Gradient perturbation optimization method for implicit matrix factorization based on differential privacy

Abstract

The invention relates to a gradient perturbation optimization method for implicit matrix decomposition based on differential privacy, and belongs to the field of computer recommendation systems and the field of information security. An implicit feedback matrix composed of 0 and 1 is used for representing feedback data of a user to an item, 0 represents negative feedback, and 1 represents positive feedback. Randomly initializing a user implicit factor matrix W and a project implicit factor matrix H; a data set and a target function L (W, H) are constructed, W and H are optimized and solved by adopting a matrix decomposition method based on Bayesian personalized sorting, and a result W is stored. Randomly initializing a noise adding item implicit factor matrix # imgabs0 # and an initial record matrix # imgabs1 # by using the trained W, substituting the W into L (W, H), constructing a target function # imgabs3 # about # imgabs2 #, calculating a gradient # imgabs6 # of # imgabs4 # about # imgabs5 #, cutting the gradient by using a cutting threshold C, and obtaining an optimal privacy budget size lambda t in each round of training by using an overall mse calculation formula, then, the gradient is disturbed by using lambda t and the sensitivity of the gradient to obtain # imgabs7, the # imgabs8 is aggregated to obtain a cumulative gradient, and # imgabs9 is used for updating an item implicit factor matrix by using the cumulative gradient and # imgabs10; # imgabs11 is repeatedly updated to obtain a final item implicit factor matrix # imgabs12, and the final item implicit factor matrix # imgabs12 is distributed to each user; and the user u calculates a predicted value # imgabs13 on the equipment of the user u according to the predicted value, sorts unobserved interaction items in a descending order, and finally selects the first K items from the interaction items to recommend to the user u. The method has good privacy protection and model accuracy.

Description

Technical Field

[0001] The invention belongs to the field of computer recommendation systems and information security, and relates to a gradient perturbation optimization method of implicit matrix decomposition based on differential privacy. Background Art

[0002] As users become more aware of privacy, the leakage and improper use of personal information have become a focus of public attention. Recommendation systems rely on in-depth mining of user behavior data, which may include sensitive information such as browsing history, purchase history, and rating history. Once this data is abused or leaked, it may cause irreversible damage to user privacy and even lead to legal risks. Therefore, it has become an inevitable requirement to introduce privacy protection mechanisms in recommendation systems. Globally, the introduction of privacy protection-related laws and regulations has further intensified the need for privacy protection. For example, China's Personal Information Protection Law (PIPL) and Cybersecurity Law (CSL) set comprehensive and strict requirements for user privacy protection. These laws not only require platforms to be transparent about the collection and use of user data, but also stipulate serious penalties for violations. Therefore, platforms need to use technical means to protect user privacy while continuing to provide high-quality recommendation services. Differential privacy is an effective way to meet this demand. Differential privacy is a privacy protection technology with strict mathematical guarantees. Its core idea is to introduce a certain degree of random noise when analyzing and processing data, thereby blurring the specific information of individual users. This mechanism ensures that even if an attacker has mastered the entire output of the model, the specific data of a single user cannot be restored. Compared with traditional privacy protection methods (such as data anonymization or encryption), differential privacy is more secure in theory and can accurately quantify the risk of privacy leakage. Summary of the invention

[0003] In view of this, the purpose of the present invention is to provide a gradient perturbation optimization method for implicit matrix decomposition based on differential privacy, so as to achieve a good balance between security and usability of the matrix decomposition recommendation model.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] S1: An implicit feedback matrix consisting of 0 and 1 is used to represent the user's feedback data on the project, where 0 indicates that the user gives negative feedback to the project, and 1 indicates that the user gives positive feedback to the project;

[0006] S2: Randomly initialize matrices W, H, (When initializing ); W is the user latent factor matrix, represents the u-th row of the matrix W, representing the latent factor vector of the u-th user; H is the project latent factor matrix, The i-th row of the matrix H represents the latent factor vector of the i-th item; is the noisy item latent factor matrix, Representation Matrix The i-th row of represents the latent factor vector of the i-th item with noise added; d represents the dimension of the latent factor vector. Before training starts The initial recorded value of

[0007] S3: Construct the data set D and the objective function L(W,H), use the matrix decomposition recommendation method based on Bayesian personalized sorting, solve the user matrix W and the project matrix H, and save the W result;

[0008] S4: Randomly initialize the matrix H, fix the matrix W obtained in S3 and substitute it into L(W,H), and reconstruct The objective function calculate about Gradient According to the sensitivity of the gradient Do two-norm clipping;

[0009] S5: Under the condition of ensuring the privacy protection strength, according to the formula mse = σ 2 trace(R (T)T R T diag -2 ((λ 1:T )))Δ 2 Optimize the solution of mse and obtain the privacy budget size λ in each round of training t ;

[0010] S6: Sampling noise from a Gaussian distribution, for gradient Add the noise corresponding to the privacy budget obtained in S5 to obtain the perturbed gradient The perturbed gradient Used to update H;

[0011] S7: According to the formula Make predictions, sort the prediction results of the non-positive feedback items in the implicit feedback matrix described in S1, and recommend the TOP-K items to the user.

[0012] Furthermore, in step S1, the implicit feedback data of the user on the project is converted into an implicit feedback matrix consisting of 0 and 1, r ui∈R is used to represent the feedback of user u on project i. The value 0 represents the user's non-positive feedback on the project, and the value 1 represents the user's positive feedback on the project. U represents the set of all users, I represents the set of all projects, and |U| and |I| represent the number of users in the user set U and the number of projects in the project set I, respectively.

[0013] Furthermore, randomly initialize the matrices W, H, (When initializing ); W is the user latent factor matrix, represents the u-th row of the matrix W, representing the latent factor vector of the u-th user; H is the project latent factor matrix, The i-th row of the matrix H represents the latent factor vector of the i-th item; is the noisy item latent factor matrix, Representation Matrix The i-th row of represents the latent factor vector of the i-th item with noise added; d represents the dimension of the latent factor vector. Before training starts The initial recorded value of .

[0014] Furthermore, in step S3, a data set D and an objective function L(W,H) are constructed, and a matrix decomposition recommendation method based on Bayesian personalized sorting is adopted to solve the user matrix W and the project matrix H, and the W result is saved. Specifically, the following steps are included:

[0015] Construct a dataset consisting of multiple triplets, where each triplet contains a user u, an item i with which the user has interacted, and an item j with which the user has not interacted. For each non-zero element in the implicit feedback matrix R, randomly select items, generate the corresponding triples<u,i,j> Based on the generated dataset D, the implicit feedback matrix is ​​decomposed into two low-dimensional matrices W and H, and an objective function about the user matrix W and the item matrix H is defined:

[0016]

[0017] in, represents the loss function, λ W represents the regularization coefficient of the user vector, denote the regularization coefficients of the vectors of users’ interacted items and non-interacted items, respectively, ‖·‖ 2 represents the norm used.

[0018] Use stochastic gradient descent to optimize the objective function L(W,H) and randomly extract triplets from the dataset D.<u,i,j> , calculate the objective function wu ,h i ,h j Gradient Subsequently, the user latent factor vector w is updated by these gradients u and the item latent factor vector h i ,h j The specific update rules are as follows:

[0019]

[0020] where η 1 represents the learning rate, where the formula for calculating the gradient is as follows:

[0021]

[0022] Repeat the above step S3 to iterate W and H. When W and H meet the stopping condition, the iteration ends and the matrix W is saved.

[0023] Further, in step S4, the matrix W obtained in step S3 is substituted into L(W,H) to construct The objective function calculate about Gradient The gradient is clipped using the clipping threshold C, which specifically includes the following steps:

[0024]

[0025] in, represents the latent factor vector of item i that user u has interacted with, represents the vector of item j that user u has not interacted with, denotes the regularization coefficients of latent factor vectors of items interacting with user u and items not interacting with user u, respectively, ‖·‖ 2 represents the l2 norm;

[0026] For any triple in the dataset D<u,i,j> , respectively find the objective function about and Gradient and The calculation formula is as follows:

[0027]

[0028] In order to obtain the positive feedback project vector h i Gradient and negative feedback item vector h j Gradient , crop them:

[0029]

[0030] in, Respectively The clipped gradient, C is the clipping threshold:

[0031] After each round of training, the clipped gradients are aggregated:

[0032]

[0033] in, yes The i-th row represents the h calculated by user u. i The gradient of represents h calculated by user u j gradient.

[0034] Furthermore, in step 5, the original stochastic gradient update model can be regarded as:

[0035]

[0036] in:

[0037]

[0038] Where: θ (t) represents the model parameters in round t, θ (0) represents the initial model parameters, represents the cumulative sum of all parameter update values ​​from the 1st iteration to the tth iteration, μ represents the learning rate, The objective function f is related to the model parameters θ (t) gradient.

[0039] Then update the model parameters according to this stochastic gradient descent, and accumulate the gradients s and x t There exists a query matrix Q such that:

[0040] S=QX

[0041] Where: S = [s 1 ,s 2 ,…,s t ] T ; X = [x 1 ,x 2 ,…x t ] T ; Q is a lower triangular matrix with all ones.

[0042] So we can perform matrix decomposition on Q, and then add corresponding noise to the gradient information of X for gradient protection. So the cumulative gradient after adding noise is Then we have:

[0043]

[0044] in: Represents the cumulative gradient from 0 to t;

[0045]

[0046] X=[x 1 ,x 2 ,…x t ] T ,x t represents the gradient at round t; ε represents the noise; λ 1:T =[λ 1 ,λ 2 ,…,λ t ] T ,λ t is the size of the privacy budget allocated in round t.

[0047] The accumulated gradient after adding noise and We can get the overall mean square error (mse) which is expressed as follows:

[0048]

[0049] Where: σ is the noise multiplier, Δ is the sensitivity,

[0050] We obtain the corresponding privacy budget size λ in each round of training by solving the MSE optimization problem. t .

[0051] Further, in step S6, we calculate the gradient obtained in step 4 Plus with mean 0 and variance The Gaussian noise is used to perturb get

[0052]

[0053] After the disturbance Update the current cumulative gradient

[0054]

[0055] Then use the gradient accumulation and update

[0056]

[0057] Furthermore, in step S7, the finally generated project latent factor matrix Distributed to each user, user u calculates the predicted value on its device The unobserved interaction items are sorted in descending order according to the predicted values, and finally the top K items are selected to be recommended to user u.

[0058] The present invention is aimed at the problem of privacy leakage in implicit matrix decomposition. At the same time, it is observed that direct perturbation on the gradient will cause the error to gradually accumulate and affect the model performance. Therefore, the matrix decomposition technology is generally used to decompose the implicit feedback data matrix of the user to the project into two low-dimensional matrices, which represent the user latent factor matrix and the project latent factor matrix respectively. Then the user latent factor matrix is ​​retained, the objective function belonging to the project latent factor matrix is ​​constructed, and the stochastic gradient descent is performed. In this stochastic gradient descent process, the size of the privacy budget in each round of training is calculated by measuring the overall error, and then the corresponding Gaussian noise is introduced by calculating its sensitivity for protection. The algorithm can ensure the security of user privacy data while ensuring the availability of the recommendation model. Other advantages, objectives and features of the present invention will be described in the subsequent description to some extent, and will be obvious to those skilled in the art based on the following investigation and research, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0060] Figure 1 : Schematic diagram of the solution process of matrix W and matrix H based on the Bayesian personalized ranking recommendation algorithm;

[0061] Figure 2 :Use gradient perturbation optimization algorithm to solve Get the final And recommend schematic diagrams to users;

[0062] Figure 3 : Comparison results of the present invention and other methods on HR indicators under different privacy budgets;

[0063] Figure 4 : Comparison results of the NDCG index between the present invention and other methods under different privacy budgets. DETAILED DESCRIPTION

[0064] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0065] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0066] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0067] Step S1: Convert the implicit feedback data of the user to the project into an implicit feedback matrix consisting of 0 and 1, r ui ∈R is used to represent the feedback of user u on project i. The value 0 represents the user's negative feedback on the project, and the value 1 represents the user's positive feedback on the project. U represents the set of all users, I represents the set of all projects, |U|, |I| represent the number of users in the user set U and the number of projects in the project set I respectively;

[0068] Step S2: Randomly initialize matrices W, H,

[0069] Step S3: Construct a dataset consisting of multiple triplets, where each triplet contains a user u, an item i with which the user has interacted, and an item j with which the user has not interacted. For each non-zero element in the implicit feedback matrix R, randomly select items, generate the corresponding triples<u,i,j> Based on the generated dataset D, the implicit feedback matrix is ​​decomposed into two low-dimensional matrices W and H, and an objective function about the user matrix W and the item matrix H is defined:

[0070]

[0071] in, represents the loss function, λ W represents the regularization coefficient of the user vector, denote the regularization coefficients of the vectors of users’ interacted items and non-interacted items, respectively, ‖·‖ 2 represents the norm used.

[0072] Use stochastic gradient descent to optimize the objective function L(W,H) and randomly extract triplets from the dataset D.<u,i,j> , calculate the objective function w u ,h i ,h j Gradient Subsequently, the user latent factor vector w is updated by these gradients u and the item latent factor vector h i ,h j The specific update rules are as follows:

[0073]

[0074] Among them, η 1 represents the learning rate, where the formula for calculating the gradient is as follows:

[0075]

[0076]

[0077] Repeat the above step S3 to iterate W and H. When W and H meet the stopping condition, the iteration ends and the matrix W is saved.

[0078] Step S4: Substitute the matrix W obtained in step S3 into L(W,H) to construct The objective function calculate about Gradient The gradient is clipped using the clipping threshold C, which specifically includes the following steps:

[0079]

[0080] in, represents the latent factor vector of item i that user u has interacted with, represents the vector of item j that user u has not interacted with, denotes the regularization coefficients of latent factor vectors of items interacting with user u and items not interacting with user u, respectively, ‖·‖ 2 represents the l2 norm;

[0081] For any triple in the dataset D<u,i,j> , respectively find the objective function about and Gradient and The calculation formula is as follows:

[0082]

[0083] In order to obtain the positive feedback project vector h i Gradient and negative feedback item vector h j Gradient , crop them:

[0084]

[0085] in, Respectively The clipped gradient, C is the clipping threshold:

[0086] After each round of training, the clipped gradients are aggregated:

[0087]

[0088] in, yes The i-th row represents the h calculated by user u. i The gradient of represents h calculated by user u j gradient.

[0089] Step 5: Accumulated gradients after adding noise We can get the overall mean square error (mse) which is expressed as follows:

[0090] mse=σ 2 trace(R (T)T R T diag -2 ((λ 1:T )))Δ 2

[0091] Where: σ is the noise multiplier, Δ is the sensitivity,

[0092] We obtain the corresponding privacy budget size λ in each round of training by solving the MSE optimization problem. t ;

[0093] Step S6: For the gradient obtained in step 4 Plus with mean 0 and variance The Gaussian noise is used to perturb get

[0094]

[0095] After the disturbance Aggregate and update the current gradient accumulation sum

[0096]

[0097] Then use the gradient accumulation and update

[0098]

[0099] Step S7: Repeat steps 4, 5, and 6 to generate the final project latent factor matrix Distributed to each user, user u calculates the predicted value on its device The unobserved interaction items are sorted in descending order according to the predicted values, and finally the top K items are selected to be recommended to user u.

[0100] Example

[0101] Figure 1 As shown: An implicit feedback matrix consisting of 0 and 1 is used to represent the user's feedback data on the project, where 0 represents negative feedback and 1 represents positive feedback. Randomly initialize the user latent factor matrix W and the project latent factor matrix H, where w u and the item latent factor vector h i ,h j Represent the latent factor vectors of users and items respectively, and the latent factor dimension is d. Construct the data set and objective function L(W,H), use the matrix decomposition method based on Bayesian personalized sorting, optimize and solve W and H, and save the result W.

[0102] Figure 2 As shown: Using the trained W, randomly initialize the latent factor matrix of the noise-added project and the initial record matrix Substitute W into L(W,H) and construct The objective function calculate about Gradient The gradient is clipped using the clipping threshold C, and the overall MSE calculation formula is used to obtain the optimal privacy budget size λ in each round of training t , and then use λ t And the sensitivity of the gradient is perturbed to obtain In the aggregation Get the cumulative gradient and Using the accumulated gradient and To update the project latent factor matrix Repeat the updating process to get the final project latent factor matrix Distributed to each user, user u calculates the predicted value on its device According to the predicted values, the unobserved interaction items are sorted in descending order, and finally the top K items are selected and recommended to user u. Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention is described in detail with reference to the preferred embodiments, ordinary technicians in this field should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A gradient perturbation optimization method based on implicit matrix decomposition with differential privacy is characterized by: The method specifically comprises the following steps: S1: An implicit feedback matrix consisting of 0 and 1 is used to represent the user's feedback data on the project, where 0 indicates that the user gives negative feedback to the project, and 1 indicates that the user gives positive feedback to the project; S2: Randomly initialize matrices W, H, (When initializing ); W is the user latent factor matrix, represents the u-th row of the matrix W, representing the latent factor vector of the u-th user; H is the project latent factor matrix, The i-th row of the matrix H represents the latent factor vector of the i-th item; is the noisy item latent factor matrix, Representation Matrix The i-th row of represents the latent factor vector of the i-th item with noise added; d represents the dimension of the latent factor vector. Before training starts The initial recorded value of S3: Construct the data set D and the objective function L(W,H), use the matrix decomposition recommendation method based on Bayesian personalized sorting, solve the user matrix W and the project matrix H, and save the W result; S4: Randomly initialize the matrix H, fix the matrix W obtained in S3 and substitute it into L(W,H), and reconstruct The objective function calculate about Gradient According to the sensitivity of the gradient Do two-norm clipping; S5: Under the condition of ensuring the privacy protection strength, according to the formula mse = σ 2 trace(R (T) TR T diag -2 ((λ 1:T )))Δ 2 Optimize the solution of mse to obtain the privacy budget size in each round of training; S6: Sampling noise from a Gaussian distribution, for gradient Add the noise corresponding to the privacy budget obtained in S5 to obtain the perturbed gradient The perturbed gradient Used to update H; S7: According to the formula Make predictions, sort the prediction results of the non-positive feedback items in the implicit feedback matrix described in S1, and recommend the TOP-K items to the user.

2. The gradient perturbation optimization method based on implicit matrix decomposition with differential privacy according to claim 1 is characterized by: Furthermore, in step S1, the implicit feedback data of the user on the project is converted into an implicit feedback matrix consisting of 0 and 1, r ui ∈R is used to represent the feedback of user u on project i; the value 0 represents the user's negative feedback on the project, and the value 1 represents the user's positive feedback on the project. U represents the set of all users, I represents the set of all projects, and |U| and |I| represent the number of users in the user set U and the number of projects in the project set I, respectively.

3. The gradient perturbation optimization method based on implicit matrix decomposition with differential privacy according to claim 1 is characterized by: Further, in the above step S2, the matrices W, H, (When initializing ); W is the user latent factor matrix, represents the u-th row of the matrix W, representing the latent factor vector of the u-th user; H is the project latent factor matrix, The i-th row of the matrix H represents the latent factor vector of the i-th item; is the noisy item latent factor matrix, Representation Matrix The i-th row of represents the latent factor vector of the i-th item with noise added; d represents the dimension of the latent factor vector. Before training starts The initial recorded value of .

4. The gradient perturbation optimization method based on implicit matrix decomposition with differential privacy according to claim 1 is characterized by: Furthermore, in step S3, a data set D and an objective function L(W,H) are constructed, and a matrix decomposition recommendation method based on Bayesian personalized sorting is adopted to solve the user matrix W and the project matrix H, and the W result is saved. The specific steps include: Construct a dataset consisting of multiple triplets, where each triplet contains a user u, an item i with which the user has interacted, and an item j with which the user has not interacted; for each non-zero element in the implicit feedback matrix R, randomly select an item from the set of items that user u has not interacted with. items, generate the corresponding triples<u,i,j> Based on the generated dataset D, the implicit feedback matrix is ​​decomposed into two low-dimensional matrices W and H, and an objective function about the user matrix W and the item matrix H is defined: in, represents the loss function, λ W represents the regularization coefficient of the user vector, denote the regularization coefficients of the vectors of users and interacting items and non-interacting items, respectively, and ||·||2 denotes the adopted norm; Use stochastic gradient descent to optimize the objective function L(W,H) and randomly extract triplets from the dataset D.<u,i,j> , calculate the objective function w u ,h i ,h j Gradient Subsequently, the user latent factor vector w is updated by these gradients u and the item latent factor vector h i ,h j ; The specific update rules are as follows: Where η1 represents the learning rate, and the formula for calculating the gradient is as follows: Repeat the above step S3 to iterate Q and H. When Q and H meet the stopping condition, the iteration ends and the matrix Q is saved.

5. The gradient perturbation optimization method based on implicit matrix decomposition with differential privacy according to claim 1 is characterized by: Further, in step S4, the matrix Q obtained in step S3 is substituted into L(W,H) to construct The objective function calculate about Gradient The gradient is clipped using the clipping threshold C, which specifically includes the following steps: in, represents the latent factor vector of item i that user u has interacted with, represents the vector of item j that user u has not interacted with, denotes the regularization coefficients of the latent factor vectors of items interacting with user u and items not interacting with user u, respectively, and ||·||2 denotes the l2 norm; For any triple in the dataset D<u,i,j> , respectively find the objective function about and Gradient and The calculation formula is as follows: In order to obtain the positive feedback project vector h i Gradient and negative feedback item vector h j Gradient , crop them: in, Respectively The clipped gradient, C is the clipping threshold: After each round of training, the clipped gradients are aggregated: in, yes The i-th row represents the h calculated by user u. i The gradient of represents h calculated by user u j gradient.

6. The gradient perturbation optimization method based on implicit matrix decomposition with differential privacy according to claim 1 is characterized by: Furthermore, in step 5, the original stochastic gradient update model can be regarded as: in: Where: θ (t) represents the model parameters in round t, θ (0) represents the initial model parameters, represents the cumulative sum of all parameter update values ​​from the 1st iteration to the tth iteration, μ represents the learning rate, The objective function f is related to the model parameters θ (t) The gradient of Then update the model parameters according to this stochastic gradient descent, and accumulate the gradients s and x t There exists a query matrix Q such that: S=QX Where: S = [s1, s2, ..., s t ] T ; X=[x1,x2,…x t ] T ; Q is a lower triangular matrix with all ones. So we can perform matrix decomposition on Q, and then add corresponding noise to the gradient information of X for gradient protection. So the cumulative gradient after adding noise is Then we have: in: Represents the cumulative gradient from 0 to t; X=[x1,x2,…x t ] T ,x t represents the gradient at round t; ε represents the noise; λ 1:T =[λ1,λ2,…,λ t ] T ,λ t is the size of the privacy budget allocated in round t; By adding noise to the cumulative gradient and We can get the overall mean square error (mse) which is expressed as follows: mse=σ 2 trace(R (T)T R T diagnosis -2 ((l 1:T )))D 2 Where: σ is the noise multiplier, Δ is the sensitivity, We obtain the corresponding privacy budget size λ in each round of training by solving the MSE optimization problem. t .

7. The gradient perturbation optimization method based on implicit matrix decomposition with differential privacy according to claim 1 is characterized by: Further, in step S6, we calculate the gradient obtained in step 4 Plus with mean 0 and variance The Gaussian noise is used to perturb get After the disturbance Update the current cumulative gradient Then use the gradient accumulation and update 8. The gradient perturbation optimization method based on implicit matrix decomposition with differential privacy according to claim 1 is characterized by: Furthermore, in step S7, the finally generated project latent factor matrix Distributed to each user, user u calculates the predicted value on its device The unobserved interaction items are sorted in descending order according to the predicted values, and finally the top K items are selected to be recommended to user u.

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