A data completion method and system of deep matrix decomposition considering dynamic constraints
By using a dynamically constrained deep matrix factorization method and taking the transformation rate of data points as a constraint, a deep matrix factorization model is trained, which solves the problem of data completion accuracy when data abruptly changes and is missing in the existing technology, and achieves a higher accuracy data completion effect.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CENT SOUTH UNIV
- Filing Date
- 2024-07-19
- Publication Date
- 2026-05-08
AI Technical Summary
Existing missing data completion methods cannot guarantee high-precision data completion when dealing with highly nonlinear data, especially when the data missing rate is as high as 80%. In particular, when critical data points at data abrupt changes are missing in process industries, the completion accuracy cannot be guaranteed.
A deep matrix factorization method considering dynamic constraints is adopted. The original dataset is obtained and preprocessed by handling missing data and standardization. The transformation rate of data points is calculated by difference operation as a dynamic constraint condition. The deep matrix factorization model is trained and then upgraded by artificial neural network to build a dynamic constraint deep matrix factorization model for data completion.
It improves the accuracy of data completion, takes into account the dynamic changes of data over time, enhances the model's ability to complete missing data, and improves the accuracy of data analysis and model training.
Smart Images
Figure CN118964839B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of industrial information technology, and in particular relates to a data completion method and system for deep matrix decomposition considering dynamic constraints. Background Technology
[0002] With the advancement of industrial informatization, a large amount of data is collected and used for monitoring, optimizing, and predicting production processes. However, due to equipment failures, sensor malfunctions, and other reasons, data often contains missing information, which seriously affects the accuracy of data analysis and model training.
[0003] Traditional methods for imputing missing data mainly include constant imputation, regression imputation, and multiple imputation. While these methods are simple and portable, they typically only consider simple relationships between data points, failing to effectively capture the complex structure of the data. Furthermore, they incur significant computational complexity and time overhead when processing large-scale datasets, limiting their application. To address the shortcomings of traditional methods, some scholars have proposed the concept of sparse matrix imputation. Commonly used sparse matrix imputation methods include matrix factorization, optimization algorithms, and machine learning methods. These matrix imputation methods are all linear imputation methods; when encountering highly nonlinear data, they are limited by the low-rank assumption, making it difficult to provide accurate results.
[0004] To better complete highly nonlinear data, three approaches have been proposed. The first approach utilizes nonnegative matrix factorization (NMF) to handle missing values in multiple related datasets or patterns, and employs multi-manifold regularization and NMF to capture and model complex nonlinear relationships in multi-view data. The second approach uses collaborative filtering to address data recovery problems with nonlinear inequality constraints in manufacturing processes, leveraging the correlation between sensor data to ensure the recovered data meets specified nonlinear constraints. The third approach employs a kernel sparse Bayesian matrix factorization method, introducing kernel functions to capture and model nonlinear relationships in the data, effectively handling missing values and noise. However, none of these three approaches consider highly incomplete data matrices, such as data missing rates reaching 80%. Therefore, a large number of missing values in nonlinear data cannot guarantee high-precision data completion results.
[0005] Deep Matrix Factorization (DMF) offers the possibility of efficiently processing highly incomplete data. The DMF model combines matrix factorization with deep neural networks, using various Artificial Neural Networks (ANNs) such as Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and Recurrent Neural Networks (RNNs). Based on a nonlinear latent variable model, DMF can recover data matrices with nonlinear characteristics, effectively handling highly missing data and has been successfully applied in recommendation systems, image processing, and other fields. However, when the missing data block is located at abrupt data changes, the data completion effect cannot be guaranteed. In process industries, sample data undergoes drastic changes, and the missing key data points at abrupt data changes cannot guarantee completion accuracy. Summary of the Invention
[0006] To overcome the shortcomings of existing technologies, this invention provides a data completion method and system for deep matrix factorization that considers dynamic constraints.
[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:
[0008] Firstly, a data completion method for depth matrix factorization considering dynamic constraints is provided, including:
[0009] Obtain the original complete dataset, and perform missing data processing on the original complete dataset to obtain the missing data processed dataset;
[0010] Standardize and preprocess the missing data set;
[0011] A deep matrix factorization model considering dynamic constraints is trained using a standardized preprocessed missing data set.
[0012] When a current dataset with missing data is received, the data is completed by using a deep matrix factorization model that takes into account dynamic constraints.
[0013] Furthermore, the original complete dataset is obtained, and data missing data processing is performed on the original complete dataset to obtain the missing data processed dataset, including:
[0014] Obtain the original complete dataset;
[0015] The original complete matrix is obtained from the original complete dataset;
[0016] The original sparse matrix is obtained by performing a dot product operation between the preset mask matrix and the original complete matrix; the preset mask matrix is set in advance according to the data missing situation, and the original sparse matrix is the missing data processing dataset.
[0017] Furthermore, the preset mask matrix includes a first mask matrix and a second mask matrix. The first mask matrix is set according to the regularity of missing data, and the second mask matrix is set according to the large segment of missing data.
[0018] Furthermore, the missing data processing dataset undergoes standardization preprocessing, including:
[0019] The original sparse matrix is preprocessed using the standard score Z-Score.
[0020] Furthermore, using the standardized preprocessed missing data set, a deep matrix factorization model considering dynamic constraints is trained, including:
[0021] Based on the original sparse matrix Y∈R after normalization and preprocessing m×n The expression for the original sparse matrix is obtained as follows:
[0022] Y = UV = f(V) = g(WV + B);
[0023] m represents the row; n represents the column; U and V are obtained by decomposing the original sparse matrix Y, and U∈R m×k and V∈R k×n f(·) represents a nonlinear mapping, and for V∈R k×n Each column in the array is executed; g(x) represents the activation function, W is the weight matrix in the artificial neural network, and B is the bias vector in the artificial neural network;
[0024] A new sparse matrix is obtained by changing the values of a pre-defined sparse matrix over time. The expression for the new sparse matrix obtained by modeling is:
[0025]
[0026] The data transformation rate of each data point in the new sparse matrix is calculated using difference operations;
[0027] By using the data transformation rate as a dynamic constraint, a deep matrix factorization model that considers dynamic constraints is trained.
[0028] Furthermore, the data transformation rate of each data point in the new sparse matrix is calculated through difference operations, including:
[0029] The observed data points in the new sparse matrix are y(t1), y(t2), ..., y(t3). n );
[0030] For the first initial data point y(t1) and the nth ending data point y(t2) n The i-th intermediate data point y(t) other than ) i ), use the central difference method to estimate y(t) i The derivative of ) is:
[0031]
[0032] The derivative at time t1, calculated using the forward difference method for the initial data point y(t1), is:
[0033]
[0034] For the final data point y(t) n ) Calculate the corresponding time t using the backward difference method n The derivative at point is:
[0035]
[0036] The derivative of each data point is used as the data transformation rate for that data point.
[0037] Furthermore, by using the data transformation rate as a dynamic constraint, a deep matrix factorization model considering dynamic constraints is trained, including:
[0038] Data transformation rate As dynamic constraints, the initial model expression is constructed:
[0039]
[0040] Where π(f) is the penalty term for f(·); λ is the regularization parameter; and β is the regularization parameter for the penalty of V. Represents the Hadamard product; M is a preset mask matrix, M ij When M = 1, the data corresponding to the position in the original sparse matrix is not missing; ij When = 0, the data at the corresponding position in the original sparse matrix is missing; ρ is an adjustable hyperparameter;
[0041] By approximating f(·) in the initial model expression using an artificial neural network, a first model expression that approximates the initial model expression is obtained:
[0042]
[0043] Where W∈R m×k Let b ∈ R be the weight matrix. m M represents the bias vector. iLet y represent the i-th column of M. i Let v represent the i-th column of Y. i Indicates V∈R k×n In the i-th column, λ is the weight decay parameter;
[0044] After performing a deep upgrade on the single-layer artificial neural network of the first model expression, the second model expression is obtained:
[0045]
[0046] Among them, Ψ (j) ={W (j) ,b (j)}, g (j) (x, Ψ) (j) ) = g (j) (W (j) x+b (j) ), j = 1, 2, ..., h+1, where h is the number of hidden layers;
[0047] The second model expression is used as the expression for the deep matrix factorization model that considers dynamic constraints.
[0048] Secondly, a data completion system for deep matrix factorization considering dynamic constraints is provided, characterized by comprising:
[0049] The missing data handling module is used to obtain the original complete dataset, perform missing data handling on the original complete dataset, and obtain the missing data handled dataset.
[0050] The standardization module is used to perform standardization preprocessing on the missing data set;
[0051] The model training module is used to train a deep matrix factorization model that takes into account dynamic constraints using a standardized preprocessed missing data set.
[0052] The data completion module is used to complete the current dataset by using a deep matrix factorization model that takes into account dynamic constraints when a current dataset with missing data is received.
[0053] The beneficial effects achieved by this invention are as follows:
[0054] Using the rate of data change as a dynamic constraint improves the model's ability to complete missing data. It takes into account how the data changes over time, emphasizing the dynamic characteristics of the data rather than just static values. By constraining the rate of data change, the deep matrix factorization model that considers dynamic constraints is guided to understand the dynamic changes in the data, thereby improving the accuracy of data completion. Attached Figure Description
[0055] Figure 1A flowchart of the data completion method for depth matrix factorization considering dynamic constraints according to the present invention;
[0056] Figure 2 This is a structural diagram of the data completion system for deep matrix decomposition considering dynamic constraints, as described in this invention. Detailed Implementation
[0057] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.
[0058] like Figure 1 As shown, this embodiment of the invention provides a data completion method for depth matrix factorization considering dynamic constraints, including:
[0059] 101. Obtain the original complete dataset, perform missing data processing on the original complete dataset, and obtain the missing data processed dataset;
[0060] In this embodiment, the original complete matrix is obtained based on the original complete dataset; the original sparse matrix is obtained by performing a dot product operation between the original complete matrix and a preset mask matrix; the preset mask matrix is pre-set according to the data missing situation, and the original sparse matrix is the missing data processing dataset. The preset mask matrix includes a first mask matrix and a second mask matrix, the first mask matrix is set according to the regular data missing situation, and the second mask matrix is set according to the large data missing segment situation;
[0061] Besides using a pre-set mask matrix for missing data processing, a random approach can also be used. Specifically, the original complete dataset is first obtained from the BSM1 wastewater treatment simulation platform. BSM1 is a widely used "simulation benchmark model" in the field of water treatment research. BSM1 simulates a 14-day wastewater treatment process, with a sampling period of 15 minutes for each variable, totaling 1344 sampling points. In addition, BSM1 considers the impact of weather changes, corresponding to three different weather conditions (sunny, rainy, and heavy rain). Missing data processing needs to be performed on the original data collected from the BSM1 platform to generate missing data. First, water-soluble variables in the secondary sedimentation tank of the BSM1 model are randomly selected as target variables, namely biodegradable organic matter (S...). S Dissolved oxygen (S) O ), nitrate and nitrite nitrogen (S NO pH value (S) ALK ), soluble and biodegradable organic nitrogen (S) NDFor the original data corresponding to three different weather conditions, three complete matrices of size 5×1344 can be obtained. Considering the field conditions, the data may be missing on a daily basis. Therefore, the data of a certain variable for a certain number of days is randomly removed. After missing data processing, the original sparse matrix Y can be obtained. Since the data in BSM1 is sampled every 15 minutes, there are 24*60 / 15=96 sampling points in a day. By removing 1344, 2688, 4032 and 5376 sampling points from the total sample, four incomplete matrices with missing rates (γ) of 20%, 40%, 60% and 80% can be obtained.
[0062] 102. Standardize and preprocess the missing data set;
[0063] Standardized preprocessing uses standard scores (Z-Score).
[0064] 103. Using a standardized preprocessed missing data set, a deep matrix factorization model considering dynamic constraints is trained.
[0065] The specific implementation process is as follows:
[0066] Based on the original sparse matrix Y∈R after normalization and preprocessing m×n The expression for the original sparse matrix is obtained as follows:
[0067] Y = UV = f(V) = g(WV + B);
[0068] m represents the row; n represents the column; U and V are obtained by decomposing the original sparse matrix Y, and U∈R m×k and V∈R k×n f(·) denotes a nonlinear mapping, and for V∈R k×n Each column in the array is executed; g(x) represents the activation function, W is the weight matrix in the artificial neural network, and B is the bias vector in the artificial neural network;
[0069] A new sparse matrix is obtained by changing the values of a pre-defined sparse matrix over time. The expression for the new sparse matrix obtained by modeling is:
[0070]
[0071] The process of calculating the data transformation rate of each data point in the new sparse matrix using difference operations is as follows:
[0072] The observed data points in the new sparse matrix are y(t1), y(t2), ..., y(t3). n );
[0073] For the first initial data point y(t1) and the nth ending data point y(t2)n The i-th intermediate data point y(t) other than ) i ), use the central difference method to estimate y(t) i The derivative of ) is:
[0074]
[0075] The derivative at time t1, calculated using the forward difference method for the initial data point y(t1), is:
[0076]
[0077] For the final data point y(t) n ) Calculate the corresponding time t using the backward difference method n The derivative at point is:
[0078]
[0079] The derivative of each data point is used as the data transformation rate of the corresponding data point;
[0080] By using the data transformation rate as a dynamic constraint, a deep matrix factorization model considering dynamic constraints is trained, including:
[0081] Data transformation rate As dynamic constraints, the initial model expression is constructed:
[0082]
[0083] Where π(f) is the penalty term for f(·); λ is the regularization parameter; and β is the regularization parameter for the penalty of V. Represents the Hadamard product; M is a preset mask matrix, M ij When M = 1, the data corresponding to the position in the original sparse matrix is not missing; ij When = 0, the data at the corresponding position in the original sparse matrix is missing; ρ is an adjustable hyperparameter;
[0084] By approximating f(·) in the initial model expression using an artificial neural network, a first model expression that approximates the initial model expression is obtained:
[0085]
[0086] Where W∈R m×k Let b ∈ R be the weight matrix. m M represents the bias vector. i Let y represent the i-th column of M. i Let v represent the i-th column of Y. i Indicates V∈R k×nThe i-th column, where λ is the weight decay parameter;
[0087] After deep upgrading the single-layer artificial neural network of the first model expression, the second model expression is obtained:
[0088]
[0089] Among them, Ψ (j) ={W (j) , b (j)}, g (j) (x, Ψ (j) ) = g (j) (W (j) x + b (j) ), j = 1, 2…h + 1, where h is the number of hidden layers;
[0090] Take the second model expression as the expression of the deep matrix factorization model considering dynamic constraints;
[0091] Since matrix factorization in the above implementation process is a process of decomposing a high-dimensional sparse matrix into a low-dimensional low-rank matrix and then generating a high-dimensional complete matrix, the number of neurons in each layer of the artificial neural network of the model should increase layer by layer. Then, the condition r < h1 < h2 < … < h k < m×n, where r is the dimension of the input layer neurons of the deep matrix factorization model considering dynamic constraints.
[0092] 104. When receiving the current data set with missing data, use the deep matrix factorization model considering dynamic constraints to complete the data in the current data set.
[0093] After the deep matrix factorization model considering dynamic constraints is constructed, when receiving the current data set with missing data, the current data set needs to be processed into a current data matrix, and the current data matrix is input into the deep matrix factorization model considering dynamic constraints. The model outputs a reconstructed matrix, and the missing data in the current data set has been completed in the reconstructed matrix.
[0094] The implementation principle of the embodiments of the present invention is:
[0095] Take the data change rate as a dynamic constraint condition to improve the data completion ability of the model. Consider the change of data over time, emphasize the dynamic characteristics of data rather than just static values. By constraining the data change rate, the deep matrix factorization model considering dynamic constraints is guided to understand the dynamic change law of data, thereby improving the data completion accuracy.
[0096] It should be noted that when performing data completion in the above embodiments, there will still be model calculation errors. Therefore, it is necessary to calculate the loss function, which consists of two parts: reconstruction error and ratio transformation rate error.
[0097] Reconstruction error, which is the difference between the actual and predicted values, is calculated for each column of the matrix and is specifically represented as follows:
[0098]
[0099] Error in the rate of change, i.e., the difference in the rate of change of the data, is specifically expressed as:
[0100]
[0101] It should be noted that in this embodiment, since the model parameters of the deep matrix factorization model considering dynamic constraints will affect the model's performance to some extent, these parameters need to be adjusted to achieve better results. After Z-Score normalization preprocessing, the optimal parameter settings are as follows: epochs are 600, the network structure is set to [1,2,4,5], which means that there is 1 neuron in the input layer, 2 hidden layers with 2 and 4 neurons respectively, 5 neurons in the output layer, the latent variable penalty parameter β is set to 0.1, the weight decay penalty parameter λ is set to 0.005, the activation function of the hidden layer is the Sigmoid function, the activation function of the output layer is a linear activation function, and the dynamic constraint parameter ρ is set to 0.01.
[0102] It should be noted that after data completion using the methods described in the above embodiments, it is necessary to use evaluation metrics to determine the quality of the data completion. For comparison, three evaluation metrics are used: relative error (RE), correlation coefficient (R²), and other metrics. 2 ) and root mean square error (RMSE).
[0103] The relative error (RE) is defined as:
[0104]
[0105] in, It is the reconstruction matrix, Y ij It is the original complete matrix. This indicates the missing location; a lower RE value is better. Comparing RE values can visually indicate the data recovery effect, but relying on only one evaluation metric is incomplete, so the correlation coefficient (R²) also needs to be considered. 2 ) and root mean square error (RMSE);
[0106] Correlation coefficient (R) 2 The definition of ) is:
[0107]
[0108] in, R is the average of the actual values of the missing entries. 2 The closer the value is to 1, the greater the correlation and the better the data recovery effect.
[0109] The root mean square error (RMSE) is a very commonly used evaluation metric, and is therefore also used to assess the accuracy of a model. It is defined as follows:
[0110]
[0111] Where N represents the number of missing entries, and since RMSE represents the sample standard deviation of the difference between the predicted and actual values, its value should be as small as possible.
[0112] Based on the depth matrix factorization method considering dynamic constraints described in the above embodiments, the following embodiments illustrate the depth matrix factorization system considering dynamic constraints.
[0113] like Figure 2 As shown, this embodiment of the invention provides a data completion system for deep matrix factorization considering dynamic constraints, comprising:
[0114] The missing data processing module 201 is used to obtain the original complete dataset, perform missing data processing on the original complete dataset, and obtain the missing data processed dataset.
[0115] The standardization processing module 202 is used to perform standardization preprocessing on the missing data processing dataset;
[0116] Model training module 203 is used to train a deep matrix factorization model that considers dynamic constraints using a standardized preprocessed missing data set.
[0117] The data completion module 204 is used to complete the current dataset by using a deep matrix factorization model that takes into account dynamic constraints when the current dataset with missing data is received.
[0118] 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 embodied 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.
[0119] 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.
[0120] 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.
[0121] 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.
[0122] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of the claims of the present invention pending approval.
Claims
1. A data completion method for depth matrix factorization considering dynamic constraints, characterized in that, include: The original complete dataset is obtained from the BSM1 wastewater treatment simulation platform, and the missing data is processed to obtain the missing data processed dataset. The missing data set is preprocessed using standardization. Based on the original sparse matrix after normalization and preprocessing The expression for the original sparse matrix is obtained as follows: ； The original sparse matrix is a missing data set, where m represents rows and n represents columns; U and V are obtained by decomposing the original sparse matrix Y, and the... and the aforementioned The Represents a nonlinear mapping, and for the... Execute each column in the; the Let W represent the activation function, W be the weight matrix in the artificial neural network, and B be the bias vector in the artificial neural network. The new sparse matrix is obtained by changing the values of the original sparse matrix over time. The expression for the new sparse matrix obtained by modeling is: ； The data transformation rate of each data point in the new sparse matrix is calculated by difference operations; The data transformation rate As dynamic constraints, the initial model expression is constructed: ； Among them, the It is the aforementioned The penalty item; It is a regularization parameter; the stated It is the aforementioned The regularization parameter for the penalty; Represents the Hadamard product; the M is a preset mask matrix. ij When M = 1, the data corresponding to the position in the original sparse matrix is not missing; ij When = 0, the data corresponding to the position in the original sparse matrix is missing; These are adjustable hyperparameters; The initial model expression An approximation process using an artificial neural network is used to obtain a first model expression that approximates the initial model expression: ； Among them, the Represents the weight matrix, the Represents the bias vector, the Indicates the The The column, the Indicates the The The column, the Indicates the The The column, the It is the weight decay parameter; After performing a deep upgrade on the single-layer artificial neural network of the first model expression, the second model expression is obtained: ； Among them, the The , The The number of hidden layers; The second model expression is used as the expression for the deep matrix factorization model that considers dynamic constraints; When a current dataset with missing data is received, the data in the current dataset is completed using the deep matrix factorization model that considers dynamic constraints.
2. The data completion method for depth matrix factorization considering dynamic constraints according to claim 1, characterized in that, The process of obtaining the original complete dataset and performing missing data processing on the original complete dataset to obtain a missing data processed dataset includes: Obtain the original complete dataset; The original complete matrix is obtained based on the original complete dataset. The original sparse matrix is obtained by performing a dot product operation between the preset mask matrix and the original complete matrix; the preset mask matrix is set in advance according to the data missing situation.
3. The data completion method for depth matrix factorization considering dynamic constraints according to claim 2, characterized in that, The preset mask matrix includes a first mask matrix and a second mask matrix. The first mask matrix is set according to the regularity of missing data, and the second mask matrix is set according to the large segment of missing data.
4. The data completion method for depth matrix factorization considering dynamic constraints according to claim 2, characterized in that, The standardization preprocessing of the missing data set includes: The original sparse matrix is preprocessed using the standard score Z-Score.
5. The data completion method for depth matrix factorization considering dynamic constraints according to claim 1, characterized in that, The step of calculating the data transformation rate of each data point in the new sparse matrix through difference operations includes: The data points in the observation portion of the new sparse matrix are: ; For the first initial data point and the nth ending data point The i-th intermediate data point outside of [other data points] The central difference method is used to estimate the... The derivative is: ； For the initial data points The corresponding time is calculated using the forward difference method. The derivative at point is: ； For the end data point The corresponding time is calculated using the backward difference method. The derivative at point is: ； The derivative of each data point is used as the data transformation rate for that data point.
6. A data completion system for deep matrix factorization considering dynamic constraints, characterized in that, include: The missing data processing module is used to obtain the original complete dataset from the BSM1 wastewater treatment simulation platform, and perform missing data processing on the original complete dataset to obtain the missing data processed dataset. A standardization processing module is used to perform standardization preprocessing on the missing data set. The model training module is used to train the model based on the normalized preprocessed original sparse matrix. The expression for the original sparse matrix is obtained as follows: ； The original sparse matrix is a missing data set, where m represents rows and n represents columns; U and V are obtained by decomposing the original sparse matrix Y, and the... and the aforementioned The Represents a nonlinear mapping, and for the... Execute each column in the; the Let W represent the activation function, W be the weight matrix in the artificial neural network, and B be the bias vector in the artificial neural network. The new sparse matrix is obtained by changing the values of the original sparse matrix over time. The expression for the new sparse matrix obtained by modeling is: ； The data transformation rate of each data point in the new sparse matrix is calculated by difference operations; The data transformation rate As dynamic constraints, the initial model expression is constructed: ； Among them, the It is the aforementioned The penalty item; It is a regularization parameter; the stated It is the aforementioned The regularization parameter for the penalty; Represents the Hadamard product; the M is a preset mask matrix. ij When M = 1, the data corresponding to the position in the original sparse matrix is not missing; ij When = 0, the data corresponding to the position in the original sparse matrix is missing; These are adjustable hyperparameters; The initial model expression An approximation process using an artificial neural network is used to obtain a first model expression that approximates the initial model expression: ； Among them, the Represents the weight matrix, the Represents the bias vector, the Indicates the The The column, the Indicates the The The column, the Indicates the The The column, the It is the weight decay parameter; After performing a deep upgrade on the single-layer artificial neural network of the first model expression, the second model expression is obtained: ； Among them, the The , The The number of hidden layers; The second model expression is used as the expression for the deep matrix factorization model that considers dynamic constraints; The data completion module is used to complete the current dataset by using the deep matrix factorization model that considers dynamic constraints when a current dataset with missing data is received.