Internet of Things data reconstruction method based on low-rank subspace and deep learning

Abstract

The invention discloses an Internet of Things data reconstruction method based on low-rank subspace and deep learning. The method comprises the following steps: firstly, deploying sensor nodes in a monitoring area, and transmitting sensing data to a base station by the sensor nodes to obtain a sensing data matrix; then, based on the low-rank subspace, constructing a reconstruction model; thirdly, constructing a time coefficient prediction network, and predicting the time coefficient matrix by using the time coefficient prediction network; taking the prediction time coefficient matrix as deep learning prior, and constructing a low-rank prior and deep learning prior coupled reconstruction model; and finally, solving the low-rank prior and deep learning prior coupled reconstruction model by using an alternating direction multiplier method to obtain a reconstructed third-order tensor, and completing Internet of Things data reconstruction. The low-rank time coefficient prior is combined with the time coefficient prior obtained by deep learning, so that the modeling capability of the space dimension and the time dimension of the data of the Internet of Things is enhanced, and higher reconstruction precision and better interpretability are realized.

Description

Technical Field

[0001] This invention belongs to the field of Internet of Things (IoT) data processing technology, specifically an IoT data reconstruction method based on low-rank subspace and deep learning. Background Technology

[0002] In Internet of Things (IoT) systems, the device layer primarily consists of numerous sensor nodes with sensing and communication capabilities. These nodes are typically deployed randomly within the target monitoring area and possess a certain degree of computing, storage, and data transmission capabilities, enabling continuous collection of information about the surrounding environment. However, due to limitations in hardware performance, unstable communication networks, and complex deployment environments, the collected IoT data often suffers from incompleteness. Incomplete data directly impacts subsequent data analysis, modeling, and application effectiveness; therefore, accurately reconstructing complete IoT data has become a research hotspot in this field.

[0003] Existing IoT data reconstruction methods can be broadly categorized into two types: traditional model-driven methods and deep learning-based data-driven methods. Traditional model-driven methods mainly include reconstruction methods based on compressed sensing, matrix completion, and tensor completion. Specifically, compressed sensing-based reconstruction methods compress and sample IoT data exhibiting sparsity in certain transform domains by constructing a measurement matrix, and then reconstruct the original data using optimization algorithms. Matrix completion-based reconstruction methods construct a two-dimensional matrix of sensor nodes and corresponding data at sampling times, utilizing its low-rank characteristic in the spatiotemporal dimension for data recovery. Tensor completion-based reconstruction methods, as a higher-order extension of the matrix, can further explore the correlations of data in multi-dimensional structures, thereby improving reconstruction accuracy. Although traditional model-driven methods offer good interpretability and perform ideally in specific scenarios, they rely on manually set priors and parameter adjustments, resulting in poor adaptability and difficulty in widespread adoption. In contrast, data-driven methods based on deep learning do not rely on explicit prior modeling. Instead, they automatically extract spatiotemporal features of IoT data directly from observational data through end-to-end neural networks, enabling adaptive reconstruction of missing data. These methods possess strong modeling capabilities and reconstruction accuracy, but still face numerous challenges in practical applications, such as a high dependence on a large number of paired labeled samples and limited generalization ability and interpretability. In the IoT environment, the practicality and scalability of these methods are further limited by high data acquisition costs and sample scarcity.

[0004] To this end, this application proposes an IoT data reconstruction method based on low-rank subspace and deep learning. Without requiring a large number of labeled samples and complex manual parameter tuning, it can effectively mine the spatiotemporal correlation in IoT data, achieve high-precision reconstruction of missing data, and at the same time have good interpretability and generalization ability. Summary of the Invention

[0005] In view of the shortcomings of existing technologies, the technical problem to be solved by this invention is to propose an IoT data reconstruction method based on low-rank subspace and deep learning.

[0006] The technical solution adopted by the present invention to solve the aforementioned technical problem is as follows: A method for reconstructing IoT data based on low-rank subspaces and deep learning, characterized by comprising the following steps: Step 1: Deploy sensor nodes within the monitoring area. The sensor nodes transmit the sensed data to the base station, obtaining a sensed data matrix, denoted as... ;in, This represents the random sampling operator. Represents a third-order tensor; Step 2: Construct a reconstruction model based on the low-rank subspace; Based on the low-rank subspace model, the third-order tensor is represented as: (2) in, Describes a spatial basis. This represents tensor-matrix multiplication along the 3rd modulus. Represents the time coefficient matrix; When the spatial basis is determined, the IoT data reconstruction problem is equivalently transformed into the reconstruction of the time coefficient matrix, resulting in the following reconstruction model: (4) in, To characterize the regularization term representing the prior information of the IoT data to be reconstructed, Describing the F-norm, For regularization parameters; Step 3: Construct a time coefficient prediction network and use it to predict the time coefficient matrix; use the predicted time coefficient matrix as a deep learning prior to construct a reconstruction model that couples low-rank prior with deep learning prior. (6) in, Represents the prediction time coefficient matrix; The random noise with the same dimension as the time coefficient matrix serves as the input to the time coefficient prediction network. These are learnable network parameters; Step 4: Solve the reconstruction model that couples low-rank priors and deep learning priors using the alternating direction multiplier method to obtain the reconstruction third-order tensor and complete the IoT data reconstruction.

[0007] Furthermore, in the time coefficient prediction network, random noise is processed by one-dimensional convolution to obtain preliminary features; the preliminary features are processed by a residual module to obtain shallow features; the shallow features are processed by a channel attention mechanism to obtain channel attention-enhanced shallow features; the channel attention-enhanced shallow features are processed by a residual module to obtain deep features; the deep features are mapped to the target space by one-dimensional convolution to obtain the predicted time coefficient matrix.

[0008] Furthermore, in step 4, the augmented Lagrangian function of the reconstruction model coupled with the low-rank prior and the deep learning prior is expressed as: (7) in, The penalty parameter is a positive number; For Lagrange multipliers; The alternating solution process is broken down into solving the following subproblems: (8) (9) (10) in, This represents the predicted values ​​of network parameters. This represents the reconstruction of the third-order tensor. Indicates the updated value of the Lagrange multiplier; The prediction of network parameters is achieved by predicting the network through training time coefficients; For the estimation of the third-order tensor, the conjugate gradient algorithm is used for iterative solution: (11) In the formula, This indicates the Hermitian transpose. Indicates the first The third-order tensor obtained in the next iteration Indicates the first The updated values ​​of the Lagrange multipliers obtained in the next iteration; The update of the Lagrange multipliers is solved iteratively using the following formula: (12) In the formula, Indicates the first The updated values ​​of the Lagrange multipliers obtained in the next iteration.

[0009] Compared with the prior art, the beneficial effects of the present invention are as follows: On the one hand, this invention introduces a low-rank subspace method, representing IoT data as the product of a spatial orthogonal basis and a time coefficient matrix, fully exploiting its low-rank structural characteristics in the spatial dimension and enhancing the modeling capability for the spatial dimension. On the other hand, a self-supervised time coefficient prediction network is designed, which does not rely on external labeled data and can adaptively learn time coefficient priors, improving the depth of capturing temporal features, thereby enhancing the model's adaptability and generalization to IoT time-series data. Under the ADMM optimization framework, the model-driven low-rank time coefficient prior and the data-driven time coefficient prior are synergistically optimized and mutually reinforcing, achieving higher reconstruction accuracy and better interpretability. Attached Figure Description

[0010] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a structural diagram of the time coefficient prediction network of the present invention; Figure 3 A comparison chart showing the errors in reconstructing temperature data for a certain region using different methods; Figure 4 This is a comparison chart showing the errors in reconstructing humidity data for a certain region using different methods. Detailed Implementation

[0011] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but this does not limit the scope of protection of this application.

[0012] This invention relates to an IoT data reconstruction method based on low-rank subspaces and deep learning (hereinafter referred to as the method, see [link]). Figures 1-4 The method includes the following steps: Step 1: Deploy sensor nodes within the monitoring area. The sensor nodes transmit the sensed data to the base station to obtain the sensed data matrix. Discretize the IoT monitoring area into There are 1 grid, with one sensor node deployed in each grid, and the number of sensor nodes is 1. Assuming the sensor nodes are spaced every time slot (The time slot is the difference between adjacent sampling times) Data is sensed once and transmitted to the base station; the sensing data from all sensor nodes at the same sampling time form a matrix. Therefore, the base station during the time period Inside, that is, continuous The sensing data received within each time slot forms a third-order tensor. , Represents the real number field. It is a positive integer; Due to data loss, during the time period If only a portion of the sensing data is transmitted to the base station, then mathematically, the data received by the base station can be considered as data from a third-order tensor. The samples were obtained by random sampling at a certain proportion. This represents the random sampling operator. Represents the third-order tensor The sensing data matrix obtained by random sampling contains G sensing data points, with unsampled points padded with zeros; sampling ratio , Among them, from the third-order tensor The data points obtained by random sampling are represented as follows: (1) in, Representing a third-order tensor Data points in , , , Let be the set of indices corresponding to valid entries in the sampling mask, representing the observed element positions in the third-order tensor, and its size is . ; Step 2: Construct a reconstruction model based on the low-rank subspace; According to the linear mixture model, the sensed data at each moment can be represented by a linear combination of a small number of spatial bases, whose combination weights change with time and are denoted as time coefficients. This reflects the strong spatial correlation of IoT multi-sensor data, and low-rank subspaces can naturally characterize this spatial correlation and have been proven to be an effective tool for processing IoT data. Based on the low-rank subspace model, the third-order tensor... Represented as: (2) in, This represents tensor-matrix multiplication along the 3rd modulus. Represents a spatial basis; This is a time coefficient matrix, representing the coefficients at time T. The time weighting of each spatial basis characterizes the intensity change of each spatial basis over time. .

[0013] By using the third-order tensor Singular Value Decomposition (SVD) is performed on the expanded matrix in the spatial dimension to update the spatial basis. : (3) in, Representing a third-order tensor Expand the left singular vector of the matrix in the spatial dimension; space base Once determined, the IoT data reconstruction problem can be equivalently transformed into a problem involving the time coefficient matrix. If the reconstruction is performed, the reconstruction model can be written as: (4) in, To characterize the regularization term representing the prior information of the IoT data to be reconstructed, Describing the F-norm, This is the regularization parameter.

[0014] Step 3: Construct a time coefficient prediction network and use the network to obtain the predicted time coefficient matrix; use the predicted time coefficient matrix as a deep learning prior to construct a reconstruction model that couples low-rank prior with deep learning prior. To further enhance the expressive power of time-dimensional modeling, adaptively represent the complex temporal characteristics of different IoT data, and overcome the limitations of traditional time coefficient priors in representing complex time-series features, a data-driven time coefficient prediction network is innovatively introduced to learn the time coefficient matrix. The deep structure prior, and the regularization term By incorporating the priors of the time coefficient prediction network, a more general coupled reconstruction model is obtained: (5) in, This represents the prediction time coefficient matrix, which is the output of the time coefficient prediction network. For the time coefficient matrix Random noise of the same dimension is used as input to the time coefficient prediction network; These are learnable network parameters.

[0015] In the time coefficient prediction network, random noise is initially processed by one-dimensional convolution to obtain preliminary features; the preliminary features are modeled by a residual module to obtain shallow features; the shallow features are processed by a channel attention mechanism to highlight key channel features to obtain channel attention-enhanced shallow features; the channel attention-enhanced shallow features are then processed by a residual module for depth modeling to obtain deep features; the deep features are mapped to the target space by one-dimensional convolution to obtain the predicted time coefficient matrix.

[0016] However, the two types of priors in equation (5) have not been effectively merged because only constraints are applied. ,Right now With sensing data matrix Approximation, and during the learning process, network parameters The optimization did not directly utilize the sensing data matrix The lack of complete information makes it difficult for the network to learn sufficient time priors. To enhance the fusion of these two types of priors, a fidelity term is added to equation (5), resulting in the following reconstruction model that couples low-rank priors and deep learning priors: (6) This model couples a spatial model-driven low-rank prior with a data-driven deep school prior, combining interpretability and expressive power; the time coefficient prediction network optimizes network parameters. Adaptive representation learning of the time coefficient matrix is ​​achieved, thereby further improving the accuracy and generalization ability of IoT data reconstruction.

[0017] Step 4: Solve the reconstruction model that couples low-rank priors and deep learning priors using the alternating direction multiplier method to obtain the reconstruction third-order tensor. ; To solve equation (6) using the alternating direction multiplier method, we first need to obtain the augmented Lagrangian function of the original objective function. Therefore, the augmented Lagrangian function of equation (6) is expressed as: (7) in, The penalty parameter is a positive number; It is a Lagrange multiplier.

[0018] Furthermore, the alternating solution process is decomposed into solving the following subproblems: (8) (9) (10) in, This represents the predicted values ​​of network parameters. This represents the reconstruction of the third-order tensor. Indicates the updated value of the Lagrange multiplier; In subproblem (8), a self-supervised time coefficient prediction network is proposed to fully characterize the implicit temporal features of IoT data. Thus, this subproblem can be regarded as a regression model of the neural network model. During the training process of the network, the parameter gradient is calculated through the standard backpropagation mechanism and updated using the Adam optimizer. The training objective is to minimize equation (8), thereby realizing the adaptive optimization of the time coefficient prediction network.

[0019] Subproblem (9) is a standard linear least squares problem, which can be solved iteratively using the conjugate gradient algorithm, resulting in: (11) In the formula, This indicates the Hermitian transpose. Indicates the first The third-order tensor obtained in the next iteration Indicates the first The updated values ​​of the Lagrange multipliers obtained in the next iteration; Subproblem (10) can be solved iteratively using the following formula: (12) In the formula, Indicates the first The updated values ​​of the Lagrange multipliers obtained in the next iteration; This completes the reconstruction of IoT data.

[0020] To verify the effectiveness of the method of the present invention, IoT data was reconstructed using both the method of the present invention and two existing methods, including structured matrix completion and basic low-rank tensor completion. Temperature and humidity data collected by a wireless sensor network deployed in a certain area were used as test data. Since data loss is unavoidable in IoT, a small subset of complete data was selected as the actual test data; specifically, the temperature data subset... This is a subset of humidity data, consisting of 288 sensing data points collected every five minutes from 640 sensor nodes throughout the day. It also contains 288 sensing data points collected every five minutes from 640 sensor nodes throughout the day. In the experimental simulation, data containing missing information was processed by... and Obtained by random sampling, i.e., using the random sampling operator. Randomly collected from real test data We obtain a sensing data matrix from the given data. The reconstruction error is characterized by the Normalized Mean Absolute Error (NMAE). NMAE reflects the relative difference between the real test data and the reconstructed data; a lower NMAE generally indicates better reconstruction accuracy. The definition of NMAE is: (13) In equation (13), , These represent real test data and reconstructed data, respectively. This represents a subset of the sampling indexes of the complete set of entries, meaning that only the reconstruction error of missing data is considered when calculating NMAE.

[0021] For each method, the random sampling and reconstruction process was repeated 30 times, and the average NMAE was calculated; the optimal parameters for each method were selected individually to ensure that the experimental results were convincing. Figure 3 , 4The figures show the reconstruction errors of temperature and humidity data collected from a certain region under different sampling ratios. As can be seen from the figures, the reconstruction error using the method of this invention is smaller than that of the other two methods, both at the same and different sampling ratios. Compared to IoT data reconstruction methods based on structured matrix completion, the method of this invention is based on a third-order tensor modeling framework, which can more completely characterize the spatiotemporal structure of the data, avoiding the information loss and structural damage inherent in matrix models during dimensionality compression. Compared to basic low-rank tensor completion methods, this invention introduces a self-supervised time coefficient prediction network to adaptively learn the deep features and complex patterns of the time dimension, enhancing the modeling ability for nonlinear dynamic changes in data and overcoming the limitations of insufficient prior representation capabilities of traditional low-rank methods. Therefore, even with extremely low sampling ratios and limited sensor data, the method of this invention can achieve higher-precision data reconstruction by coupling the advantages of model-driven and data-driven approaches.

[0022] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for reconstructing IoT data based on low-rank subspaces and deep learning, characterized in that, Includes the following steps: Step 1: Deploy sensor nodes within the monitoring area. The sensor nodes transmit the sensed data to the base station, obtaining a sensed data matrix, denoted as... ;in, This represents the random sampling operator. Represents a third-order tensor; Step 2: Construct a reconstruction model based on the low-rank subspace; Based on the low-rank subspace model, the third-order tensor is represented as: (2) in, Describes a spatial basis. This represents tensor-matrix multiplication along the 3rd modulus. Represents the time coefficient matrix; When the spatial basis is determined, the IoT data reconstruction problem is equivalently transformed into the reconstruction of the time coefficient matrix, resulting in the following reconstruction model: (4) in, To characterize the regularization term representing the prior information of the IoT data to be reconstructed, Describing the F-norm, For regularization parameters; Step 3: Construct a time coefficient prediction network and use it to predict the time coefficient matrix; use the predicted time coefficient matrix as a deep learning prior to construct a reconstruction model that couples low-rank prior with deep learning prior. (6) in, Represents the prediction time coefficient matrix; The random noise with the same dimension as the time coefficient matrix serves as the input to the time coefficient prediction network. These are learnable network parameters; Step 4: Solve the reconstruction model that couples low-rank priors and deep learning priors using the alternating direction multiplier method to obtain the reconstruction third-order tensor and complete the IoT data reconstruction.

2. The IoT data reconstruction method based on low-rank subspace and deep learning according to claim 1, characterized in that, In the time coefficient prediction network, random noise is processed by one-dimensional convolution to obtain preliminary features; the preliminary features are processed by a residual module to obtain shallow features; the shallow features are processed by a channel attention mechanism to obtain channel attention-enhanced shallow features; the channel attention-enhanced shallow features are processed by a residual module to obtain deep features. Deep features are mapped to the target space through one-dimensional convolution to obtain the prediction time coefficient matrix.

3. The IoT data reconstruction method based on low-rank subspace and deep learning according to claim 1 or 2, characterized in that, In step 4, the augmented Lagrangian function of the reconstruction model, which couples low-rank priors with deep learning priors, is expressed as: (7) in, The penalty parameter is a positive number; For Lagrange multipliers; The alternating solution process is broken down into solving the following subproblems: (8) (9) (10) in, This represents the predicted values ​​of network parameters. This represents the reconstruction of the third-order tensor. Indicates the updated value of the Lagrange multiplier; The prediction of network parameters is achieved by predicting the network through training time coefficients; For the estimation of the third-order tensor, the conjugate gradient algorithm is used for iterative solution: (11) In the formula, This indicates the Hermitian transpose. Indicates the first The third-order tensor obtained in the next iteration Indicates the first The updated values ​​of the Lagrange multipliers obtained in the next iteration; The update of the Lagrange multipliers is solved iteratively using the following formula: (12) In the formula, Indicates the first The updated values ​​of the Lagrange multipliers obtained in the next iteration.

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