Adaptive-based local differential privacy protection method for high-dimensional data

Abstract

The application discloses a kind of based on adaptive high-dimensional data local differential privacy protection method, using rough set theory and mutual information, the data of different relevance and sensitivity are clustered grouping, different grouping is used different random response probability, permanent random response and temporary random response are carried out.Local differential privacy processing data, using SNE method for dimension reduction and adaptive sampling gradient optimization in server end, with low-dimensional data joint probability distribution approximates the joint distribution of all attributes, according to the sampling strategy and the approximate joint distribution constitutes release dataset.The application solves the problem of high-dimensional data with dimension disaster and local differential privacy combination and maximum degree maintaining data relevance, and more reasonably allocates privacy budget according to the different data sensitivity to some extent, improves data availability and reduces communication cost.

Description

Technical Field

[0001] This invention relates to the field of differential privacy in data privacy protection, specifically to a localized differential privacy protection method based on adaptive high-dimensional data. Background Technology

[0002] The development of smart devices has led to the widespread application of sensors in daily life. In the era of big data, the security of personal privacy information is increasingly attracting attention. For example, location-based services (LBS) and mobile crowd-sensing (MCS) collect users' location information while providing services. Anonymization of privacy information is a good way to protect it, leading to the emergence of various privacy protection methods, such as K-anonymity, secure multi-party computation, pseudonym mechanisms, and differential privacy. Among these, differential privacy is particularly effective at resisting attacks from adversaries with various background knowledge, and compared to other protection methods, it can quantify and analyze the degree of protection offered by the privacy model.

[0003] In 2006, D. Work proposed differential privacy to address the privacy breaches associated with statistical databases. Differential privacy uses noise to distort sensitive data, making it a privacy protection technique based on data distortion. However, the amount of noise required is independent of the dataset size; even for large datasets, a small amount of noise can achieve a high level of privacy protection. Centralized differential privacy performs well when a trusted third party is present, but this assumption may not hold true in reality. Localized differential privacy offers strong privacy protection, preventing privacy attacks from untrusted third parties and providing more comprehensive protection for sensitive information.

[0004] Currently, research on localized differential privacy protection technology mainly focuses on simple data types, such as frequency or mean statistics for relational data and set-valued data containing one or more attributes. However, simple data types are far from sufficient for the unprecedented data analysis needs of today. For correlated data, differential privacy protection is not ideal. For complex data types such as graph structures, the difficulty lies in the fact that the structural characteristics of graphs make queries highly sensitive globally, resulting in excessive noise. While graph data publishing based on localized differential privacy technology does not have the problem of excessive sensitivity, the independent perturbation processes of each user make it difficult for data collectors to construct highly usable graph structures from the perturbed data. For example, using quantification methods such as mutual information can destroy the correlation between data; thus, ensuring the correlation between the original data is a major challenge. Most existing high-dimensional data publishing technologies are based on centralized scenarios, such as centralized differential privacy publishing technologies. However, in reality, most third parties or servers are untrustworthy. In summary, the sensitivity issues caused by complex attribute relationships between high-dimensional data and simultaneous changes in related attributes, as well as the high-dimensional publishing problems in distributed environments, remain to be addressed.

[0005] Existing research, while satisfying differential privacy, decomposes the joint probability distribution of high-dimensional data into multiple low-dimensional marginal probability distributions, and then approximates the joint probability distribution using these marginal probabilities through some inference mechanism. However, a problem arises: if segmentation is to be performed, the correlation between data attributes must be considered, requiring the assessment of the degree of correlation between each pair of attributes. When there are n attributes, this presents a challenge. This kind of corresponding correlation requires the privacy budget to be... Subsequent partitioning will inevitably introduce significant noise, leading to substantial errors when inferring the joint probability density. While clustering or grouping methods can reduce dimensionality, they still suffer from high communication costs. Furthermore, sampling and reducing dimensionality from different dimensions decreases data usability. Artificially allocating privacy budgets based on data with varying sensitivities can also result in excessive noise, rendering the data unusable. Summary of the Invention

[0006] Based on the problems and shortcomings of existing research methods mentioned above, this invention provides a localized differential privacy protection method based on adaptive high-dimensional data.

[0007] The purpose of this invention is to propose a localized differential privacy high-dimensional data publishing method based on rough set classification, adaptive sampling according to data sensitivity, and adaptive privacy budget allocation. This method aims to solve the problem of combining high-dimensional data with localized differential privacy while maintaining data correlation to the greatest extent possible, and to allocate the privacy budget more reasonably according to different data sensitivities, thereby improving data availability and reducing communication costs.

[0008] To achieve the above objectives, the technical solution adopted in this invention is to use rough set theory and mutual information to cluster data with different correlations and sensitivities, and to apply different random response probabilities to different groups, performing permanent and temporary random responses. For the data after localized differential privacy processing, the SNE method is used on the server side for dimensionality reduction and adaptive sampling gradient optimization. The joint probability distribution of the low-dimensional data is used to approximate the joint distribution of all attributes, and the published dataset is constructed based on the sampling strategy and the approximate joint distribution.

[0009] The localized differential privacy protection method based on adaptive high-dimensional data includes the following steps:

[0010] Step 1: Preprocessing of local data:

[0011] Rough set theory is used to evaluate the correlation between data and calculate the mutual information between attributes of each group of data. Based on the correlation and mutual information, all data are grouped using clustering methods.

[0012] Step 2: Develop a probabilistic strategy for random responses:

[0013] Based on the mutual information between each set of data attributes calculated in the previous step, the probability of random response is set. There are two parts to the probability setting. The first part is the response probability f when performing a permanent random response, and the second part is the probability p and q when performing a temporary random response. The former is the probability of negative data being flipped into positive data, and the latter is the probability of positive data remaining unchanged. Similarly, 1-p and 1-q are the probabilities of negative data remaining unchanged and positive data being flipped into negative data, respectively.

[0014] Step 3: Perform localized differential privacy processing on the data:

[0015] After selecting the response parameters, localized differential privacy processing is performed on the grouped data from step 1. The binary data is processed into a random response and then stored locally, i.e., a permanent random response. When the server requests to query the data on the local end, another random response is performed, and the data after the response is sent to the server, i.e., a temporary random response.

[0016] Step 4: Use the SNE method for dimensionality reduction:

[0017] The joint probability distribution of high-dimensional data is decomposed into multiple low-dimensional marginal probability distributions, and the joint probability distribution is approximated by inference using these marginal probabilities. A probability distribution among high-dimensional objects is constructed using the SNE method, such that similar objects have a higher probability of being selected, while dissimilar objects have a lower probability. SNE then reconstructs the probability distributions of these points in a low-dimensional space, making the two probability distributions as similar as possible.

[0018] Step 5, Adaptive Sampling:

[0019] Gradient optimization of SNE dimensionality reduction is performed using an adaptive sampling method based on auxiliary information.

[0020] Step 6: Dataset Synthesis

[0021] After the data dimensionality reduction is completed, a new dataset is generated and published based on the adaptive sampling probability and the required amount of data.

[0022] Furthermore, the Gaussian distribution in SNE is replaced with a t-distribution for further optimization. For points with similarity greater than a specified threshold, the distance in the low-dimensional space of the t-distribution needs to be slightly smaller; while for points with similarity less than the specified threshold, the distance in the low-dimensional space of the t-distribution needs to be greater. That is, points within the same cluster (closer in distance) are clustered more closely, while points between different clusters (farther in distance) are more dispersed.

[0023] The present invention has the following beneficial effects:

[0024] The present invention provides a localized differential privacy-preserving publishing method for high-dimensional data based on SNE dimensionality reduction using adaptive sampling gradient optimization. This method publishes a new synthetic dataset, which protects the data privacy of each user while maintaining the availability of high-dimensional data to the greatest extent. It can cope with attackers with full background knowledge, and reasonably allocates the privacy budget according to the sensitivity and relevance of the data, thereby reducing the signal-to-noise ratio and communication cost.

[0025] This invention avoids data leakage in situations where third parties or servers are untrusted, and to some extent solves the "curse of dimensionality" problem of high-dimensional data. It combines localized differential privacy with SNE data dimensionality reduction and adaptively optimizes sampling gradients to divide high-dimensional data into multiple independent sets of low-dimensional attributes, ensuring that the synthesized dataset and the original dataset have similar probability distributions and statistical properties. It solves the problem of localized privacy protection of user data while maintaining data availability in situations where large amounts of high-dimensional data are generated by multiple sensors. Attached Figure Description

[0026] Figure 1 This is an overall flowchart of an embodiment of the present invention;

[0027] Figure 2 A flowchart of the overall process for localized differential privacy;

[0028] Figure 3 This is a diagram comparing centralized differential privacy and localized differential privacy.

[0029] Figure 4 A flowchart for classifying attributes. Detailed Implementation

[0030] The present invention will now be described in further detail with reference to the accompanying drawings.

[0031] First refer to Figure 2 It is the entire localized differential privacy communication process. The user generates data on the local end and sends it to the server or third party through the base station or hotspot. The server processes the data and publishes it for the querying party to perform data analysis. Figure 3 The paper presents a comparison of centralized differential privacy and local differential privacy processes, demonstrating that local differential privacy can avoid situations where third-party data collectors are untrustworthy.

[0032] Reference Figure 1 This is a flowchart of the processing operation of the present invention. The present invention provides a localized differential privacy-preserving publishing method for high-dimensional data based on SNE dimensionality reduction using adaptive sampling gradient optimization. After the user generates the original data, the data is grouped locally based on rough set theory and sensitivity calculation, and random response probabilities are set. The grouped data is then subjected to permanent random responses according to a given probability. When the server requests a response, a temporary random response is sent to the server. On the server side, SNE dimensionality reduction is performed on the high-dimensional data, and the gradient selection is optimized based on adaptive sampling. Furthermore, to improve optimization, the Gaussian distribution in the low-dimensional space of SNE is replaced with a t-distribution to represent the similarity between two points. The t-distribution is less affected by outliers, has a better fit, and better preserves the overall characteristics of the data. After sampling, a new dataset is synthesized, and finally, the data is published. The specific implementation steps are as follows:

[0033] Step 1, Preprocessing of local data:

[0034] The main purpose of this step is to assess the sensitivity and relevance of the data, providing a data basis for data grouping and random response probability allocation.

[0035] Step 1-1: Calculate the correlation of data based on rough set theory:

[0036] By employing the concept of attribute dependency in rough set theory, the correlation of data attributes is measured, and the equivalence classes arising from indistinguishable relations for each attribute are obtained. Continuous attribute values ​​are partitioned to become discrete numerical values. Based on the following formulas, lower and upper approximations of subsets of the universe of discourse U are obtained relative to other attributes:

[0037]

[0038]

[0039] In rough set theory, knowledge is represented using information tables or information systems. An information table can be represented by a quadruple s = (U, A, V, f), where U is a non-empty finite set of objects, A is a non-empty finite set of attributes, B represents any subset of attribute set A, and V = ∪ a∈A V a V a Let be the range of attribute 'a', f be the information function from the sample space to the attribute space, X be any subset of U, x be an element in the universe of discourse U, and the equivalence relation constitutes a knowledge partition in the universe of discourse U, denoted by U / B. Any element [x] in U / B... B This is called an equivalence class, B - (X) and B + (X) denote the lower and upper approximations of X, respectively.

[0040] Then, attribute subsets are divided according to the correlation between data. That is, data are grouped according to the correlation between data. Data in the same attribute subset have a high correlation, and vice versa. Data in different attribute subsets have a low correlation. Figure 4 A flowchart for classifying attributes.

[0041] Steps 1-2: Calculate the sensitivity of the data based on mutual information.

[0042] Information entropy refers to the average amount of information contained in each piece of received information. Mutual information is a special form of the broader relative information entropy. In information entropy, an equivalence class partition is regarded as a probability distribution, and the proportion of each equivalence class in the universe of discourse U is regarded as the probability of that equivalence class occurring. For an information table s = (U, A, V, f), U / B = {X1,X2,…,X} n The information entropy H(B) on attribute B is:

[0043]

[0044] Where p(X) i" ) represents the equivalence class X i" The proportion of each attribute within the domain U. Based on this, the information entropy of each attribute in each attribute subset is calculated. Then, the mutual information between each group of data is calculated using the following formula:

[0045]

[0046] Here, (X, Y) are two random variables with a joint probability distribution p(x, y) and corresponding marginal distributions p(x) and p(y), respectively. The mutual information I(X; Y) is the relative entropy between the joint probability p(x, y) and the marginal distributions p(x) and p(y). Mutual information between data is used to measure data sensitivity; the greater the mutual information between two data points, the greater the sensitivity between them.

[0047] Step 2, Develop a probabilistic strategy for random responses:

[0048] Based on the mutual information between the data in each group calculated in the previous step, the probability of random response is set. There are two parts to the probability setting. The first part is the response probability f when performing a permanent random response, and the second part is the probability p and q when performing a temporary random response. The former is the probability of negative data being flipped into positive data, and the latter is the probability of positive data remaining unchanged. Similarly, 1-p and 1-q are the probabilities of negative data remaining unchanged and positive data being flipped into negative data, respectively.

[0049] Step 3: Perform localized differential privacy processing on the data:

[0050] After selecting the response parameters, the grouped data is processed for localized differential privacy. The binary data is processed once for a random response and stored locally, which is called a permanent random response. When the server requests to query the data on the local end, another random response is processed and the data is sent to the server, which is called a temporary random response.

[0051] Step 3-1: Perform a permanent random response on the grouped data:

[0052] Each set of data changes according to a given probability f in the following ways:

[0053]

[0054] The data after the permanent random response is stored locally. When the server sends a query request, the data stored locally is then temporarily randomized and published.

[0055] Step 3-2: Apply a temporary random response to the data following the permanent random response.

[0056] For the data after a permanent random response, B' i" Data with a value of 1 remains constant with probability p, and changes to 0 with probability 1–p. B' i" Data that is 0 changes to 1 with probability q, and remains unchanged with probability 1–q, that is:

[0057]

[0058] Based on the server's request, the data after completing the temporary random response is published to the server. At this point, the data sent to the server is no longer sent according to the previous groups, but is a dataset sent according to the server's request.

[0059] Step 4: Use the SNE method for dimensionality reduction:

[0060] The data following the temporary random responses published by the server in step 3 undergoes SNE dimensionality reduction. The SNE method maps data points to a probability distribution through affine transformation, constructing a high-dimensional probability distribution among objects. Similar objects have a higher probability of being selected, while dissimilar objects have a lower probability of being selected. First, the Euclidean distance between data points is converted into conditional probabilities to express the similarity between points. The similarity between data points mentioned later is also represented using conditional probabilities. High-dimensional data r1,...,r after n temporary random responses are obtained. n Calculate data r i and r j The probability distribution p between ij Numerically p ij Proportional to r i and r j The similarity between them, used as r i Centered on r, a Gaussian distribution is selected. j The conditional probability p of being the nearest neighbor j|i To represent r i and r j Similarity between them:

[0061]

[0062] Where i, j, and m all range from 1 to n, and the parameter σ i Let r be the variance of the Gaussian distribution, for different points r i The values ​​are different, and the similarity of data to itself is set to 0 because only the similarity between data points needs to be considered. (Using r) j Centered on r, a Gaussian distribution is selected. i The conditional probability p of being the nearest neighbor i|j To represent r in higher dimensional space j and r i The similarity between them, and also setting p i|i =0, r m For n data points, the non-r i Data points.

[0063] We then reconstruct the probability distributions of these data in a low-dimensional space, making the two probability distributions as similar as possible. For the low-dimensional data, we establish a Gaussian distribution with a variance of... The similarity between low-dimensional spatial data is calculated as follows:

[0064]

[0065] q i|j In low-dimensional space r j and r i The similarity between them. When p i|j =q i|j When the similarity of high-dimensional data equals that of low-dimensional data, it indicates a good dimensionality reduction effect and complete preservation of local features. Therefore, the next step is to optimize the KL divergence between the two distributions, with the objective function being:

[0066]

[0067] Among them, P i Represents a given point r i The true conditional probability distribution of other data points under the given condition, Q i This represents the corresponding theoretical distribution, where different distances in the low-dimensional mapping correspond to different penalty weights. SNE tends to preserve local features in the data, using the concept of perplexity (the number of effective nearest neighbors of a given point) and employing binary search to find the optimal σ. In the initial optimization phase, a certain amount of Gaussian noise is introduced in each iteration, the amount of which is determined based on the specific data. Simulated annealing is then used to gradually reduce this noise, avoiding getting trapped in local optima. The selection of hyperparameters such as the learning rate and decay time varies depending on the data.

[0068] Step 5, Adaptive Sampling:

[0069] Based on the method mentioned in step 4, SNE is relatively robust to the adjustment of perplexity. A value between 5 and 50 is selected, and a binary search method is used to find a suitable σ. The gradient is then solved using the SGD optimization algorithm. During the update process, a sample i needs to be randomly selected. t The optimization and update process is as follows:

[0070]

[0071] θ t =θ t-1 -γ t d t

[0072] d t For input sample i t At that time, the performance function f with respect to parameter θ t-1 The derivative, or gradient, of θ. tLet C be the updated model parameter vector, γ be the learning rate, and to avoid the uncertainty of random selection, an adaptive selection method based on side information is chosen. Side information refers to certain attribute values ​​of the samples. k For the set of instances with auxiliary information k in the dataset received by the server, SGD minimizes the empirical risk as follows:

[0073]

[0074]

[0075]

[0076] Where D is the set of auxiliary information attributes of the data, n is the number of samples received by the server from the dataset, P(i') is the probability of sampling a single instance from the entire dataset, and p k For C k The probability of sampling an instance is determined by setting the probability p. k To adjust the optimization process of SGD.

[0077] After determining the auxiliary information of the dataset, the dataset received by the server is divided into k groups using this auxiliary information. For example, if the dataset's auxiliary information attribute set includes three attributes: 1, 2, and 3, then the dataset can be divided into three groups: C1, C2, and C3. Then, the selection probability p of each group is calculated. k According to p k Calculate the probability P(i') and gradient d of sampling a single instance. t Finally, the model parameters θ are calculated and updated. The gradient of the conditional probability of i at j in the objective function of SNE is 2(p i|j -q j|i )(y i -y j Similarly, the conditional probability gradient of j under i is 2(p j|i -q j|i )(y i -y j Finally, the complete gradient is obtained:

[0078]

[0079] y i and y j For the low-dimensional data points, where i and j range from 1 to n, the parameter update, in addition to the current gradient, also introduces the exponential decay term of the previous gradient accumulation, as follows:

[0080]

[0081] Among them, Y (t) Let represent the solution after t iterations, η represent the learning rate, and α(t) represent the momentum after t iterations.

[0082] In the low-dimensional space, the Gaussian distribution in the original SNE is replaced with a t-distribution to represent the similarity between two data points. After using the t-distribution, the conditional probability distribution is replaced by a joint probability distribution; that is, P is the joint probability distribution of all points in the high-dimensional space, and Q is the joint probability distribution in the low-dimensional space. The objective function is:

[0083]

[0084] Where p ij and q i|j For p i|j and q i|j The corresponding joint probability distribution, p ii and q ii If p is 0, assume that for any i, p ij =p ji q ij =q ji The similarity between data in low-dimensional space is:

[0085]

[0086] The optimized gradient is:

[0087]

[0088] Step 6, Dataset Synthesis:

[0089] After dimensionality reduction, a subset of initial nodes are randomly selected for each group. Then, data sampling is performed based on the selection probability P(i') calculated in the previous step. Unsampled data is selected based on the data similarity q in the low-dimensional space. ij Sampling is performed, and nodes with high similarity to the selected nodes are selected as new initial nodes. The data sampling and selection process in step 6 is repeated based on the new initial nodes until the required amount of data is reached, and a new dataset is synthesized.

[0090] Finally, the above specific embodiments are provided for illustrative purposes only and are not intended to limit the scope of protection of this invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A localized differential privacy protection method based on adaptive high-dimensional data, characterized in that, Specifically, the steps include the following: Step 1: Preprocessing of local data: Rough set theory is used to evaluate the correlation between data and calculate the mutual information between attributes of each group of data. Based on the correlation and mutual information, all data are grouped using clustering methods. Step 2: Develop a probabilistic strategy for random responses. Based on the mutual information between each set of data attributes calculated in the previous step, the probability of random response needs to be set. There are two parts to the probability setting: the first part is the response probability when performing a permanent random response. The second part is the probability of making a temporary random response. and The former represents the probability of negative data flipping into positive data, while the latter represents the probability of positive data remaining unchanged. Similarly, 1- and 1- These represent the probabilities of negative data remaining unchanged and positive data being flipped into negative data, respectively. Step 3: Perform localized differential privacy processing on the data: After selecting the response parameters, localized differential privacy processing is performed on the grouped data in step 1. The binary data is processed into a random response and then stored locally, which is a permanent random response. When the server requests to query the data on the local end, another random response is performed and the data after the response is sent to the server, which is a temporary random response. Step 4: Use the SNE method for dimensionality reduction: The joint probability distribution of high-dimensional data is decomposed into multiple low-dimensional marginal probability distributions, and the joint probability distribution is approximated by inference using multiple marginal probabilities. A probability distribution among high-dimensional objects is constructed using the SNE method, so that similar objects have a higher probability of being selected and dissimilar objects have a lower probability of being selected. SNE then constructs the probability distribution of these points in the low-dimensional space, making the two probability distributions as similar as possible. Step 4 is explained in detail below: On the server side, SNE (Simplified Neural Network) is used to reduce the dimensionality of the data after the temporary random response published in step 3. The SNE method maps data points to a probability distribution through affine transformation, constructing a high-dimensional probability distribution between objects. Similar objects have a higher probability of being selected, while dissimilar objects have a lower probability of being selected. First, the Euclidean distance between data points is converted into conditional probability to express the similarity between points. The similarity between data points mentioned later is also represented using conditional probability. High-dimensional data after a temporary random response , ..., Calculate data and probability distribution between Numerically Proportional to and The similarity between them is used to Centered on a Gaussian distribution, select Conditional probability of being a nearest neighbor to indicate and Similarity between them: in , and The value range is 1 to ,parameter Let the variance be a Gaussian distribution, for different points The values ​​are different, and the similarity of data to itself is set to 0 because only the similarity between data points needs to be considered; Centered on a Gaussian distribution, select Conditional probability of being a nearest neighbor To represent higher-dimensional space and Similarity between them, in addition to setting , for In the data, non- Data points; We then reconstruct the probability distributions of these data in a low-dimensional space, making the two probability distributions as similar as possible. For the low-dimensional data, we establish a Gaussian distribution with variance of... The similarity between low-dimensional spatial data is calculated as follows: Representing low-dimensional space and Similarity between them; when When the similarity of high-dimensional data equals that of low-dimensional data, it indicates that the dimensionality reduction is effective and local features are well preserved. Therefore, the next step is to optimize the KL divergence between the two distributions, with the objective function being: in, Indicates a given point The true conditional probability distribution of other data points under the given circumstances. This represents the corresponding theoretical distribution, where different distances in the low-dimensional mapping correspond to different penalty weights. SNE tends to preserve local features in the data, using the concept of perplexity, i.e., the number of effective nearest neighbors of a point, and employs binary search to find the optimal value. In the initial optimization phase, a certain amount of Gaussian noise is introduced in each iteration. The amount of noise introduced is determined based on the specific data. Then, simulated annealing is used to gradually reduce the noise to avoid getting trapped in local optima. The learning rate and decay time hyperparameters are selected differently depending on the data. Step 5, Adaptive Sampling: Gradient optimization of SNE dimensionality reduction is performed using an adaptive sampling method based on auxiliary information; Step 6: Dataset Synthesis After the data dimensionality reduction is completed, a new dataset is generated and published based on the adaptive sampling probability and the required amount of data.

2. The localized differential privacy protection method based on adaptive high-dimensional data according to claim 1, characterized in that, The Gaussian distribution in the SNE was replaced with a t-distribution for further optimization.

3. The localized differential privacy protection method based on adaptive high-dimensional data according to claim 1 or 2, characterized in that, The specific method for step 1 is as follows: Step 1-1: Calculate the correlation of data based on rough set theory: By employing the concept of attribute dependency in rough set theory, the correlation of data attributes is measured, and the equivalence classes arising from indistinguishable relations for each attribute are obtained. Continuous attribute values ​​are partitioned to become discrete numerical values. Based on the following formula, the universe of discourse is obtained according to each attribute relative to other attributes. Lower and upper approximations of subsets of: In rough set theory, knowledge is represented using information tables or information systems, and an information table can be represented by a quadruple. express, It is a non-empty finite set of objects. It is a non-empty finite set of attributes. Represents attribute set Any subset of , , It is an attribute The range of values, It is an information function that moves from the sample space to the attribute space. express any subset, It is the domain An element on the domain, the equivalence relation in the domain This constitutes a knowledge division, using express, any element This is called an equivalence class. and They represent of Lower approximation and upper approximation; Then, attribute subsets are divided according to the correlation between data. That is, data are grouped according to the correlation between data. Data in the same attribute subset have a high correlation, and vice versa. Steps 1-2: Calculate the sensitivity of the data based on mutual information. Information entropy refers to the average amount of information contained in each piece of received information, while mutual information is a special form of the broader relative information entropy. In information entropy, an equivalence class partition is regarded as a probability distribution within the universe of discourse. The proportion of each equivalence class in the information table is considered as the probability of that equivalence class occurring. , , ,property Information entropy for: in Represents equivalence classes In the domain The proportion of each attribute in the subset is used to calculate the information entropy of each attribute within that subset. Then, the mutual information between each group of data is calculated using the following formula: in Let there be two random variables, and their joint probability distribution be... The corresponding edge distributions are as follows: and mutual information It is a joint probability With marginal distribution The relative entropy; the mutual information between data is used to measure data sensitivity. The greater the mutual information between two data points, the greater the sensitivity between them.

4. The localized differential privacy protection method based on adaptive high-dimensional data according to claim 3, characterized in that, The specific method for step 3 is as follows: Step 3-1: Perform a permanent random response on the grouped data: Each set of data is based on a given probability. The changes will be made according to the following circumstances: The data after the permanent random response is stored locally. When the server sends a query request, the data stored locally is then temporarily randomized and published. Step 3-2: Apply a temporary random response to the data following the permanent random response. For data after a permanent random response Data with a value of 1 are expressed with probability Keep it unchanged, with 1– The probability change is 0. Data with a value of 0 are expressed with probability. Become 1, with 1– The probability remains unchanged, that is: Based on the server's request, the data after completing the temporary random response is published to the server. At this point, the data sent to the server is no longer sent according to the previous groups, but is a dataset sent according to the server's request.

5. The localized differential privacy protection method based on adaptive high-dimensional data according to claim 4, characterized in that, Step 5 is explained in detail below: Based on the method mentioned in step 4, SNE is relatively robust to adjusting the perplexity. A value between 5 and 50 is selected, and then a binary search method is used to find a suitable value. The gradient is solved using the SGD optimization algorithm, and a sample needs to be randomly selected during the update process. The optimization and update process is as follows: For input samples At that time, performance function For parameters The derivative, i.e., the gradient, This is the updated model parameter vector. To define the learning rate, and to avoid the uncertainty of random selection, an adaptive selection method based on auxiliary information is chosen. The auxiliary information received by the server in the data set is Given a set of instances, SGD minimizes the empirical risk as follows: in, A set of auxiliary information attributes for the data. The number of samples in the dataset received by the server. To sample the probability of a single instance from the entire dataset, From The probability of sampling an instance. By setting probability To adjust the optimization process of SGD; After determining the auxiliary information of the dataset, the dataset received by the server is divided into... Group them, and then calculate the selection probability for each group. ,according to Calculate the probability of sampling a single instance. and gradient Finally, the model parameters are calculated and updated. The objective function of SNE exist The gradient of the conditional probability is Similarly exist The conditional probability gradient under is Finally, the complete gradient is obtained: and For data points in low dimension, where , The value range is from 1 to In addition to the current gradient, parameter updates also require the introduction of an exponentially decaying term from the accumulation of previous gradients, as follows: in, Iteration The next solution, Indicates the learning rate. Iteration The momentum of the second time.

6. The localized differential privacy protection method based on adaptive high-dimensional data according to claim 5, characterized in that, In low-dimensional space, the Gaussian distribution in the original SNE is replaced with a t-distribution to represent the similarity between two data points; after using the t-distribution, the joint probability distribution is used to replace the conditional probability distribution, i.e. It is the joint probability distribution of points in a high-dimensional space. It is a joint probability distribution in a low-dimensional space, and the objective function is: in and for and The corresponding joint probability distribution, and =0, for any , , The similarity between data in low-dimensional space is: The optimized gradient is: 。 7. The localized differential privacy protection method based on adaptive high-dimensional data according to claim 5 or 6, characterized in that, Step 6, Dataset Synthesis: After the data dimensionality reduction is completed, a subset of initial nodes are randomly selected in each group, and then the selection probabilities calculated in the previous step are used. Data sampling is performed, and unsampled data is selected based on data similarity in low-dimensional space. Sampling is performed, and nodes with high similarity to the selected nodes are selected as new initial nodes. The data sampling and selection process in step 6 is repeated based on the new initial nodes until the required amount of data is reached, and a new dataset is synthesized.

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