconstructed value curve of the PC-GAIN model; and Figure D shows the reconstructed value curve of the TAGL model. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.

[0051] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0052] Please see Figures 1-5 The time-varying dependency-aware temporal data interpolation method for information retrieval and analysis provided in this embodiment of the invention addresses the problem that existing time-varying data interpolation methods are unable to capture time-varying dependencies between variables and cannot take into account both global trends and local dynamics. This is achieved by constructing a time-varying dependency-aware global-local fusion diffusion model (TAGL). The specific details of this method are described in detail below.

[0053] I. Definition and Diffusion Model of Multivariate Time Series Interpolation Task

[0054] (I) Problem Description

[0055] Will Consider it as a containing A multivariate sequence of entries, each of which Recorded time index place One variable signal; the observed incomplete sequence is represented as and using a binary mask , where if the variable In time If the value is observed, then ,otherwise .

[0056] The goal of multivariate time series interpolation is to base the results on the observed data. To recover missing values ,in, The Hadamard product is formally defined as the learning mapping function:

[0057]

[0058] in, It is an approximate truth value The key challenges of reconstructing the complete sequence are: (1) the complex and time-varying interdependencies between variables; and (2) the balance between long-range global trends and fine-grained local dynamics.

[0059] (ii) Diffusion Model

[0060] Diffusion models model complex, high-dimensional data through a "noise-denoising" process, given a sample from... Pure data samples of distribution The forward process will pass through Step by step, add Gaussian noise:

[0061]

[0062] in, It is a variance scheduler used to control noise levels. It is the identity matrix; when When (the total number of steps in the diffusion process), It will approximate an isotropic Gaussian distribution.

[0063] The inverse process aims to learn the transition distribution Gradually reduce the noise level Restore to original data :

[0064]

[0065] in, and By parameterizing the neural network, the training objective of the model is to minimize the difference between the actual injected noise and the predicted noise:

[0066]

[0067] in, This represents the Gaussian perturbation introduced during the forward diffusion process.

[0068] In time series interpolation, the inverse denoising process of the diffusion model uses the observed entries and mask As a condition, iterative reconstruction of missing values ​​takes into account both global time consistency and local variations, and is highly efficient for processing incomplete and noisy time series data.

[0069] II. Design of Window Segmentation Module Based on Fast Fourier Transform (FFT)

[0070] In multivariate time series, the relationships between variables evolve dynamically over time. Traditional fixed-window segmentation lacks flexibility. This module determines the window size based on the inherent periodicity of the data to achieve adaptive segmentation.

[0071] 1. Time series embedding: defining a multivariate time series as... , of which each Indicates at time step Place The observed values ​​of each variable are input as a time segment. Before performing frequency analysis, the original sequence is mapped to a representative embedding. This embedding provides a more robust and expressive representation for subsequent periodic feature extraction; the embedding is then processed by FFT to identify the dominant periodic components, which are then used to adaptively divide the time series into windows of variable length.

[0072] Specifically, the input fragment is mapped to embedded features using the following formula. :

[0073]

[0074] in, express The normalized version, This is a scaling factor used to balance the weights of convolutional features. It is a one-dimensional convolutional filter. Represents a learnable location code. Corresponding to periodic timestamp encoding.

[0075] 2. FFT-based segmentation

[0076] First, we use FFT to transform the time series from the time domain to the frequency domain, that is, to transform the potential time series periodicity into explicit frequency components. Then, we extract these periodic features and map them to a variable window length that matches the inherent periodicity of the data, thereby realizing a more adaptive and data-driven segmentation method.

[0077] Specifically, the amplitude vector is first calculated. To capture the most prominent periodic features in a sequence, the formula is as follows:

[0078]

[0079] in, Used to extract the amplitude corresponding to each frequency in the FFT spectrum. This indicates averaging along the feature dimension, while This represents the final amplitude vector.

[0080] From again Select the one with the largest amplitude value A frequency, denoted as The timescales associated with these frequencies are calculated as follows:

[0081] in, It is the initial reference window length. Indicates the first Window length on each scale.

[0082] Based on the derived scale The time series is divided into variable-length windows, each defined as follows:

[0083] This segmentation strategy enables the model to capture dynamic relationship changes at different time granularities, overcoming the limitation of traditional fixed windows in adapting to non-stationary data behavior.

[0084] III. Design of the Symbol Relevance Feature Extraction (SCGNN) Module

[0085] To explicitly capture positive and negative dependencies between variables, SCGNN includes a polarity-aware graph construction module and a neighbor aggregation module that considers positive and negative correlations, as detailed below:

[0086] 1. Polarity-aware graph construction

[0087] To explicitly capture both positive and negative dependencies, a "positive-negative dependency-aware graph" is constructed, where interactions between variables are represented by signed edges. This process involves two phases: calculating the Pearson correlation coefficient and separating positive and negative correlations.

[0088] First, identify pairwise correlations between variables to construct a polarity-aware graph. Formally, this diagram is defined as ,in, Represents a set of variable nodes. Represents an edge set; for a given variable Its candidate correlation set is defined as all other variables: For variable nodes and Their time series within the dynamic window are respectively represented as and ; and The Pearson correlation weights between them are then calculated as follows:

[0089]

[0090] in, and They represent and The mean within this dynamic window; the numerator measures and The covariance between the two values ​​is used, while the denominator is normalized using their standard deviation.

[0091] To distinguish the polarity of correlation, a threshold-based strategy is adopted; specifically, for each variable... Its positively correlated neighbor set Includes correlation values ​​exceeding a positive threshold The variable, and its negatively correlated neighbor set Then the correlation value is less than The variables consist of; formally, these neighbor sets are defined as follows:

[0092]

[0093] This graph construction method can clearly distinguish between positive and negative correlations, laying the foundation for accurate modeling of interactions between variables in the future.

[0094] 2. Neighbor aggregation considering positive and negative correlations

[0095] After constructing a correlation graph that considers positive and negative correlations, the model performs message passing to explicitly aggregate information from positive and negatively correlated neighbors, thereby updating the representation of each variable; this process first aggregates neighbor information and then merges this information into the final features.

[0096] For each variable Neighbor information is aggregated by summing the contributions from positively correlated neighbors and negatively correlated neighbors, respectively; the aggregated representation is defined as follows:

[0097]

[0098] in, and Representing variables respectively or In the The feature representation of the layer, and That is the corresponding relevance weight.

[0099] The aggregated neighbor features are then fused with the variable's own historical representation from the previous layer to preserve local information:

[0100]

[0101] in, It is a learnable linear transformation matrix. It is a non-linear activation function used to facilitate the modeling of complex interactions. Finally, we apply feature normalization to stabilize the training process and avoid representation explosion:

[0102]

[0103] This aggregation process can explicitly aggregate positive and negative correlation neighbor information, characterize the heterogeneous impact of positive and negative correlation on temporal behavior, and generate rich representations as structured conditional priors for the diffusion process, while improving the accuracy and consistency of interpolation.

[0104] IV. Design of the Global-Local Fusion Diffusion Interpolation Module

[0105] The global trend and local dynamics are processed separately through a dual-channel diffusion process, and a dynamic fusion mechanism is used to achieve global-local information fusion, as detailed below:

[0106] 1. Local signal estimation: To avoid discontinuities at the boundaries of adjacent windows, local signal estimation is performed from each window. Extract a smaller sub-window Constructing a "time bridge" context by fusing overlapping data fragments This bridge will pass through The prediction, at the same time, is based on its Direct neighbors within, and from previous windows (Left overlap) and subsequent windows The overlapping region (right-side overlap) is used as a condition to ensure continuity; in this way, the model can learn a smooth transition across the window boundary during training and denoising.

[0107] Formally, given an original time series We first divide it into A continuous time window The initial local noise for each window is defined as:

[0108]

[0109] in, Display window Local noise, and The set of noise predictions representing all windows; after introducing a time bridge, the context-conditional local noise predictions for the entire sequence are reformulated as:

[0110]

[0111] in, This represents the overall noise estimate, while Indicates child window Noise prediction is based on its context This process is conditional; it enables the model to capture fine-grained local dynamics while maintaining smooth temporal consistency across adjacent windows.

[0112] 2. Global signal extraction: To capture long-range dependencies, intermediate latent variables are extracted. Downsampling as a compact representation ,in, , , Represents feature dimension, Represents timing length. Represents the original feature dimension. Represents the original timing length, while maintaining the proportion. Remain unchanged to maintain the time-feature structure:

[0113]

[0114] Then fill using the mean-filling strategy. The boundary, thus obtaining :

[0115]

[0116] This prompts the model to focus on generating the central region; based on the observation data Structured transvariate features from signed correlation GNNs (Graph Neural Networks) As a condition, noise prediction network estimation Conditional noise; trend direction score is defined as:

[0117]

[0118] To avoid artifacts at the fill boundaries, the conditional noise prediction results will be cropped back to the original size:

[0119]

[0120] Finally, an upsampling operation is applied to restore the trend direction score to its original dimension:

[0121]

[0122] in, An interpolation method that preserves global trends is adopted; this process can effectively capture long-range dependencies and provide global consistency guarantees for the interpolation results.

[0123] 3. Dynamic Weighted Information Fusion: To fuse global and local information, a dynamic weighted fusion mechanism is designed; the fused noise prediction combines local contextual noise and global conditional trend scores.

[0124]

[0125] in, It is an adjustable scaling factor used to balance the effects of global and local signals;

[0126] Then the fused noise This is applied to the reverse diffusion process, thereby achieving global-local fusion while adhering to the denoising mechanism:

[0127]

[0128] in, Cumulative coefficient This fusion mechanism achieves a balance between global consistency and local fidelity, ensuring that the interpolation results possess both long-range trend accuracy and fine-grained dynamic realism.

[0129] V. Design of TAGL Model Training Process

[0130] The local and global channels are trained with separate noise prediction networks, and the training process is as follows:

[0131] 1. Local channel training: The conditional input for local channels is a sub-window extracted from a variable-length window. ), and contextual information that incorporates overlapping segments of adjacent windows ( Composed of; time steps Local conditions at the location and global conditions The definition is as follows:

[0132]

[0133] in, Indicates the diffusion step Noisy input at the location, and These are sub-windows and their temporal bridge contexts; each denoising network is optimized to predict the injected noise under its respective conditions.

[0134] Specifically, local branch minimization:

[0135]

[0136] in, From its data distribution Mid-sampling, This is real noise added during the forward diffusion process; the specific training process is shown in Algorithm 1:

[0137]

[0138] Algorithm 1 illustrates the training process for local channels. In each iteration, the model samples a clean data sample from the training distribution and injects Gaussian noise to construct a noisy input. (Lines 2-5); The time series has been pre-divided into variable-length windows by an FFT-based segmentation module; therefore, the training process directly operates within these predefined windows. The operation is performed on the above; for each window, the algorithm extracts a sub-window. And a time bridge context is constructed by utilizing the overlapping area of ​​adjacent windows. (Lines 7-9) ensure a smooth transition across window boundaries; subsequently, a local denoising network... by and diffusion step size As a condition, the injected noise is predicted (line 10); the error between the predicted noise and the actual noise (line 11) is accumulated over all windows, and the (model) parameters are updated accordingly (line 13); by minimizing this local objective, the local channel learns to capture fine-grained short-term changes while maintaining temporal smoothness across consecutive windows.

[0139] 2. Global Channel Training: The conditional input for the global channel includes: downsampled and mean-filled latent information ( ), the non-missing parts of the observation data ( ) and structured transvariate dependency features generated by SCGNN ( ); defined as follows:

[0140]

[0141] in, yes Information after downsampling and mean filling This represents the observed non-missing values, while It encodes the intervariate dependencies learned by SCGNN;

[0142] Minimize global branches:

[0143]

[0144] in, From its data distribution Mid-sampling, This is real noise added during the forward diffusion process; the specific training process is shown in Algorithm 2:

[0145]

[0146] Algorithm 2 describes the training process for the global channels; in each iteration, the model samples a clean sample and generates a noisy input by injecting Gaussian noise. (Lines 2-5); To capture long-term trends, It is first downsampled into a compact representation. (Line 6); Subsequently, the model applies mean-filling to obtain... This operation aims to encourage the model to focus on generating the central region while reducing boundary artifacts (line 7); the conditions for the global channel are determined by... Composition, in which This represents the observed non-missing values, while Encodes the structured intervariate dependencies extracted by the signed correlation GNN (line 8); global denoising network Based on this condition and diffusion step size, the injected noise is predicted (line 9); the network minimizes the error between the predicted noise and the actual noise (line 10) and updates the parameters accordingly (line 11); by iteratively optimizing this objective, the global channel learns to model long-range structural dependencies and maintains global consistency throughout the interpolation process.

[0147] During the inference phase, the outputs of local and global channels are adaptively integrated through a dynamic fusion mechanism to guide the final denoising process and obtain complete time-series data interpolation results.

[0148] VII. Experimental Verification Design and Result Analysis

[0149] To verify the effectiveness of this method, the following experiment was conducted:

[0150] 1. Experimental Environment

[0151] Datasets: To verify the effectiveness of TAGL, experiments were conducted on three commonly used benchmark datasets, as shown in Table 1. (1) The Air Quality Index (AQI) dataset contains hourly air pollution readings recorded by 12 monitoring stations in Beijing from March 1, 2013 to February 28, 2017. (2) The Tennessee-Eastman Process (TEP) dataset is a well-known benchmark in the field of chemical engineering, which simulates an industrial chemical reaction process. This dataset records multiple process variables such as temperature, pressure, and flow rate, and provides fault labels. (3) The Energy dataset from UCI contains 28 variables related to the prediction of household appliance energy consumption, including appliance and lighting consumption, indoor and outdoor temperature and humidity, wind speed, and visibility.

[0152] Table 1. Basic Information Statistics of the Three Datasets

[0153]

[0154] Baseline Models: To evaluate the performance of the TAGL model and highlight its advantages, it was benchmarked against a diverse range of representative methods. These methods include: RNN-oriented models (e.g., M-RNN and BRITS), VAE-driven methods (e.g., D3VAE and CTA), GAN-based techniques (e.g., E2GAN, PC-GAIN, and MDCGAN), and diffusion-oriented frameworks (e.g., CSDI, SSSD, and MTSCI); details of these baseline models are summarized below:

[0155] M-RNN: A type of multidirectional recurrent neural network that treats missing entries as a continuous stream of data and approximates the missing data by estimating the values ​​between these streams.

[0156] BRITS: A robust framework for filling gaps in multivariate time series data. It applies recursive time series modeling while capturing dependencies between features.

[0157] D3VAE: A bidirectional variational autoencoder equipped with diffusion, denoising, and decoupling mechanisms; it employs a coupled, diffusion-based probabilistic model to process time series, avoiding the introduction of arbitrary noise.

[0158] CTA: A continuous-time autoencoder that maps sequential inputs to potential continuous trajectories and then performs data recovery and interpolation by decoding these trajectories.

[0159] E2GAN: An end-to-end generative adversarial network that reconstructs incomplete sequences by generating the most plausible complete sequence in specified steps.

[0160] PC-GAIN: An unsupervised imputation technique that utilizes the hidden category patterns inherent in missing entries to improve imputation accuracy.

[0161] MDCGAN: A conditional GAN ​​with multiple discriminators that accurately recovers missing values ​​by capturing the distributed representation of the data.

[0162] CSDI: A conditional score-driven diffusion method that leverages the correlation between observed variables to enhance the effect of sequence imputation.

[0163] SSSD: A diffusion model based on structured state-space formulas, designed specifically for time series completion tasks.

[0164] MTSCI: A conditional diffusion model for consistent multivariate time series imputation. It integrates complementary masking strategies and hybrid mechanisms to simultaneously enhance data consistency both within and between variables.

[0165] Table 2 Performance comparison on the three datasets

[0166]

[0167] Experimental setup: The Adam optimizer was used with a learning rate of 0.001 to ensure training reliability and efficiency. For the AQI dataset, the mini-batch size was set to 16, while for other datasets it was set to 32. The number of diffusion iterations was fixed at 100 to balance computational cost and model performance. Model parameters were set as follows: hidden layer dimension... The size of the middle layer is 128. The scaling factor is 64. The performance rating is 7.0; the denoising network is optimized and trained for 120 epochs; to alleviate overfitting, an early stopping rule is applied: if the loss fails to decrease within 10 consecutive epochs, training will automatically terminate; the evaluation metrics are mean absolute error (MAE) and root mean square error (RMSE), with smaller values ​​indicating better interpolation quality.

[0168] 2. Experimental Results and Analysis

[0169] 2.1 Performance Comparison: The interpolation results of TAGL compared with the baseline model are summarized in Table 2; several key observations can be drawn from this table:

[0170] First, TAGL consistently achieves state-of-the-art performance across all datasets and evaluation metrics, surpassing all baseline methods. This improvement is primarily attributed to the global-local fusion diffusion architecture, which, combined with a polarized sign correlation feature extraction module, effectively balances macroscopic structure with fine-grained local dynamics.

[0171] Secondly, generative methods (e.g., methods based on VAE, GAN, and diffusion models) generally outperform traditional RNN-based methods; this highlights the limitations of simple sequence modeling, as RNNs struggle to capture the complex, high-dimensional dependencies and long-range correlations inherent in multivariate time series; in contrast, generative models can leverage richer data distributions to achieve more realistic imputation results.

[0172] Finally, the diffusion-based approach outperformed VAE and GAN-based approaches, highlighting the advantages of diffusion models in generating stable and high-fidelity interpolation results. Notably, TAGL achieved the most significant performance improvement, which confirms the effectiveness of several key components, including FFT-based window segmentation, polar sign correlation graph modeling, and global-local fusion diffusion, which greatly extend the capabilities of the standard diffusion framework.

[0173] 2.2 Ablation Experiment

[0174] To evaluate the contribution of each component in TAGL, ablation experiments were conducted by selectively removing its three core modules:

[0175] (1) w / oFFT (without FFT): Remove the FFT-based window segmentation module. In this case, the time series is divided into fixed-length windows without adaptive adjustment.

[0176] (2) w / oSign (without sign): Removes the correlation feature extraction module with polarity sign, which disables explicit modeling of the correlation between positive and negative variables;

[0177] (3) w / oLocal (excluding local): Remove the local signal estimation channel in the dual-channel diffusion process, which will cause it to lose its ability to capture fine-grained short-term changes;

[0178] (4) w / oGlobal: Removes the global signal estimation channel in the dual-channel diffusion process, which disables modeling for long-range time dependencies and global consistency.

[0179] Experimental results are as follows Figure 2As shown, overall, removing any module leads to a significant performance degradation, highlighting the crucial role each design element plays in achieving accurate and consistent interpolation. Specifically, without FFT-based window segmentation, the model loses its ability to adaptively capture time-varying periodic structures, resulting in suboptimal time alignment. Excluding polarized correlation features degrades performance because negative correlations are ignored, while they typically provide complementary signals to positive correlations. Finally, the lack of global or local information causes the most severe performance degradation, as the model cannot simultaneously capture long-range trends and fine-grained local variations, leading to incomplete and inconsistent interpolation results.

[0180] In summary, the results of the ablation experiments validated the rationality of each module design and demonstrated that the combined effect of FFT-based window partitioning, polarized correlation extraction, and global-local fusion is crucial for TAGL to achieve superior performance.

[0181] 2.3 Impact of Missing Rate

[0182] The missing data rate was adjusted from 10% to 90%, and the data values ​​were randomly masked. To ensure fair and representative comparisons, robust baseline models from different method categories—BRITS, CTA, MDCGAN, and MTSCI—were selected and benchmarked against the TAGL framework. Figure 3 As shown, TAGL consistently exhibits the highest imputation accuracy across all missing rates; this confirms that the fusion diffusion process (which co-models global temporal trends and local dynamics) enables TAGL to preserve both large-scale structure and fine-grained variations even under extremely sparse conditions.

[0183] Furthermore, TAGL's performance degradation is more gradual with increasing missing data rates. While all models inevitably experience accuracy decline at higher missing data rates, TAGL's performance drop is much more gradual compared to the baseline model. This indicates that TAGL not only demonstrates superior accuracy at moderate sparsity but also exhibits strong robustness (or "resilience") in extremely challenging scenarios with up to 90% missing data. Overall, the results highlight TAGL's adaptability and robustness across various sparsity levels, demonstrating its practical value in real-world applications where data missing data is both unpredictable and potentially severe.

[0184] 2.4 Impact of Correlation Threshold

[0185] In the process of polarity-aware graph construction, a threshold is applied. To distinguish between positive and negative correlations; to assess their impact, to explore changes Its impact on model performance; Figure 4This report presents the MAE and RMSE of TAGL on the AQI, TEP, and Energy datasets under different threshold settings; such as Figure 4 As shown, increasing the threshold typically leads to performance improvements across all datasets, and in... The TAGL model achieves optimal results when the threshold is too low; when the threshold is too low, the TAGL model cannot fully capture the potential relationships between variables, thus limiting the overall accuracy. Conversely, when the threshold becomes too high, the model becomes overly sensitive to spurious correlations, which amplifies noise and leads to performance degradation, as evidenced by the steadily increasing MAE and RMSE values.

[0186] 2.5 Case Studies

[0187] To visually demonstrate the effect of TAGL, in Figure 5 The results are presented in the figure, showing the interpolation results on the AQI dataset and compared with two representative baseline models, BRITS and PC-GAIN. In each subplot, the blue curve represents the true value, while the red curve shows the interpolated value obtained by the corresponding model.

[0188] BRITS and PC-GAIN reflect two different design philosophies: global and local. Specifically, BRITS uses a bidirectional RNN structure to model global correlations through recursive dynamics, thereby capturing long-range contextual information; however, it is difficult to adapt to abrupt local changes. In contrast, PC-GAIN uses a generative adversarial framework to emphasize local data distribution and generate realistic local imputation results; however, it lacks global consistency constraints, resulting in poor overall performance.

[0189] like Figure 5 As shown, these limitations are quite evident: BRITS fails to align with local fluctuations, while PC-GAIN exhibits inconsistency at the global scale. In contrast, TAGL integrates global and local information within a unified diffusion framework, significantly improving global consistency and local fidelity while maintaining the inherent stability of the diffusion process. Therefore, TAGL achieves interpolation results that closely match the true values ​​in different time modes.

[0190] In summary, this method effectively addresses the limitations of existing methods by employing FFT-based window segmentation, polarized relevance feature extraction, and global-local fusion diffusion interpolation. It achieves high-precision and robust time-series data interpolation in various scenarios, providing high-quality data support for information retrieval and analysis driven by multivariate time-series data.

[0191] It should be noted that, in this invention, although the specification describes the embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A time-varying dependent perceptual time-series data interpolation method for information retrieval and analysis, characterized in that, Includes the following steps: Step 1: Perform adaptive window segmentation on the multivariate time series to capture the inherent periodicity of the data; Step 2: Extract the correlation features between variables with polar signs, and explicitly distinguish between positive and negative correlations; Step 3: Construct a dual-channel diffusion process to capture both the global time trend and local dynamic changes; Step 4: Integrate the dual-channel outputs through a dynamic fusion mechanism to obtain complete time-series data interpolation results.

2. The time-varying dependent perceptual time-series data interpolation method for information retrieval and analysis according to claim 1, characterized in that, In step 1, the adaptive window segmentation is implemented based on FFT, specifically including: The original time series is mapped to embedded features that include location encoding and periodic timestamp encoding; The embedded features are processed by FFT to extract the amplitude vector and filter the time scale corresponding to the dominant frequency; The time series is divided into windows of variable length according to the time scale to accommodate the non-stationary nature of the data.

3. The time-varying dependent perceptual time-series data interpolation method for information retrieval and analysis according to claim 1, characterized in that, In step 2, the extraction of signed correlation features specifically includes: Calculate the Pearson correlation coefficient between variables within a dynamic window to quantify the strength of the association between variables; Based on a preset correlation threshold, positively correlated neighbor sets and negatively correlated neighbor sets are separated to construct a polarity-aware graph. Message passing is performed on the polarity-aware graph to aggregate positive and negative correlation neighbor information, and then merge it with the variable's own historical representation. After feature normalization, correlation features with polarity signs are generated.

4. The time-varying dependent sensing time-series data interpolation method for information retrieval and analysis according to claim 1, characterized in that, In step 3, the dual-channel diffusion process includes a local signal estimation channel and a global signal extraction channel. The local signal estimation channel is used to capture fine-grained short-term changes, and the global signal extraction channel is used to capture long-range time dependencies.

5. The time-varying dependency-aware time-series data interpolation method for information retrieval and analysis according to claim 4, characterized in that, The implementation process of the local signal estimation channel includes: The time series is divided into multiple consecutive windows, and sub-windows are extracted from each window; Contextual information is constructed based on the overlapping area of ​​the preceding and subsequent windows, forming a time bridge across windows; Using the sub-window and context information as conditions, local noise is estimated through a noise prediction network to ensure the continuity and smooth transition of window boundaries.

6. The time-varying dependency-aware temporal data interpolation method for information retrieval and analysis according to claim 4, characterized in that, The implementation process of the global signal extraction channel includes: The noisy input during the diffusion process is downsampled to obtain a compact representation that maintains the temporal-feature structure ratio; The boundary of the compact representation is processed using a mean-filling strategy to reduce boundary artifacts; Global noise is estimated using a noise prediction network, conditioned on the compact representation after filling, the non-missing part of the observation data, and the correlation features with polar signs. An upsampling operation is performed on the global noise to restore it to the original data dimension.

7. The time-varying dependent perceptual time-series data interpolation method for information retrieval and analysis according to claim 1, characterized in that, In step 4, the dynamic fusion mechanism specifically includes: An adjustable scaling factor is introduced to perform weighted fusion of the local noise output from the local signal estimation channel and the global noise output from the global signal extraction channel, balancing global consistency and local fidelity. The fused noise is applied to the reverse diffusion process to gradually remove the noise and reconstruct the complete time series data.

8. The time-varying dependent perceptual time-series data interpolation method for information retrieval and analysis according to claim 1, characterized in that, It also includes a model training step, which includes local channel training and global channel training. The model parameters are updated by minimizing the local noise prediction error and the global noise prediction error, respectively, using the gradient descent method.

9. The time-varying dependent perceptual time-series data interpolation method for information retrieval and analysis according to claim 8, characterized in that, The model training process employs an early stopping rule, terminating training when the loss does not decrease within a preset period to prevent overfitting.

10. The time-varying dependent sensing time-series data interpolation method for information retrieval and analysis according to claim 3, characterized in that, The preset correlation threshold ranges from 0.1 to 0.4, and is used to accurately distinguish between positive and negative correlations, thereby optimizing the accuracy of dependency modeling between variables.

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