CN112131604A - High-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology - Google Patents

Abstract

The invention relates to a high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology, and compared with the prior art, it solves the defects of large publishing error, poor usability and low efficiency of high-dimensional privacy data by adding noise. The invention includes the following steps: acquisition of high-dimensional data; clustering and division of attribute subsets; building a noise-added Bayesian network; generating a noise-added conditional distribution; and publishing a synthetic data set. Under the high-dimensional big data environment, the present invention can shorten the running time of the data release algorithm while ensuring data privacy, security and availability, and realize the effective release of private data in the high-dimensional big data environment.

Description

High-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology

technical field

The invention relates to the technical field of high-dimensional data privacy processing, in particular to a high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology.

Background technique

With the continuous development and application of information technology, a wealth of data resources have been accumulated in information systems of all walks of life, and these data often contain enormous research value. However, since the original data usually contains many personal private information, publishing it directly will lead to the leakage of sensitive information. Therefore, the data needs to be processed using special privacy protection technology before it is released. Traditional privacy protection technologies (such as k-anonymity, l-diversity, and t-secrecy, etc.) can protect personal privacy to a certain extent, but they are difficult to resist background knowledge attacks and are far from enough to ensure the security of private information. The proposal of differential privacy provides a new solution for privacy publishing, which can quantify the protection strength of data privacy and provide stronger privacy protection for data publishing.

Existing research has made many efforts to release low-dimensional data, but with the advent of the era of big data, high-dimensional data is more common in real life. For high-dimensional data, the direct use of the low-dimensional data publishing method will introduce a huge noise value, which in turn makes the availability of the published results low. Diverse value ranges” etc. Therefore, how to solve the privacy problem of high-dimensional data release and the low availability of data has become a new research focus.

A commonly used approach to solving high-dimensional data publishing problems is dimensionality reduction. First, reduce the dimensionality of the data to obtain low-dimensional data, add noise to the converted low-dimensional data set, and then generate a new data set for publication. Qardaji et al. (see literature Qardaji WH, Yang Weining, Li Ninghui.Priview:Practical differentially private release of marginal contingency tables[C].Proc of the 2014ACM SIGMOD Int Confon Management of Data.New York:ACM, 2014:1435-1446) The proposed Priview method estimates the joint distribution of high-dimensional data by constructing a K-way marginal distribution of attribute pairs. Day et al (see the literature Day WY, LiNingHui. Differentially Private publishing of high-dimensional data Release using sensitivity control [C]. Proc of the 10th ACM Symp on Information, Computer and Communication Security ( ^ASIACCS 2015). New York: ACM, 2015 , 451-462) proposed a differential privacy publishing method based on threshold filtering technology, which achieved the purpose of limiting the sensitivity range by constructing a low-sensitivity quality function.

However, the above methods do not take into account the dependencies between attributes, so researchers further perform dimensionality reduction processing based on the correlation between attributes, such as Xu et al. (see the literature Xu C, Ren J, Zhang Y, et al. DPPro:Differentially Private High-Dimensional Data Release via Random Projection[J].IEEE Transactions on Information Forensics and Security,2017:1-1.) designed a high-dimensional data release algorithm based on random projection technology, which can generate high-dimensional data A synthetic dataset with similar squared Euclidean distances between vectors as the original dataset achieves differential privacy. There are also studies on the mining of data dimensional correlations by constructing probability maps, Zhang et al. (see Zhang Jun, Cormode G, Procopiuc C M, et al. The PrivBayes method proposed by Conf On Management of Data. New York: ACM, 2014: 1423-1434.) uses a Bayesian network based on an exponential mechanism to infer the correlation between attributes, so as to obtain a model that can reflect the inherent characteristics of high-dimensional data. low-dimensional datasets. Chen et al. (see literature Chen Rui, Xiao Qian, Zhang Yu, et al. Differentially private high-dimension data publication via sample-based inference [C]. Proc of the 21st ACM SIGMOD Int Conf On Knowledge Discovery and Data Mining. New York: The JTree method proposed by ACM, 2015: 129-138.) utilizes Markov network to build a joint tree to deal with the problem of high-dimensional data publishing.

When constructing a probability map based on the correlation between attributes for dimensionality reduction processing, the key step required is to discriminate the correlation between two attributes. However, when there are many attribute pairs, it means that the limited privacy budget needs to be divided multiple times, which is bound to cause a lot of noise, and the higher the data dimension, the more complex the resulting network structure, resulting in a super-exponential growth of expressions. The algorithm running time is also greatly increased.

That is, the traditional Bayesian network directly constructs a Bayesian network for all attributes. In this way, the AP pair of attributes is too large in candidate space and the privacy budget is divided many times. Adding noise will greatly reduce the selection accuracy of the index mechanism, which will eventually lead to The availability of the algorithm is low, and in the high-dimensional attribute environment, the running time of the algorithm increases exponentially with the increase of the number of nodes.

Therefore, how to achieve effective and feasible privacy data release for high-dimensional data has become a technical problem that needs to be solved urgently.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the defects of high-dimensional privacy data with large publishing error, poor usability and low efficiency, and to provide a high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology to solve the above problems .

In order to achieve the above object, technical scheme of the present invention is as follows:

The high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology includes the following steps:

11) Acquisition of high-dimensional data: acquire the high-dimensional data to be published to form the original data set D, and perform attribute induction on the high-dimensional data to form a high-dimensional data attribute set;

12) Clustering division of attribute subsets: By calculating the correlation between high-dimensional data attributes, the high-dimensional attribute set is divided into c attribute subsets by attribute clustering method, and then the original data set D is divided according to the attribute subsets. Divide into c data subsets D _i (i=1,..,c);

使构建的每个贝叶斯网络满足ε_1i的差分隐私；13) Constructing a Noisy Bayesian Network: Use a greedy Bayesian method to construct a Noisy Bayesian network N _i ( _i =1,.. ,c), where the allocated total privacy budget is ε ₁ , and each data subset allocates a privacy budget according to the proportion of the number of attributes it has to the total number of attributes owned by c attribute subset clusters

Make each Bayesian network constructed to satisfy the differential privacy of ε _1i ;

使构建的每个条件概率分布满足ε_2i的差分隐私；ε₁与ε₂之和等于给定的总隐私预算ε，即ε＝ε₁+ε₂，使得整个数据发布过程满足ε的差分隐私；14) Generate noise conditional distribution: For each Bayesian network N _i , calculate its joint probability distribution Pr[V _i ,∏ _i ] and add noise to obtain Pr ^* [V _i ,∏ _i ], and then calculate the noise added Conditional probability distribution Pr ^* [V _i |∏ _i ], where the total privacy budget allocated is ε ₂ , and each Bayesian network accounts for the proportion of the total number of attribute nodes owned by c Bayesian networks according to the number of attribute nodes Allocate a privacy budget

Make each conditional probability distribution constructed to satisfy the differential privacy of ε _2i ; the sum of ε ₁ and ε ₂ is equal to the given total privacy budget ε, that is, ε = ε ₁ +ε ₂ , so that the entire data publishing process satisfies the differential privacy of ε ;

15) Release of synthetic datasets: For c data subsets, each attribute is sequentially sampled in increasing order of i according to its Bayesian network N _i and noise-added conditional distribution Pr ^* [V _i |∏ _i ] to generate perturbations Data set D _i ^* (i=1,..,c), according to which a synthetic data set D ^* is generated. The synthetic data set D ^* is high-dimensional private data, and the high-dimensional private data is finally released.

The clustering division of the attribute subset includes the following steps:

21) For the high-dimensional data set, calculate the correlation between the attributes of the high-dimensional data, and the calculation method is as follows:

Given any two properties V _i and V _j , the relative dependencies between the properties are expressed as

Among them, I represents the mutual information between two attributes, and H represents the joint entropy value between the two attributes; for any attribute V _i , the sum of its relationship to other attributes is expressed as

22) randomly select c attributes as central attributes, where c is the number of attribute subsets;

计算V_i与各中心属性之间的相对依赖关系，并将其分配给依赖值最大的中心属性C_r所在子集簇，重复此步骤直至分配完所有属性；23) For

Calculate the relative dependency between _Vi and each central attribute, and assign it to the subset cluster where the central attribute C _r with the largest dependency value is located, and repeat this step until all attributes are allocated;

24) Update the central attribute. For each attribute subset, if the sum of the relationship between attribute _Vi and other attributes is greater than the sum of the relationship between the central attribute and other attributes, that is, MR(V _i )≥MR(V _j )(V _j ∈ C _r , j≠ _i ), then set Vi as the new C _r ;

25) Repeat steps 23) and 24) until the c central attributes remain unchanged, or when the number of iterations reaches a preset value, terminate the iteration to obtain c attribute subsets, and then obtain c data subsets D _i (i =1,..,c).

The construction of the noisy Bayesian network includes the following steps:

已选取属性节点集合S为

A为数据集属性数列；31) Initialization: Initialize the Bayesian network N to be

The selected attribute node set S is

A is the data set attribute sequence;

添加到N；32) Initial node selection: randomly select an attribute V ₁ as the initial node of the Bayesian network, add V ₁ to the set S, and pair the attribute-parent node set AP

add to N;

对于

和

将(V,∏)存入AP对候选集Ω中，其中k为贝叶斯网络的度；33) AP pair candidate set enumeration: Initialize AP pair candidate set Ω as

for

and

Store (V,∏) in the AP pair candidate set Ω, where k is the degree of the Bayesian network;

34) AP pair score solution: Use function F as the score function to calculate the score F(V,∏) of all AP pairs in Ω. The solution formula is as follows:

where P°[V, Π] is the set of all maximal joint distributions of AP pair (V, Π);

35) AP pair selection: select AP pair (V _i , ∏ _i ) to add to network N based on the index mechanism, and add V _i to S; its expression is as follows:

成比例，其中，△F为评分函数的全局敏感性，

n＝|D|；such that the sampling probability of picking an AP pair from Ω is the same as

is proportional to , where ΔF is the global sensitivity of the scoring function,

n=|D|;

36) Bayesian network update: Repeat the process of steps 33) to 35) for all attributes in A except V ₁ , until all attribute nodes are selected in sequence, that is, a complete Bayesian network N is obtained.

The generating the noise-added conditional distribution includes the following steps:

41) Initialization: initialize the noise-added conditional distribution set P ^* ;

42) Noise-added joint distribution generation:

Calculate the original joint distribution Pr[V _i ,∏ _i ] according to the Bayesian network _Ni ,

得到加噪的联合分布Pr^*[V_i,∏_i]，将Pr^*[V_i,∏_i]中的负值设置为0，进行标准化；Add Laplace Noise

Obtain the noise-added joint distribution Pr ^* [V _i ,∏ _i ], set the negative value in Pr ^* [V _i ,∏ _i ] to 0 for standardization;

43) Noise-added conditional distribution generation:

基于Pr^*[V_i,∏_i]计算得到Pr^*[V_k+1|∏_k+1],...,Pr^*[V_d|∏_d]，将其加入加噪条件分布集P^*；for

Calculated based on Pr ^* [V _i ,∏ _i ], Pr ^* [V _k+1 |∏ _k+1 ],...,Pr ^* [V _d |∏ _d ] was added to the noise condition distribution set P ^* ;

基于Pr^*[V_k+1,∏_k+1]计算得到Pr^*[V₁|∏₁],...,Pr^*[V_k|∏_k]，将其加入加噪条件分布集P^*。for

Based on Pr ^* [V _k+1 ,∏ _k+1 ], Pr ^* [V ₁ |∏ ₁ ],...,Pr ^* [V _k |∏ _k ] is calculated and added to the noise condition distribution set P ^* .

beneficial effect

Compared with the prior art, the method for publishing high-dimensional privacy data based on the Bayesian network attribute clustering analysis technology of the present invention can ensure the security and availability of data privacy, shorten the running time of the data publishing algorithm, and realize high-dimensional and large-scale data. Effective publication of private data in a data environment.

The invention preserves the correlation between the data by exploiting the dimensional correlation, and ensures that the synthetic data set and the original data set have the probability distribution and statistical characteristics as similar as possible; The attribute subset cluster can reduce the number of divisions of the privacy budget and shorten the running time of the program to generate the Bayesian network; considering that the divided low-dimensional attribute subsets are relatively independent, when the dimension of the original data set is high, it can be Applying the MapReduce programming model to the construction of Bayesian networks and perturbed datasets can effectively solve the problem of computational efficiency in the big data environment.

Description of drawings

Fig. 1 is the method sequence diagram of the present invention;

Fig. 2 is the algorithm flow frame diagram involved in the present invention;

Fig. 3 (a) is the SVM (money) classification result under the NLTCS data set of the present invention;

Fig. 3 (b) is the SVM (bathing) classification result under the NLTCS data set of the present invention;

Fig. 3 (c) is the SVM (traveling) classification result under the NLTCS data set of the present invention;

Fig. 4 (a) is the SVM (mortgage) classification result under the ACS data set of the present invention;

Figure 4(b) is the SVM (multi-gen) classification result under the ACS data set of the present invention;

Fig. 4 (c) is the SVM (school) classification result under the ACS data set of the present invention;

Fig. 5 (a) is SVM (gender) classification result under the Adult data set of the present invention;

Fig. 5 (b) is the SVM (martial) classification result under the Adult data set of the present invention;

Fig. 5 (c) is the SVM (education) classification result under the Adult data set of the present invention;

Figure 6(a) is the comparison of the running time of the method of the present invention and the PrivBayes method when K=2;

Figure 6(b) is a comparison diagram of the running time of the method of the present invention and the PrivBayes method when K=3.

Detailed ways

In order to have a further understanding and understanding of the structural features of the present invention and the effects achieved, the preferred embodiments and accompanying drawings are used in conjunction with detailed descriptions, and the descriptions are as follows:

As shown in Figure 1 and Figure 2, a high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology according to the present invention includes the following steps:

The first step is to acquire high-dimensional data: acquire the high-dimensional data to be published, perform attribute induction on the high-dimensional data, and form a high-dimensional data attribute set.

The second step is the clustering of attribute subsets: by calculating the correlation between the attributes of the high-dimensional data, the high-dimensional attribute set is divided into c attribute subsets by the attribute clustering method, and then the original data is divided according to the attribute subsets. Set D is divided into c data subsets D _i (i=1, .., c). When building a noisy Bayesian network, the increase of attribute nodes will cause a sharp decrease in the privacy budget, which seriously affects the availability of data publishing. By defining the relationship function, the interdependence between attributes is measured and obtained, and the idea of K-means clustering algorithm is applied to divide the attribute subset clusters, which can explore the interdependence between attributes in advance and reduce the selection range of attribute pairs. Therefore, the present invention combines the attribute clustering algorithm with the construction of a noisy Bayesian network for high-dimensional private data release, which effectively ensures the availability of the high-dimensional data release results and improves the algorithm operation efficiency in a big data environment. The specific steps are as follows:

(1) For high-dimensional data sets, calculate the correlation between high-dimensional data attributes, and the calculation method is as follows:

Given any two properties V _i and V _j , the relative dependencies between the properties are expressed as

Among them, I represents the mutual information between two attributes, and H represents the joint entropy value between the two attributes; for any attribute V _i , the sum of its relationship to other attributes is expressed as

(2) randomly select c attributes as central attributes, where c is the number of attribute subsets;

计算V_i与各中心属性之间的相对依赖关系，并将其分配给依赖值最大的中心属性C_r所在子集簇，重复此步骤直至分配完所有属性；(3) For

Calculate the relative dependency between _Vi and each central attribute, and assign it to the subset cluster where the central attribute C _r with the largest dependency value is located, and repeat this step until all attributes are allocated;

(4) Update the central attribute. For each attribute subset, if the sum of the relationship between attribute _Vi and other attributes is greater than the sum of the relationship between the central attribute and other attributes, that is, MR(V _i )≥MR(V _j )(V _j ∈C _r , j≠ _i ), then set Vi as the new C _r ;

(5) Repeat the above steps (3) and (4) until the c central attributes remain unchanged, or when the number of iterations reaches a preset value, terminate the iteration, obtain c attribute subsets, and then obtain c data subsets D _i (i=1,..,c).

使构建的每个贝叶斯网络满足ε_1i的差分隐私。The third step is to construct a noisy Bayesian network. Construct a noisy Bayesian network _Ni (i=1,..,c) using a greedy Bayesian method on the resulting data subset D _i (i=1,..,c), where the total privacy of the assignment The budget is ε ₁ , and each data subset allocates a privacy budget according to the proportion of the number of attributes it has to the total number of attributes owned by c attribute subset clusters

Make each Bayesian network constructed to satisfy differential privacy of ε _1i .

Bayesian network uses the conditional probability between attribute nodes to represent the degree of dependence between nodes, and can better maintain the consistency and integrity of the probability between attributes during dimension reduction. For each attribute subset cluster, there is a high degree of interdependence among the attributes within the group, and the inter-attribute correlation can be further exploited by constructing a Bayesian network. The specific steps are as follows:

已选取属性节点集合S为

A为数据集属性数列；(1) Initialization: Initialize the Bayesian network N to be

The selected attribute node set S is

A is the data set attribute sequence;

添加到N；(2) Initial node selection: randomly select an attribute V ₁ as the initial node of the Bayesian network, add V ₁ to the set S, and connect AP to

add to N;

对于

和

将(V,∏)存入AP对候选集Ω中，其中k为贝叶斯网络的度；(3) AP pair candidate set enumeration: Initialize AP pair candidate set Ω as

for

and

Store (V,∏) in the AP pair candidate set Ω, where k is the degree of the Bayesian network;

(4) AP pair score solution: Use the function F as the score function to calculate the score F(V,∏) of all AP pairs in Ω. The solution formula is as follows:

where P°[V, Π] is the set of all maximal joint distributions of AP pair (V, Π);

(5) AP pair selection: select AP pair (V _i , ∏ _i ) to add to network N based on the index mechanism, and add V _i to S; its expression is as follows:

成比例，其中，△F为评分函数的全局敏感性，

n＝|D|；such that the sampling probability of picking an AP pair from Ω is the same as

is proportional to , where ΔF is the global sensitivity of the scoring function,

n=|D|;

(6) Bayesian network update: Repeat the above steps (3) to (5) for all attributes in A except V ₁ , until all attribute nodes are selected in turn, that is, a complete Bayesian network N is obtained.

来分配隐私预算，使构建的每个条件概率分布满足ε_2i的差分隐私；ε₁与ε₂之和等于给定的总隐私预算ε，即ε＝ε₁+ε₂，使得整个数据发布过程满足ε的差分隐私。其具体步骤如下：The fourth step is to generate the noise condition distribution. For each Bayesian network N _i , calculate its joint probability distribution Pr[V _i ,∏ _i ] and add noise to obtain Pr ^* [V _i ,∏ _i ], then calculate the noise conditional probability distribution Pr ^* [V _i |∏ _i ], where the total privacy budget allocated is ε ₂ , according to

to allocate the privacy budget, so that each conditional probability distribution constructed satisfies the differential privacy of ε _2i ; the sum of ε ₁ and ε ₂ is equal to the given total privacy budget ε, that is, ε = ε ₁ +ε ₂ , so that the entire data publishing process Differential privacy that satisfies ε. The specific steps are as follows:

(1) Initialization: Initialize the noise-added conditional distribution set P ^* ;

(2) Noise-added joint distribution generation:

Calculate the original joint distribution Pr[V _i ,∏ _i ] according to the Bayesian network _Ni ,

得到加噪的联合分布Pr^*[V_i,∏_i]，将Pr^*[V_i,∏_i]中的负值设置为0，进行标准化；Add Laplace Noise

Obtain the noise-added joint distribution Pr ^* [V _i ,∏ _i ], set the negative value in Pr ^* [V _i ,∏ _i ] to 0 for standardization;

(3) The noise-added conditional distribution is generated:

基于Pr^*[V_i,∏_i]计算得到Pr^*[V_k+1|∏_k+1],...,Pr^*[V_d|∏_d]，将其加入加噪条件分布集P^*；for

Calculated based on Pr ^* [V _i ,∏ _i ], Pr ^* [V _k+1 |∏ _k+1 ],...,Pr ^* [V _d |∏ _d ] was added to the noise condition distribution set P ^* ;

基于Pr^*[V_k+1,∏_k+1]计算得到Pr^*[V₁|∏₁],...,Pr^*[V_k|∏_k]，将其加入加噪条件分布集P^*。for

Based on Pr ^* [V _k+1 ,∏ _k+1 ], Pr ^* [V ₁ |∏ ₁ ],...,Pr ^* [V _k |∏ _k ] is calculated and added to the noise condition distribution set P ^* .

根据此生成合成数据集D^*，合成数据集D^*即为高维隐私数据，最终将高维隐私数据进行发布。The fifth step, the release of synthetic datasets: For c data subsets, each attribute is sampled sequentially in increasing order of i according to its Bayesian network N _i and the noisy conditional distribution Pr ^* [V _i |∏ _i ], Generate a perturbed dataset

According to this, a synthetic dataset D ^* is generated, and the synthetic dataset D ^* is high-dimensional private data, and the high-dimensional private data is finally released.

In order to verify the effectiveness and operation efficiency of the method of the present invention, the following will use specific experiments on real data sets to verify and illustrate. Experimental environment: Windows10 operating system, Intel(R) Core(TM) i5-6200CPU (2.30GHz), 12GB memory. The algorithm codes involved are implemented in Python and Java languages.

Experimental data: The three datasets NLTCS, ACS, and Adult used in the experiment are widely used in high-dimensional data publishing. The NLTCS dataset is derived from the American Nursing Survey Center and contains 21,574 records from the Nursing Survey of Persons with Disabilities; the ACS dataset is derived from the ACS sample set of IPUUMUSA and contains 47,461 rows of personal information obtained from 2013 and 2014; the Adult dataset Sourced from the U.S. Census Center and contains 45,222 pieces of personal information. The specific details of the three datasets are shown in Table 1:

Table 1 Data set information description comparison table

Referring to Figures 3(a)-(c), 4(a)-(c), and 5(a)-(c), respectively, on the three data sets of NLTCS, ACS, and Adult, the method of the present invention and Comparison of the average misclassification rate of PrivBayes method, NoPrivacy method, Laplace noise addition method and Majority method on the SVM classification task based on the change of parameter ε.

On the NLTCS dataset, predictions are made based on (1) whether it can manage money; (2) whether it can swim; (3) whether it can travel as a classification attribute. On the ACS dataset, predictions are made using (1) whether to own a mortgage; (2) whether to live in a multi-generational family; (3) whether to go to school. On the Adult dataset, predictions are made based on (1) whether he is male; (2) whether he is married; (3) whether he has a college degree or not.

From Fig. 3, Fig. 4 and Fig. 5, it can be found that compared with the PrivBayes method, the attribute misclassification rate of the method of the present invention in different data sets has been improved, and is better than the Laplace noise addition method and the Majority method to a large extent, This shows that the method of the present invention can effectively ensure the release of data privacy information, and at the same time, the utility of the data set is also improved.

Referring to Fig. 6(a)-(b), we show the comparison of the running time between the method of the present invention and the PrivBayes method when the degree of Bayesian network is k=2, k=3 on the three data sets of NLTCS, ACS, and Adult respectively (due to The value of 3600 is too large, and Figure 6(b) here provides a truncated image). It can be seen from the figure that the running time of the method of the present invention is roughly equal to that of the PrivBayes method when the dimension of the data set is small, but as the dimension of the data set increases, the running time of the method of the present invention is shorter than that of the PrivBayes method, as shown in Figure 6(a) Among them, the PrivBayes method on the Adult dataset is about 4 times that of the method of the present invention. In addition, as the Bayesian network degree k increases, the efficiency of shortening the running time of the method of the present invention is more significant, which shows the effectiveness of the running efficiency of the method of the present invention in a high-dimensional big data environment. And when the dimension of the data set is higher, the MapReduce parallel programming mode can be used on the framework constructed by the method of the present invention, thereby further shortening the data publishing time.

Under the background of high-dimensional data release, the present invention proposes a differential privacy high-dimensional data release method based on attribute clustering Bayesian network. First, attribute clustering is performed to obtain each data subset, and then a Bayesian network that satisfies differential privacy is constructed based on the exponential mechanism, and each attribute is sequentially sampled according to the Bayesian network and the noise-added conditional distribution to obtain the perturbed data set, and finally a new The dataset is published. By carrying out experiments on real data sets, the usability and operation efficiency of the method of the present invention are verified from two aspects of SVM misclassification rate and algorithm running time.

The foregoing has shown and described the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited by the above-mentioned embodiments. The above-mentioned embodiments and descriptions describe only the principles of the present invention. Without departing from the spirit and scope of the present invention, there are various Variations and improvements are intended to fall within the scope of the claimed invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims (4)

1. a high-dimensional privacy data publishing method based on Bayesian network attribute cluster analysis technology, is characterized in that, comprises the following steps: 11) Acquisition of high-dimensional data: acquire the high-dimensional data to be published to form the original data set D, and perform attribute induction on the high-dimensional data to form a high-dimensional data attribute set; 12) Clustering division of attribute subsets: By calculating the correlation between high-dimensional data attributes, the high-dimensional attribute set is divided into c attribute subsets by attribute clustering method, and then the original data set D is divided according to the attribute subsets. Divide into c data subsets D _i (i=1,..,c); 13) Constructing a Noisy Bayesian Network: Use a greedy Bayesian method to construct a Noisy Bayesian network N _i ( _i =1,.. ,c), where the allocated total privacy budget is ε ₁ , and each data subset allocates a privacy budget according to the proportion of the number of attributes it has to the total number of attributes owned by c attribute subset clusters

Make each Bayesian network constructed to satisfy the differential privacy of ε _1i ; 14) Generate noise conditional distribution: For each Bayesian network N _i , calculate its joint probability distribution Pr[V _i ,∏ _i ] and add noise to obtain Pr ^* [V _i ,∏ _i ], and then calculate the noise added Conditional probability distribution Pr ^* [V _i |∏ _i ], where the total privacy budget allocated is ε ₂ , and each Bayesian network accounts for the proportion of the total number of attribute nodes owned by c Bayesian networks according to the number of attribute nodes Allocate a privacy budget

Make each conditional probability distribution constructed to satisfy the differential privacy of ε _2i ; the sum of ε ₁ and ε ₂ is equal to the given total privacy budget ε, that is, ε = ε ₁ +ε ₂ , so that the entire data publishing process satisfies the differential privacy of ε ; 15) Release of synthetic datasets: For c data subsets, each attribute is sequentially sampled in increasing order of i according to its Bayesian network N _i and noise-added conditional distribution Pr ^* [V _i |∏ _i ] to generate perturbations data set

According to this, a synthetic dataset D ^* is generated, and the synthetic dataset D ^* is high-dimensional private data, and the high-dimensional private data is finally released. 2. the high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology according to claim 1, is characterized in that, the clustering division of described attribute subset comprises the following steps: 21) For the high-dimensional data set, calculate the correlation between the attributes of the high-dimensional data, and the calculation method is as follows: Given any two properties V _i and V _j , the relative dependencies between the properties are expressed as

Among them, I represents the mutual information between two attributes, and H represents the joint entropy value between the two attributes; for any attribute V _i , the sum of its relationship to other attributes is expressed as

22) randomly select c attributes as central attributes, where c is the number of attribute subsets; 23) For

Calculate the relative dependency between _Vi and each central attribute, and assign it to the subset cluster where the central attribute C _r with the largest dependency value is located, and repeat this step until all attributes are allocated; 24) Update the central attribute. For each attribute subset, if the sum of the relationship between attribute _Vi and other attributes is greater than the sum of the relationship between the central attribute and other attributes, that is, MR(V _i )≥MR(V _j )(V _j ∈ C _r , j≠ _i ), then set Vi as the new C _r ; 25) Repeat steps 23) and 24) until the c central attributes remain unchanged, or when the number of iterations reaches a preset value, terminate the iteration to obtain c attribute subsets, and then obtain c data subsets D _i (i =1,..,c). 3. the high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology according to claim 1, is characterized in that, described constructing noise Bayesian network comprises the following steps: 31) Initialization: Initialize the Bayesian network N to be

The selected attribute node set S is

A is the data set attribute sequence; 32) Initial node selection: randomly select an attribute V ₁ as the initial node of the Bayesian network, add V ₁ to the set S, and pair the attribute-parent node set AP

add to N; 33) AP pair candidate set enumeration: Initialize AP pair candidate set Ω as

for

and

Store (V,∏) in the AP pair candidate set Ω, where k is the degree of the Bayesian network; 34) AP pair score solution: Use function F as the score function to calculate the score F(V,∏) of all AP pairs in Ω. The solution formula is as follows:

where P°[V, Π] is the set of all maximal joint distributions of AP pair (V, Π); 35) AP pair selection: select AP pair (V _i , ∏ _i ) to add to network N based on the index mechanism, and add V _i to S; its expression is as follows:

such that the sampling probability of picking an AP pair from Ω is the same as

is proportional to , where ΔF is the global sensitivity of the scoring function,

36) Bayesian network update: Repeat the process of steps 33) to 35) for all attributes in A except V ₁ , until all attribute nodes are selected in sequence, that is, a complete Bayesian network N is obtained. 4. The high-dimensional privacy data publishing method based on Bayesian network attribute clustering analysis technology according to claim 1, wherein the generating the noise-added conditional distribution comprises the following steps: 41) Initialization: initialize the noise-added conditional distribution set P ^* ; 42) Noise-added joint distribution generation: Calculate the original joint distribution Pr[V _i ,∏ _i ] according to the Bayesian network _Ni , Add Laplace Noise

Obtain the noise-added joint distribution Pr ^* [V _i ,∏ _i ], set the negative value in Pr ^* [V _i ,∏ _i ] to 0 for standardization; 43) Noise-added conditional distribution generation: for

Calculated based on Pr ^* [V _i ,∏ _i ], Pr ^* [V _k+1 |∏ _k+1 ],...,Pr ^* [V _d |∏ _d ] was added to the noise condition distribution set P ^* ; for

Based on Pr ^* [V _k+1 ,∏ _k+1 ], Pr ^* [V ₁ |∏ ₁ ],...,Pr ^* [V _k |∏ _k ] is calculated and added to the noise condition distribution set P ^* .

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