Graph data privacy protection method and device based on subgraph simplification
By performing noise processing and sub-graph simplification on graph data, the problem that sub-graph counting methods in the prior art is difficult to take into account accuracy, efficiency and privacy protection, and efficient and low-overhead graph data privacy protection is achieved.
Patent Information
- Application Number
- CN202411799346.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-09
- Publication Date
- 2025-05-13
AI Technical Summary
In the prior art In the privacy protection of graph data, sub-graph counting methods are difficult to take into account the estimation accuracy, operation efficiency, and communication overhead, and require users to participate in synchronization.
By simplifying the sub-graph, the two-part graphs are subjected to noise processing, and the number of common neighbor nodes is determined as the unbiased estimate of the simple sub-graph, and the number of butterflies is used to calculate the sub-graph count of the complex sub-graph.
It improves the estimation accuracy and operation efficiency of sub-graph counting, reduces communication overhead, and avoids the problem of user synchronization, and realizes effective privacy protection for user graph data.
Smart Images
Figure CN119989394A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of differential privacy and subgraph statistical technology, and in particular to a graph data privacy protection method and device based on subgraph simplification. Background Art
[0002] In the era of big data, data collection, sharing and analysis have become the norm, and mining valuable information from data is an important topic. As a basic task of graph data analysis, subgraph counting can play a role in downstream tasks such as recommendation systems, link prediction, and clustering coefficient calculation. It is of practical significance to perform various subgraph counting in different types of graph data. In the statistical process, subgraph counting of graph data usually contains private information, including but not limited to users' purchase records, sensitive relationships, etc. Unprotected collection and publication of subgraph counting will infringe on users' privacy. How to collect data and perform subgraph counting while protecting user privacy is an important issue. In terms of privacy protection, Differential Privacy (DP) is widely recognized as a powerful standard for privacy protection, which can provide quantitative privacy protection without assuming prior knowledge of attackers. Among them, Local Differential Privacy (LDP) can provide privacy protection in the data collection stage.
[0003] In the prior art, interactive subgraph counting methods can usually achieve higher calculation accuracy, but users not only need to download noise subgraphs from the server, resulting in large communication overhead, but also need to wait for the server's response, resulting in user synchronization problems. The estimation accuracy of non-interactive subgraph counting methods is limited by the noise addition mechanism and the correction mechanism. The introduction of excessive noise will lead to insufficient estimation accuracy of subgraph counts, and node sampling to avoid the introduction of excessive noise will also lead to insufficient estimation accuracy. Secondly, the operating efficiency of the method is limited by the noise addition mechanism and the correction mechanism. The noisy graph data is very dense, and subgraph matching in a dense noise graph leads to insufficient operating efficiency, which is not suitable for large-scale graphs. Summary of the invention
[0004] The present invention provides a graph data privacy protection method and device based on subgraph simplification, which are used to solve the problem that the subgraph counting method cannot achieve estimation accuracy, operation efficiency and communication overhead when protecting user graph data privacy in the prior art, and also requires user participation in synchronization.
[0005] The present invention provides a graph data privacy protection method based on subgraph simplification, the method comprising the following steps: Determine the privacy budget combination value according to the average node degree of the first node in the bipartite graph to be estimated; Based on the privacy budget combination value, respectively perform noise processing on the node degree of the first node and the neighbor node vector of the first node to obtain a noisy bipartite graph; Determine the number of common neighbor nodes between any two first nodes in the bipartite graph to be estimated, and determine a first unbiased estimate of the noisy bipartite graph for a simple subgraph according to the number of common neighbor nodes; An unbiased estimate is made of the number of butterflies corresponding to the number of common neighbor nodes according to the variance value of the first unbiased estimate to obtain the number of butterflies for the complex subgraph in the bipartite graph to be estimated. The number of butterflies corresponding to the number of common neighbor nodes is the number of combinations of any two nodes selected from the common neighbor nodes. The number of butterflies in the bipartite graph to be estimated is the subgraph count corresponding to the graph data that needs to be privacy protected in the bipartite graph to be estimated.
[0006] In some embodiments, determining the privacy budget combination value according to the average node degree of the first node in the bipartite graph to be estimated includes: Acquire an initial privacy budget value, where the initial privacy budget value is the sum of the first privacy budget value and the second privacy budget value; Determine a random response probability of an average node degree according to the second privacy budget value; Constructing a noise-added variance function of a first node in the bipartite graph to be estimated based on the first privacy budget value, the average node degree, and the random response probability; A privacy budget combination value is constructed according to the first privacy budget value and the second privacy budget value when the noise variance function obtains a minimum value.
[0007] In some embodiments, the bipartite graph to be estimated further includes a second node, and determining a first unbiased estimate of the noisy bipartite graph for a simple subgraph according to the number of the common neighbor nodes includes: For any two first nodes in the bipartite graph to be estimated, determining a neighbor relationship between the second node and the two first nodes in the noisy bipartite graph; Determine the number of the second nodes in each neighbor relationship according to the number of the common neighbor nodes, and determine the corresponding probability of occurrence of the number in the noise bipartite graph; Under each neighbor relationship, the product of the occurrence probability and the quantity is determined as the expected value of the number of the second node corresponding to the noisy bipartite graph: The expected values of the number under each neighbor relationship are summed, and the first unbiased estimate of the noisy bipartite graph for the simple subgraph is calculated based on the summed result.
[0008] In some embodiments, the neighbor relationship between the second node and the two first nodes in the noisy bipartite graph includes: The second node is a common neighbor node of the two first nodes; The second node is a neighbor node of any one of the two first nodes; The second node is not a neighbor node of any one of the two first nodes.
[0009] In some embodiments, performing an unbiased estimation on the number of butterflies corresponding to the number of common neighbor nodes according to the variance value of the first unbiased estimate to obtain the number of butterflies of the bipartite graph to be estimated for the complex subgraph includes: The difference between the number of butterflies corresponding to the number of common neighbor nodes and the variance value of the first unbiased estimate is used as a second unbiased estimate of the complex subgraph corresponding to any two first nodes in the bipartite graph to be estimated; The second unbiased estimation values corresponding to any two first nodes in the bipartite graph to be estimated are counted to obtain the number of butterflies of the bipartite graph to be estimated for the complex subgraph.
[0010] In some embodiments, the variance value of the first unbiased estimate is determined by: Determining the node degree variance of any two first nodes in the first unbiased estimate; Under each neighbor relationship, determining a corresponding number variance according to the number of occurrences of the second node in the noisy bipartite graph, wherein the neighbor relationship is an adjacent relationship between the second node and any two first nodes in the bipartite graph to be estimated; The node degree variance is summed with the number variance under each neighbor relationship to obtain the variance value of the first unbiased estimate.
[0011] The present invention also provides a graph data privacy protection device based on subgraph simplification, the device comprising the following modules: A determination module, used to determine a privacy budget combination value according to an average node degree of the first node in the bipartite graph to be estimated; A noise adding module, used for performing noise adding processing on the average node degree and the neighbor nodes of the first node respectively based on the privacy budget combination value to obtain a noisy bipartite graph; An estimation module, configured to determine the number of common neighbor nodes between any two first nodes in the bipartite graph to be estimated, and determine a first unbiased estimation value of the noisy bipartite graph for a simple subgraph according to the number of common neighbor nodes; A counting module is used to perform an unbiased estimate on the number of butterflies corresponding to the number of common neighbor nodes according to the variance value of the first unbiased estimate, and obtain the number of butterflies for the complex subgraph of the bipartite graph to be estimated, the number of butterflies corresponding to the number of common neighbor nodes is the number of combinations of any two nodes selected from the common neighbor nodes, and the number of butterflies of the bipartite graph to be estimated is the subgraph count corresponding to the graph data that needs to be privacy protected in the bipartite graph to be estimated.
[0012] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for protecting graph data privacy based on subgraph simplification as described above is implemented.
[0013] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the graph data privacy protection methods based on subgraph simplification as described above.
[0014] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements any of the above-mentioned graph data privacy protection methods based on subgraph simplification.
[0015] The graph data privacy protection method and device based on subgraph simplification provided by the present invention add noise to the estimated bipartite graph through a privacy budget, and determine the number of common neighbor nodes between two first nodes in the noisy bipartite graph as the number of simple subgraphs, and determine the number of combinations of two nodes arbitrarily selected from the common neighbor nodes as the number of butterflies, as the number of complex subgraphs. Finally, the unbiased estimate of the simple subgraph is used to calculate the unbiased estimate of the number of butterflies, thereby realizing the subgraph counting of the complex subgraph in the estimated bipartite graph. Compared with the prior art, it can have the advantages of estimation accuracy, operation efficiency, and low communication overhead, and the privacy protection process does not require user synchronization. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced one by one below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0017] Figure 1 It is a flowchart of the graph data privacy protection method based on subgraph simplification provided by the present invention.
[0018] Figure 2 It is a schematic diagram of a butterfly-shaped graph in a bipartite graph provided by the present invention.
[0019] Figure 3 It is a structural schematic diagram of the graph data privacy protection device based on subgraph simplification provided by the present invention.
[0020] Figure 4 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION
[0021] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0022] The graph data privacy protection method based on subgraph simplification provided by the present invention can be applied to downstream tasks such as recommendation systems, link prediction, clustering coefficient calculation, etc., and can be specifically deployed in a server or terminal that executes the corresponding downstream tasks, and is used to count subgraphs of the user's graph data to protect the user's privacy information. Subgraph counts usually contain privacy information, including but not limited to the user's purchase records, sensitive relationships, etc.
[0023] The following describes the graph data privacy protection method and device based on subgraph simplification of the present invention in conjunction with the accompanying drawings. Figure 1 is a flow chart of the graph data privacy protection method based on subgraph simplification provided by the present invention, such as Figure 1 As shown, the method includes the following steps 101 to 104.
[0024] Step 101: Determine a privacy budget combination value according to the average node degree of the first node in the bipartite graph to be estimated.
[0025] In an embodiment of the present invention, the user's graph data is a bipartite graph, and a differential privacy method is used when counting subgraphs. This method requires the allocation of a privacy budget, that is, determining the privacy budget combination value according to the average node degree of the first node in the bipartite graph to be estimated.
[0026] First, get the initial privacy budget value , will be based on the initial privacy budget value Count the subgraphs of the estimated bipartite graph and the initial privacy budget value is the first privacy budget and the second privacy budget The sum of , according to the second privacy budget Determine the random response probability P of the average node degree, expressed as .
[0027] The bipartite graph to be estimated is denoted by , where U and V represent different nodes in the bipartite graph to be estimated. A node can represent a user. The first node is denoted as U, with a number of m, and the second node is denoted as V, with a number of n. E is the edge between nodes, representing the association between users. The average node degree of the first node U is denoted as .
[0028] Then, according to the differential privacy algorithm, based on the first privacy budget value, the average node degree and the random response probability, the noise variance function of the first node in the estimated bipartite graph is constructed, which is expressed as the following formula (1): (1) Finally, the first privacy budget value when the noise variance function is minimized is and the second privacy budget , construct the privacy budget combination value, denoted as By calculating the minimum value of the noise variance function of formula (1), the corresponding privacy budget combination value can be calculated and then sent to each first node U in the bipartite graph to be estimated.
[0029] In an embodiment of the present invention, when counting subgraphs of a bipartite graph to be estimated, a privacy budget is allocated to user nodes in the bipartite graph to be estimated and noise is added through a differential privacy method, thereby protecting the privacy of the user. By setting noise and sensitivity in a targeted manner, full utilization of the privacy budget is ensured, thereby improving the availability of noise data.
[0030] Step 102: Based on the privacy budget combination value, the node degree of the first node and the neighbor node vector of the first node are noised to obtain a noisy bipartite graph.
[0031] Through step 101, after allocating a privacy budget combination value to each first node in the bipartite graph to be estimated, the node degree of the first node and the neighbor node vector of the first node are noised based on the privacy budget combination value.
[0032] For each first node , first take the privacy budget combination value is the privacy budget of the first node, with 1 as the sensitivity, The node degree Noise processing is performed, specifically, the node degree Add Laplace noise to get the corresponding node degree , which can be specifically written as: .
[0033] For the first node Neighbor node vector , then the privacy budget combination value is Noise is added to the privacy budget, and the neighbor node vector Each 0 / 1 bit in the vector value is represented by The probability of flipping, otherwise retain the original vector value, so as to obtain the corresponding noisy neighbor node list , R represents the flip probability.
[0034] Through the above noise addition process, the noise data of all first nodes U are finally obtained as follows: , , and according to Construct the noisy bipartite graph after adding noise .
[0035] The embodiment of the present invention adopts an automatic noise adding mechanism, calls a differential privacy algorithm, and automatically performs noise adding processing on the bipartite graph to be estimated according to the privacy budget to construct a noisy bipartite graph. Users do not need to download the noise subgraph to perform privacy noise adding, which reduces communication overhead, saves the response time of waiting for data download, and solves the problem that privacy protection requires user participation in synchronization.
[0036] Step 103: Determine the number of common neighbor nodes between any two first nodes in the bipartite graph to be estimated, and determine a first unbiased estimate of the noisy bipartite graph for a simple subgraph according to the number of common neighbor nodes.
[0037] Next, in the noisy bipartite graph In the above example, we count simple subgraphs. Since there are simple subgraphs and complex subgraphs in the bipartite graph, the number of simple subgraphs is the number of common neighbor nodes between any two first nodes in the bipartite graph G to be estimated, which is recorded as , represents any two first nodes and The number of common neighbor nodes between them. A complex subgraph is composed of at least one simple subgraph, and the number of complex subgraphs is The number of combinations of any two nodes selected from common neighbor nodes is also called the butterfly number and is denoted by In the embodiment of the present invention, to achieve privacy protection, the subgraph count to be finally determined is the number B of butterflies including all first nodes in the bipartite graph G to be estimated.
[0038] For example, Figure 2 As shown, the first node and another first node The number of common neighbor nodes is 2, that is, and , so the first node , and the second node , It forms a butterfly shape, so it contains the first node , Number of butterflies is 1, that is, the number of complex subgraphs is 1.
[0039] In a noisy bipartite graph When performing simple subgraph counting in , first determine any two first nodes ( and ) , and according to the number of common neighbor nodes Determining the first unbiased estimate of a noisy bipartite graph for a simple subgraph .
[0040] In some embodiments, the bipartite graph to be estimated G further includes a second node V. For any two first nodes ( and ), determine the second node V and the two first nodes in the noisy bipartite graph There are three types of neighbor relationships in the network, which are described one by one below.
[0041] The first kind of neighbor relationship is that the second node is a common neighbor node of the two first nodes. In the example, the second node V is the two first nodes ( and )’s common neighbor nodes.
[0042] The second kind of neighbor relationship is that the second node is the neighbor node of any of the two first nodes. In the example, the second node V is the first node The neighbor node or the first node neighbor nodes.
[0043] The third type of neighbor relationship is that the second node is not a neighbor node of any of the two first nodes. The second node V is neither the first node The neighbor node is not the first node neighbor nodes.
[0044] Here, the number of second nodes in each neighbor relationship is determined according to the number of common neighbor nodes, and the corresponding occurrence probability of the number in the noisy bipartite graph is determined.
[0045] In the first neighbor relationship, the number of second nodes V is the number of any two first nodes in the bipartite graph G to be estimated ( and ) According to the differential privacy algorithm, when adding noise, there is a probability to flip the value of the neighbor node, and this number is obtained In a noisy bipartite graph The probability of occurrence is .
[0046] Under the second neighbor relationship, the number of second nodes V is expressed as , also according to the differential privacy algorithm, we can get this number In a noisy bipartite graph The probability of occurrence is .in, , are the first nodes in the bipartite graph G to be estimated. and the first node The degree, are any two first nodes in the bipartite graph G to be estimated ( and ) is the number of common neighbor nodes between them.
[0047] Under the third neighbor relationship, the number of second nodes V is expressed as , also according to the differential privacy algorithm, we can get this number In a noisy bipartite graph The probability of occurrence is .in, , are the first nodes in the bipartite graph G to be estimated. and the first node The degree, are any two first nodes in the bipartite graph G to be estimated ( and ), n is the total number of second nodes V in the bipartite graph G to be estimated.
[0048] Next, the expected value of data under each neighbor relationship is calculated. Under each neighbor relationship, the product of the occurrence probability and the number is determined as the expected value of the number corresponding to the second node in the noisy bipartite graph.
[0049] Under the first neighbor relationship, the second node V in the noisy bipartite graph The expected value of the corresponding number It is expressed as the following formula (2): (2) Under the second neighbor relationship, the second node V in the noisy bipartite graph The expected value of the corresponding number It is expressed as the following formula (3): (3) Under the third neighbor relationship, the second node V in the noisy bipartite graph The expected value of the corresponding number It is expressed as the following formula (4): (4) Finally, the expected value of the number under each neighbor relationship is summed up, and the first unbiased estimate of the simple subgraph of the noisy bipartite graph is obtained based on the summed result.
[0050] Here, we first sum the target expected values of the second node under the three neighbor relationships to obtain the sum result. , expressed as the following formula (5): (5) Then sum the result Substituting into the calculation formula of unbiased estimation, we get the first unbiased estimate of the noisy bipartite graph for the simple subgraph , the calculation formula of unbiased estimation is as follows: (6) In the above formula (6), is the sum of the target expected values of the second node under the three neighbor relationships, Representing a noisy bipartite graph The first node The degree, Representing a noisy bipartite graph The first node The degree of random response is P.
[0051] By substituting the above formulas (2) to (4) into formula (5), and then substituting formula (5) into formula (6), the first unbiased estimate of the noisy bipartite graph for the simple subgraph can be calculated: .
[0052] Here, the first unbiased estimate is calculated according to the above formula (6) When is an unknown value. In the noisy bipartite graph after the estimated bipartite graph is noised, this is unchanged. In a noisy bipartite graph, any two first nodes ( and The number of common neighbor nodes between , which can be calculated by matrix multiplication ,in, is the neighbor node list matrix after adding noise, T is the transpose of the matrix, from which the corresponding , that is, satisfy = Therefore, by substituting formulas (2) to (4) into formula (5), we can calculate the only unknown Then substitute it into formula (6) to get the first unbiased estimate .
[0053] In an embodiment of the present invention, when estimating the number of butterflies in a complex subgraph, a noisy bipartite graph is first used to perform an unbiased estimation of a simple subgraph, and the expected value of the second node under different neighbor relationships is calculated, thereby achieving an unbiased estimation of the simple subgraph in the noisy bipartite graph and laying a foundation for the subsequent unbiased estimation of the complex subgraph.
[0054] Step 104: perform an unbiased estimate on the number of butterflies corresponding to the number of common neighbor nodes according to the variance value of the first unbiased estimate, and obtain the number of butterflies for the complex subgraph in the bipartite graph to be estimated.
[0055] After unbiased estimation of the number of simple subgraphs in the noisy bipartite graph is performed in step 103, this unbiased estimation is noisy and cannot be directly used as the subgraph count of the bipartite graph to be estimated. Therefore, according to the nature of the noise, the variance value of this unbiased estimate needs to be determined next. This variance value reflects the distribution of simple subgraphs in the noisy bipartite graph, that is, the error as noise. The variance value includes two parts, the first part is the node degree variance of the first node in the noisy bipartite graph, and the second part is the number variance of the second node in the noisy bipartite graph, which is described in detail below.
[0056] First, in the first part, determine the first unbiased estimate The node degree variance of any two first nodes in , expressed as the following formula: (7) In the above formula (7), is the first privacy budget value, and P is the random response probability.
[0057] The second part is the number variance of the second node in the noisy bipartite graph. This number variance still needs to be calculated separately according to the neighbor relationship of the second node. Under each neighbor relationship, according to the second node V in the noisy bipartite graph The corresponding number variance is determined by the number of occurrences in , where the neighbor relationship is the neighbor relationship between the second node and any two first nodes in the bipartite graph to be estimated. For details, please refer to the three neighbor relationships in the above step 102.
[0058] Under the first adjacent relationship, select any two first nodes in the bipartite graph G to be estimated ( and ) between the common neighbor nodes of the second node V, then in the noisy bipartite graph In the above example, the second node V is determined to be any two first nodes ( and ) between the two nodes. Since adding noise to the bipartite graph does not change the adjacent relationship between the nodes, The number of common neighbor nodes in the graph is the same as that in the estimated bipartite graph. According to the differential privacy algorithm, when adding noise, the neighbor nodes have a probability of flipping, and the probability corresponding to this number of occurrences is obtained as , then the variance of the number under the first adjacent relationship is It is expressed as the following formula: (8) Under the second neighbor relationship, first count the first nodes belonging to any node in the estimated bipartite graph G. Neighbor node or first node The number of the second node V of the neighbor node is expressed as , correspondingly in the noisy bipartite graph , the number of occurrences is Similarly, according to the differential privacy algorithm, when adding noise, the neighbor nodes have a probability of flipping, and the probability corresponding to this number of occurrences is obtained as , then the variance of the number under the second adjacent relationship is It is expressed as the following formula: (9) Similarly, under the third adjacent relationship, in the estimated bipartite graph G, count the nodes that do not belong to any first node Neighbor nodes of the first node are not The number of the second node V of the neighbor node is expressed as , correspondingly in the noisy bipartite graph , the number of occurrences is According to the differential privacy algorithm, when adding noise, the neighbor nodes have a probability of flipping, and the probability corresponding to this number of occurrences is obtained as , then the variance of the number under the third adjacent relationship is It is expressed as the following formula: (10) Finally, the variances calculated from the two parts are summed, that is, the variance of the node degree is summed with the variance of the number of neighbor relationships under each condition, to obtain the variance value of the first unbiased estimate , expressed as the following formula (11): (11) In an embodiment of the present invention, after an unbiased estimation is made on a simple subgraph in a noisy bipartite graph, the distribution of the simple subgraph in the noisy bipartite graph is determined by calculating the variance value in the noisy bipartite graph, that is, the error caused by adding noise is determined. This adding noise error is used to optimize the estimation of the complex subgraph in the estimated bipartite graph, which helps to improve the accuracy of counting the complex subgraphs.
[0059] Since the ultimate goal of the embodiment of the present invention is to count the complex subgraphs in the estimated bipartite graph, that is, to determine the number of butterflies corresponding to the complex subgraphs. As mentioned above, in the estimated bipartite graph G, determine any two first nodes ( and The number of common neighbor nodes between , this number is for simple subgraphs and is used for unbiased estimation. The complex subgraph is composed of simple subgraphs, so it contains any two first nodes ( and ) can be written as , specifically expressed as The number of combinations obtained by randomly selecting two nodes from common neighbor nodes, because according to Figure 2 As shown, only the first two nodes ( and ) can only form a butterfly-shaped complex subgraph by finding two common neighbor nodes. Thus, the transformation between simple subgraph and complex subgraph is realized.
[0060] Next, an unbiased estimate is made on the number of butterflies corresponding to the number of common neighbor nodes based on the variance value of the first unbiased estimate, and the number of butterflies for the complex subgraph in the bipartite graph to be estimated is obtained.
[0061] According to the above transformation of simple subgraphs and complex subgraphs, the number of common neighbor nodes The corresponding number of butterflies is , while in the noisy bipartite graph, the variance of the first unbiased estimate has been calculated. This variance is the error caused by the noise. Therefore, in the estimated bipartite graph, this error needs to be removed, so the number of common neighbor nodes is The corresponding number of butterflies The variance value with the first unbiased estimate The difference between the two first nodes of the bipartite graph to be estimated ( and ) corresponds to the second unbiased estimate of the complex subgraph , the corresponding simplified formula is as follows: (11) This second unbiased estimate is only for any two first nodes ( and ), and in the bipartite graph to be estimated, it is necessary to calculate the number of butterflies B corresponding to the complex subgraph containing all the first nodes U.
[0062] Therefore, we further count the second unbiased estimates corresponding to any two first nodes U in the estimated bipartite graph G, and obtain the number of butterflies B for the complex subgraph of the estimated bipartite graph, so as to count all the butterflies in the estimated bipartite graph. The statistical process first calculates the second unbiased estimates corresponding to each two first nodes U in the estimated bipartite graph one by one, and then sums them up, which can be expressed as the following formula: (12) In the above formula (12), m is the total number of first nodes U in the bipartite graph G to be estimated, i represents any i-th first node, j represents any j-th first node, It means that any two first nodes ( and ) is the number of complex subgraph butterflies.
[0063] By calculating the number B of all butterflies in the bipartite graph to be estimated, this number of butterflies B is the subgraph count corresponding to the graph data that needs to be privacy protected in the bipartite graph to be estimated. The subgraph count of the graph data contains the privacy information of the user nodes in the bipartite graph G to be estimated. Combined with the differential privacy algorithm, the subgraph count required by the user's privacy is realized.
[0064] In the embodiment of the present invention, when counting subgraphs of complex subgraphs, the number of butterflies of the complex subgraphs is converted into the number of combinations of simple subgraphs, thereby realizing the conversion of complex subgraphs and simple subgraphs. When counting, simple subgraphs are counted first, then noise errors are eliminated, and complex subgraphs are counted in combination with the conversion relationship, thereby improving the estimation accuracy of subgraph counts. Even for large-scale graphs, the complexity of subgraph matching for complex subgraphs can be effectively reduced, thereby improving the operating efficiency of subgraph counting.
[0065] The graph data privacy protection device based on subgraph simplification provided by the present invention is described below. The graph data privacy protection device based on subgraph simplification described below and the graph data privacy protection method based on subgraph simplification described above can refer to each other.
[0066] like Figure 3As shown, the graph data privacy protection device based on subgraph simplification includes a determination module 301 , a noise adding module 302 , an estimation module 303 , and a counting module 304 . Specifically, a determination module 301 is used to determine a privacy budget combination value based on the average node degree of the first node in the bipartite graph to be estimated; a noise adding module 302 is used to perform noise processing on the node degree of the first node and the neighbor node vector of the first node based on the privacy budget combination value to obtain a noisy bipartite graph; an estimation module 303 is used to determine the number of common neighbor nodes between any two first nodes from the bipartite graph to be estimated, and determine a first unbiased estimate of the noisy bipartite graph for a simple subgraph based on the number of common neighbor nodes; a counting module 304 is used to perform an unbiased estimate of the number of butterflies corresponding to the number of common neighbor nodes based on the variance value of the first unbiased estimate to obtain the number of butterflies of the bipartite graph to be estimated for a complex subgraph, the number of butterflies corresponding to the number of common neighbor nodes is the number of combinations of any two nodes selected from the common neighbor nodes, and the number of butterflies of the bipartite graph to be estimated is the subgraph count corresponding to the graph data to be privacy protected in the bipartite graph to be estimated.
[0067] Figure 4 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 4 As shown, the electronic device may include: a processor (processor) 410 , a communication interface (Communications Interface) 420 , a memory (memory) 430 and a communication bus 440 , wherein the processor 410 , the communication interface 420 , and the memory 430 communicate with each other through the communication bus 440 . The processor 410 can call the logic instructions in the memory 430 to execute a graph data privacy protection method based on subgraph simplification, which includes: determining a privacy budget combination value based on the average node degree of the first node in the bipartite graph to be estimated; performing noise processing on the node degree of the first node and the neighbor node vector of the first node based on the privacy budget combination value to obtain a noisy bipartite graph; determining the number of common neighbor nodes between any two first nodes from the bipartite graph to be estimated, and determining a first unbiased estimate of the noisy bipartite graph for a simple subgraph based on the number of common neighbor nodes; performing an unbiased estimate of the number of butterflies corresponding to the number of common neighbor nodes based on the variance value of the first unbiased estimate to obtain the number of butterflies for a complex subgraph in the bipartite graph to be estimated, the number of butterflies corresponding to the number of common neighbor nodes being the number of combinations of any two nodes selected from the common neighbor nodes, and the number of butterflies of the bipartite graph to be estimated being the subgraph count corresponding to the graph data to be privacy protected in the bipartite graph to be estimated.
[0068] In addition, the logic instructions in the above-mentioned memory 430 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.
[0069] On the other hand, the present invention also provides a computer program product, which includes a computer program, which can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the graph data privacy protection method based on subgraph simplification provided by the above methods, the method including: determining a privacy budget combination value based on the average node degree of the first node in the bipartite graph to be estimated; performing noise processing on the node degree of the first node and the neighbor node vector of the first node based on the privacy budget combination value to obtain a noisy bipartite graph; determining the number of common neighbor nodes between any two first nodes from the bipartite graph to be estimated, and determining a first unbiased estimate of the noisy bipartite graph for a simple subgraph based on the number of common neighbor nodes; performing an unbiased estimate of the number of butterflies corresponding to the number of common neighbor nodes based on the variance value of the first unbiased estimate to obtain the number of butterflies for a complex subgraph in the bipartite graph to be estimated, the number of butterflies corresponding to the number of common neighbor nodes is the number of combinations of any two nodes selected from the common neighbor nodes, and the number of butterflies of the bipartite graph to be estimated is the subgraph count corresponding to the graph data to be privacy protected in the bipartite graph to be estimated.
[0070] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the graph data privacy protection method based on subgraph simplification provided by the above-mentioned methods, the method comprising: determining a privacy budget combination value based on the average node degree of the first node in the bipartite graph to be estimated; performing noise processing on the node degree of the first node and the neighbor node vector of the first node based on the privacy budget combination value to obtain a noisy bipartite graph; determining the number of common neighbor nodes between any two first nodes from the bipartite graph to be estimated, and determining a first unbiased estimate of the noisy bipartite graph for a simple subgraph based on the number of common neighbor nodes; performing an unbiased estimate of the number of butterflies corresponding to the number of common neighbor nodes based on the variance value of the first unbiased estimate to obtain the number of butterflies for a complex subgraph in the bipartite graph to be estimated, the number of butterflies corresponding to the number of common neighbor nodes being the number of combinations of any two nodes selected from the common neighbor nodes, and the number of butterflies of the bipartite graph to be estimated being the subgraph count corresponding to the graph data to be privacy protected in the bipartite graph to be estimated.
[0071] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.
[0072] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.
[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A graph data privacy protection method based on subgraph simplification, characterized in that: The method comprises: Determine the privacy budget combination value according to the average node degree of the first node in the bipartite graph to be estimated; Based on the privacy budget combination value, respectively perform noise processing on the node degree of the first node and the neighbor node vector of the first node to obtain a noisy bipartite graph; Determine the number of common neighbor nodes between any two first nodes in the bipartite graph to be estimated, and determine a first unbiased estimate of the noisy bipartite graph for a simple subgraph according to the number of common neighbor nodes; An unbiased estimate is made of the number of butterflies corresponding to the number of common neighbor nodes according to the variance value of the first unbiased estimate to obtain the number of butterflies for the complex subgraph in the bipartite graph to be estimated. The number of butterflies corresponding to the number of common neighbor nodes is the number of combinations of any two nodes selected from the common neighbor nodes. The number of butterflies in the bipartite graph to be estimated is the subgraph count corresponding to the graph data that needs to be privacy protected in the bipartite graph to be estimated.
2. The graph data privacy protection method based on subgraph simplification according to claim 1 is characterized in that: The step of determining the privacy budget combination value according to the average node degree of the first node in the bipartite graph to be estimated includes: Acquire an initial privacy budget value, where the initial privacy budget value is the sum of the first privacy budget value and the second privacy budget value; Determine a random response probability of an average node degree according to the second privacy budget value; Constructing a noise-added variance function of a first node in the bipartite graph to be estimated based on the first privacy budget value, the average node degree, and the random response probability; A privacy budget combination value is constructed according to the first privacy budget value and the second privacy budget value when the noise variance function obtains a minimum value.
3. The graph data privacy protection method based on subgraph simplification according to claim 1 is characterized in that: The bipartite graph to be estimated further includes a second node, and determining a first unbiased estimate of the noisy bipartite graph for a simple subgraph according to the number of the common neighbor nodes includes: For any two first nodes in the bipartite graph to be estimated, determining a neighbor relationship between the second node and the two first nodes in the noisy bipartite graph; Determine the number of the second nodes in each neighbor relationship according to the number of the common neighbor nodes, and determine the corresponding probability of occurrence of the number in the noise bipartite graph; Under each neighbor relationship, the product of the occurrence probability and the quantity is determined as the expected value of the number of the second node corresponding to the noisy bipartite graph: The expected values of the number under each neighbor relationship are summed, and the first unbiased estimate of the noisy bipartite graph for the simple subgraph is calculated based on the summed result.
4. The graph data privacy protection method based on subgraph simplification according to claim 3 is characterized in that: The neighbor relationship between the second node and the two first nodes in the noisy bipartite graph includes: The second node is a common neighbor node of the two first nodes; The second node is a neighbor node of any one of the two first nodes; The second node is not a neighbor node of any one of the two first nodes.
5. The graph data privacy protection method based on subgraph simplification according to claim 1 is characterized in that: The step of performing an unbiased estimation on the number of butterflies corresponding to the number of common neighbor nodes according to the variance value of the first unbiased estimate to obtain the number of butterflies of the bipartite graph to be estimated for the complex subgraph includes: Taking the difference between the number of butterflies corresponding to the number of common neighbor nodes and the variance value of the first unbiased estimate as the second unbiased estimate of the complex subgraph corresponding to any two first nodes in the bipartite graph to be estimated; The second unbiased estimation values corresponding to any two first nodes in the bipartite graph to be estimated are counted to obtain the number of butterflies of the bipartite graph to be estimated for the complex subgraph.
6. The graph data privacy protection method based on subgraph simplification according to claim 5 is characterized in that: The variance value of the first unbiased estimate is determined by: Determining the node degree variance of any two first nodes in the first unbiased estimate; Under each neighbor relationship, determining a corresponding number variance according to the number of occurrences of the second node in the noisy bipartite graph, wherein the neighbor relationship is an adjacent relationship between the second node and any two first nodes in the bipartite graph to be estimated; The node degree variance is summed with the number variance under each neighbor relationship to obtain the variance value of the first unbiased estimate.
7. A graph data privacy protection device based on subgraph simplification, characterized in that: The device comprises: A determination module, used to determine a privacy budget combination value according to an average node degree of the first node in the bipartite graph to be estimated; A noise adding module, configured to perform noise adding processing on the node degree of the first node and the neighbor node vector of the first node respectively based on the privacy budget combination value to obtain a noisy bipartite graph; An estimation module, used to determine the number of common neighbor nodes between any two first nodes in the bipartite graph to be estimated, and determine a first unbiased estimation value of the noisy bipartite graph for a simple subgraph according to the number of common neighbor nodes; A counting module is used to perform an unbiased estimate on the number of butterflies corresponding to the number of common neighbor nodes according to the variance value of the first unbiased estimate, and obtain the number of butterflies for the complex subgraph of the bipartite graph to be estimated, the number of butterflies corresponding to the number of common neighbor nodes is the number of combinations of any two nodes selected from the common neighbor nodes, and the number of butterflies of the bipartite graph to be estimated is the subgraph count corresponding to the graph data that needs to be privacy protected in the bipartite graph to be estimated.
8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the method for protecting graph data privacy based on subgraph simplification as described in any one of claims 1 to 6 is implemented.
9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the graph data privacy protection method based on subgraph simplification as described in any one of claims 1 to 6 is implemented.
10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the graph data privacy protection method based on subgraph simplification as described in any one of claims 1 to 6 is implemented.