CN115878906B - A social graph generation method and system that protects personal similarity - Google Patents

Abstract

The invention provides a social graph generation method for protecting personal similarity, which comprises the following steps: acquiring an initial social graph, calculating attribute similarity between associated nodes in the initial social graph, forming an initial similarity sequence according to all attribute similarity in the initial social graph, and carrying out Laplacian noise processing on the initial similarity sequence to obtain a noise-added similarity sequence; post-processing is carried out on the noise-added similarity sequence to obtain a final similarity sequence; and writing the final similarity sequence into the initial social graph to generate a private social graph. The social graph generated by the method can effectively protect the node attributes and prevent attribute inference of the associated node parts in the using process.

Description

A social graph generation method and system that protects personal similarity

Technical field

The invention belongs to the technical field, and specifically relates to a social graph generation method and system for protecting personal similarity.

Background technique

A social graph is a social structure graph composed of many nodes. Nodes usually refer to individuals or organizations. The attributes of nodes can represent the attributes of individuals. For example, personal attributes include height, weight, age, etc.; the edges connecting nodes Represents the strength of the relationship between two nodes, and the nodes connected by edges are associated nodes; the social graph associates casual acquaintances with people or organizations in closely knit family relationships. Because of the need for data analysis, it is often necessary to publish or share social graphs. The attributes of nodes in the existing technology are usually very sensitive and vulnerable to attacks from various links.

In order to solve the above problems, existing technologies usually use differential privacy technology to protect the attributes of nodes; differential privacy technology assumes that all information about an individual is provided by the individual himself, but when similarity occurs, the situation is different. It is mentioned in sociological research and psychological theory that similarity is ubiquitous as the main representation of symmetrical relationships. In social networks, the direct relationship between users shows homogeneity, that is, when there is an edge between two nodes , nodes with similar degrees will naturally form stronger connections, so when using a node attribute, some private information of the associated nodes will inevitably be disclosed.

Therefore, there is an urgent need for a social graph that can protect personal similarity and that can effectively protect node attributes during the use of the social graph.

Contents of the invention

The present invention aims to solve the technical problems existing in the prior art and provide a social graph generation method and system that protects personal similarity, so that the generated social graph can effectively protect node attributes and prevent associated node components during use. Property inference.

In order to achieve the above objects of the present invention, according to the first aspect of the present invention, the present invention provides a social graph generation method that protects personal similarity, including the following steps: obtaining an initial social graph, and calculating the number of associated nodes in the initial social graph. Based on the attribute similarity between all the attributes in the initial social graph, an initial similarity sequence is formed, and the initial similarity sequence is subjected to Laplacian noise processing to obtain a noisy similarity sequence; the noisy similarity sequence is processed Post-processing to obtain the final similarity sequence; the specific steps of post-processing are as follows: traverse each attribute similarity in the noisy similarity sequence, if the attribute similarity is less than 0 or greater than the maximum attribute similarity in the initial similarity sequence, then Assign the attribute similarity to the maximum attribute similarity in the initial similarity sequence; if the attribute similarity is greater than 0 and less than the maximum attribute similarity in the initial similarity sequence, the attribute similarity remains at the original value; the final similarity The sequence is written into the initial social graph to generate a private social graph.

Further, the specific steps of Laplacian noise processing are as follows: divide the initial similarity sequence into multiple sets; and any attribute similarity in the initial similarity sequence only appears once in multiple sets; for each The sets are separately processed by Laplacian noise.

Further, the steps for performing Laplacian noise processing on each set are as follows: set the first privacy parameter, traverse all sets, and if the total number of attribute similarities in the set is greater than the first privacy parameter, give the The first noise is added to each attribute similarity in the set; if the total number of attribute similarities in the set is less than the first privacy parameter, the second noise is added to each attribute similarity in the set.

Further, both the first noise and the second noise are obtained by calculating the probability density function; the probability density function is as follows: Among them, P represents the probability, x represents the added noise value, x≤0, and λ represents the noise scale.

Further, the calculation formula of the noise scale of the first noise is as follows: λ ₁ =kp/ò; the calculation formula of the noise scale of the second noise is as follows: λ ₂ =rp/ò; where λ ₁ represents the noise scale of the first noise , λ ₂ represents the noise scale of the second noise, k represents the first privacy parameter, r represents the total number of attribute similarities in the set, p represents the maximum attribute similarity in the initial similarity sequence, ò represents the second privacy parameter; 2. Privacy parameters are obtained through settings.

Further, the steps for calculating the attribute similarity between associated nodes in the initial social graph are as follows: obtaining the attribute vector of the associated node in the social attribute graph, calculating the distance between the associated nodes through the attribute vector of the associated node and the distance formula, according to The associated node and associated distance generate the attribute similarity of the associated node.

Furthermore, the distance formula is specifically: Among them, i represents node i, j represents node j, node i and node j are associated nodes, l _ij represents the association distance between associated nodes i and j, x _i represents the attribute vector of node i, and x _j represents the attribute vector of node j. , S represents the covariance matrix between x _i and x _j .

Further, the attribute similarity is expressed as (i, j, l _ij ), where i represents node i, j represents node j, and l _ij represents the association distance between associated nodes i and j.

Further, the steps for writing the final similarity sequence into the initial social graph to generate a private social graph are as follows: Divide the initial social graph into node sets, edge sets and node attribute sets; use the final similarity sequence to replace the Node attribute sets generate private social graphs.

In order to achieve the above objects of the present invention, according to the second aspect of the present invention, the present invention provides a social graph generation system that protects personal similarity, and realizes any of the above social graphs that protect personal similarity during operation. The steps of the graph generation method; the system includes an acquisition module, a calculation module, a noise adding module, a post-processing module and a generation module; the acquisition module is used to obtain the initial social graph; the calculation module is used to calculate the attribute similarity of the associated nodes in the initial social graph , and form an initial similarity sequence; the noise-adding module is used to perform noise processing on the initial similarity sequence to obtain the noise-added similarity sequence; the post-processing module is used to perform post-processing on the noise-added similarity sequence to obtain the final similarity Sequence; the generation module is used to write the final similarity sequence into the initial social graph to generate a privacy social graph.

Basic principles and beneficial effects of the present invention: This solution hides the specific attribute values of nodes by calculating attribute similarity, quantifies the similarity of associated nodes in the social graph and then retains the similarity between nodes; in order to hide the similarity, This solution uses the definition of differential privacy and protects similarity based on noise processing and post-processing methods, making the similarity of nodes available but not visible, avoiding attribute inference between associated nodes through similarity, and improving social security. The protection strength of the graph minimizes the damage to the data utility.

Description of the drawings

Figure 1 is a schematic diagram of the steps of a social graph generation method for protecting personal similarity according to the present invention;

Figure 2 is a schematic diagram of the steps of using the query model to extract the initial similarity sequence according to the present invention;

Figure 3 is a schematic diagram of the steps of the initial similarity sequence segmentation process of the present invention;

Figure 4 is a KS-distance comparison diagram of four real social network data sets;

Figure 5 is a Mallows-distance comparison diagram of four real social network data sets;

Figure 6 is a schematic structural diagram of a social graph generation system for protecting personal similarity in the present invention.

Detailed ways

Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and cannot be understood as limiting the present invention.

In the description of the present invention, it should be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", The orientations or positional relationships indicated by "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and are not Any indication or implication that the referred device or element must have a specific orientation, be constructed and operate in a specific orientation should not be construed as a limitation on the invention.

In the description of the present invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "connection" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or both. The internal connection between components may be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meaning of the above terms can be understood according to the specific situation.

As shown in Figure 1, the present invention provides a social graph generation method that protects personal similarity, including the following steps:

Obtain the initial social graph and calculate the attribute similarity between the associated nodes in the initial social graph,

An initial similarity sequence is formed based on the similarity of all attributes in the initial social graph. The initial similarity sequence is subjected to Laplacian noise processing to obtain the noise-added similarity sequence; the noise-added similarity sequence is post-processed to obtain the final similarity. sequence;

The specific steps of post-processing are as follows: traverse each attribute similarity in the noisy similarity sequence. If the attribute similarity is less than 0 or greater than the maximum attribute similarity in the initial similarity sequence, assign the attribute similarity to the initial value. The maximum attribute similarity in the similarity sequence; if the attribute similarity is greater than 0 and less than the maximum attribute similarity in the initial similarity sequence, the attribute similarity remains at the original value;

The final similarity sequence is written into the initial social graph to generate a private social graph.

Specifically, the social graph with node attributes can be expressed as a triplet G(V,E,X), where V=(v ₁ ,…,v _n ) represents the node set and E=(e ₁ ,… , _en ) represents the edge set, X=(x ₁ ,...,x _n ) represents the node attribute set; where x ₁ represents the attribute vector of node v ₁ ;

Specifically, the principle of this embodiment introducing differential privacy technology to perform Laplacian noise on the initial social graph is as follows:

If an algorithm satisfies the differential privacy algorithm and its input is a graph, then modifying an edge in the input graph will have a very limited impact on the output result. If k edges in the input graph are modified, the impact on the output result is very limited, then the algorithm satisfies k-edge differential privacy;

For the two specified social graphs G ₁ (V ₁ ,E ₁ ,X ₁ ) and G ₂ (V ₂ ,E ₂ ,X ₂ ), if V ₁ =V ₂ , |E ₂ |=|E ₁ |- k, then G ₁ and G ₂ are said to be adjacent on edge k;

Assume that the random algorithm M satisfies differential privacy, and range (M) is a set of possible outputs of algorithm M. Then for any two k-edge adjacent social graphs G ₁ and G ₂ and any subset S of range (M) Satisfy the following formula:

Pr(M(G ₁ )∈S)≤e ^ò ×Pr(M(G ₂ )∈S)

Among them, ò represents the set second privacy parameter.

Specifically, the steps for calculating attribute similarity between associated nodes in the initial social graph are as follows:

Obtain the attribute vector of the associated node in the social attribute graph, calculate the distance between the associated nodes through the attribute vector of the associated node and the distance formula, and generate the attribute similarity of the associated node based on the associated node and the associated distance.

Furthermore, the distance formula is specifically:

Among them, i represents node i, j represents node j, node i and node j are associated nodes, l _ij represents the association distance between associated nodes i and j, x _i represents the attribute vector of node i, and x _j represents the attribute vector of node j. , S represents the covariance matrix between x _i and x _j .

Specifically, the distance between the associated nodes of an edge is used as the label of the edge, and is written into the initial social graph to form a new social graph, denoted as G'(V,E,L), where L represents the initial social graph. Attribute similarity sequence, that is, the initial similarity sequence. As shown in Figure 2, the new social graph is put into the query model to extract the initial similarity sequence L.

Further, the attribute similarity is expressed as (i, j, l _ij ), where i represents node i, j represents node j, and l _ij represents the association distance between associated nodes i and j.

Specifically, the specific steps of Laplacian noise processing are as follows:

Divide the initial similarity sequence into multiple sets; any attribute similarity in the initial similarity sequence only appears once in multiple sets; perform Laplacian noise processing on each set separately. This embodiment proposes a truncated Laplacian mechanism T: given a monotonically increasing function F, that is, for any neighborhood data set G ₁ , G ₂ ∈G, F(G ₁ )≤F(G ₂ ), then the mechanism T(G)=F(G ₁ )+lap ^- (ΔF/ò) satisfies the differential privacy of ò, where lap ^- (ΔF/ò) represents the added Laplacian noise, which is negative The value, ΔF/ò determines the size of the added Laplacian noise, ΔF represents the sensitivity of the query model, and ò represents the set second privacy parameter.

Specifically, the process of dividing the initial similarity sequence is shown in Figure 3. The initial similarity sequence L is divided into multiple sets according to its associated nodes. Any element includes the distance between associated nodes, that is, attribute similarity; for example, l _ij ∈L, l _ij is the distance between associated nodes i and j. Once l _ij is divided to/> then it will not be allocated to/> The number of sets and the number of initial similarity sequences L in each set are set according to the number of edges in the initial social graph. In this embodiment, the number of sets and the number of initial similarity sequences L in each set are as follows: As shown in Figure 2 and Figure 3, and any element in the initial similarity sequence L is in the set /> Appears only once in .

Specifically, the steps for performing Laplacian noise processing on each set are as follows: set the first privacy parameter, traverse all sets, and if the total number of attribute similarities in the set is greater than the first privacy parameter, give the The first noise is added to each attribute similarity in the set; if the total number of attribute similarities in the set is less than the first privacy parameter, the second noise is added to each attribute similarity in the set.

Furthermore, both the first noise and the second noise are calculated through the probability density function; the probability density function is as follows:

Among them, P represents the probability, x represents the added noise value, x≤0, and λ represents the noise scale. It can be seen from the probability density function that the mean value of truncated Laplacian is 0 and the variance is λ ² , and only increases the noise on one side of the Laplacian distribution, while truncating the noise on the other side; it is different from the traditional method of completing differential privacy. Compared with the Laplacian mechanism (mean value is 0, variance is 2λ ² ), the truncated Laplacian mechanism proposed in this embodiment has a smaller variance while providing the same level of privacy protection, making the data of the social graph in After protection, the volatility is smaller, and the social graph has higher data utility during use.

Furthermore, the calculation formula of the noise scale of the first noise is as follows:

λ ₁ =kp/ò

The calculation formula of the noise scale of the second noise is as follows:

λ ₂ =rp/ò

Among them, λ ₁ represents the noise scale of the first noise, λ ₂ represents the noise scale of the second noise, k represents the first privacy parameter, r represents the total number of attribute similarities in the set, and p represents the maximum attribute in the initial similarity sequence. Similarity, ò represents the second privacy parameter; the second privacy parameter is obtained by setting.

From the above noise size formula, it can be known that if the initial similarity is not segmented, the noise size of all attribute similarities is kp/ò; the initial similarity sequence is segmented first and then noise is added to make the size segmentation after noise In order to kp/ò and rp/ò(k>r), therefore dividing the initial similarity sequence into multiple sets can avoid adding too much noise and improve the data utility of the social graph.

Specifically, the noisy similarity sequence is obtained through the above formula Perform post-processing on the noisy similarity sequence to obtain the final similarity sequence/> Use final similarity sequence/> Replace the node attribute set X in the initial social graph to generate a private social graph/>

In the specific implementation process, experiments were conducted on four real social network data sets according to a social graph generation method that protects personal similarity described in this plan; the four real social network data sets include Karate, Footbal, LastFM-Asia and Facebook; In order to evaluate the privacy effect of the social graph generated according to a social graph generation method that protects personal similarity described in this embodiment, we use two indicators to evaluate its accuracy and privacy. First, we use the Kolmogorov-Smirnoff distance (KS-distance) to verify whether the attribute similarity before and after interference obeys the same distribution; then we use the distance formula described in this embodiment to accurately describe the difference between the tails of the two distributions. Figures 4 and 5 show the corresponding changing trends of KS-distance and the distance calculated by the distance formula as the privacy budget changes, where k=15 by default. According to Figures 4 and 5, it can be concluded that the distance calculated using the distance formula described in this embodiment is more stable for graphs of different sizes, and the calculated distance increases as the number of edges in the graph increases.

As shown in Figure 6, in order to achieve the above objects of the present invention, according to the second aspect of the present invention, the present invention provides a social graph generation system that protects personal similarity, and realizes any of the above during operation. The steps of a social graph generation method that protects personal similarity; the system includes an acquisition module, a calculation module, a noise adding module, a post-processing module and a generation module; the acquisition module is used to obtain the initial social graph; the calculation module is used to calculate the initial social graph attribute similarity of the associated nodes in the middle, and form an initial similarity sequence; the noise-adding module is used to perform noise processing on the initial similarity sequence to obtain the noise-added similarity sequence; the post-module is used to post-process the noise-added similarity sequence. Set processing to obtain the final similarity sequence; the generation module is used to write the final similarity sequence into the initial social graph to generate a privacy social graph.

In the description of this specification, reference to the terms "one embodiment," "some embodiments," "an example," "specific examples," or "some examples" or the like means that specific features are described in connection with the embodiment or example. , structures, materials or features are included in at least one embodiment or example of the invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art will appreciate that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and purposes of the invention. The scope of the invention is defined by the claims and their equivalents.

Claims (7)

1. The social graph generation method for protecting personal similarity is characterized by comprising the following steps of:

acquiring an initial social graph, calculating attribute similarity between associated nodes in the initial social graph, forming an initial similarity sequence according to all attribute similarity in the initial social graph, and carrying out Laplacian noise processing on the initial similarity sequence to obtain a noise-added similarity sequence; post-processing is carried out on the noise-added similarity sequence to obtain a final similarity sequence;

the post-treatment comprises the following specific steps: traversing each attribute similarity in the noise-added similarity sequence, and if the attribute similarity is smaller than 0 or larger than the maximum attribute similarity in the initial similarity sequence, assigning the attribute similarity as the maximum attribute similarity in the initial similarity sequence; if the attribute similarity is greater than 0 and less than the maximum attribute similarity in the initial similarity sequence, the attribute similarity keeps the original value;

writing the final similarity sequence into the initial social graph to generate a private social graph;

the specific steps of the Laplacian noise treatment are as follows:

dividing the initial similarity sequence into a plurality of sets; and any attribute similarity in the initial similarity sequence only appears once in the plurality of sets; respectively carrying out Laplacian noise treatment on each set;

the steps of Laplacian noise treatment are specifically as follows:

setting a first privacy parameter, traversing all the sets, and adding first noise to each attribute similarity in the set if the total number of attribute similarity in the set is larger than the first privacy parameter; if the total number of attribute similarity in the set is smaller than the first privacy parameter, adding second noise to each attribute similarity in the set;

the first noise and the second noise are obtained through probability density function calculation; the probability density function is as follows:

wherein P represents probability, x represents added noise value, x is less than or equal to 0, and lambda represents noise scale.

2. The social graph generating method for protecting personal similarity as recited in claim 1, wherein the noise scale of the first noise is calculated as follows:

λ ₁ ＝kp/ò

the noise scale of the second noise is calculated as follows:

λ ₂ ＝rp/ò

wherein lambda is ₁ A noise scale, lambda, representing the first noise ₂ Representing the noise scale of the second noise, k representing the first privacy parameter, r representing the total number of attribute similarities in the set, p representing the maximum attribute similarity in the initial similarity sequence, co representing the second privacy parameter; the second privacy parameter is obtained by setting.

3. The social graph generating method for protecting personal similarity according to claim 1 or 2, wherein the step of calculating attribute similarity between associated nodes in the initial social graph comprises the following steps:

and obtaining attribute vectors of the associated nodes in the social attribute graph, calculating the distance between the associated nodes through the attribute vectors of the associated nodes and a distance formula, and generating attribute similarity of the associated nodes according to the associated nodes and the associated distance.

4. The social graph generating method for protecting personal similarity as claimed in claim 3, wherein the distance formula is specifically:

wherein i represents node i, j represents node j, node i and node j are associated nodes, l _ij Representing the association distance, x, of the associated nodes i and j _i Attribute vector, x representing node i _j Attribute vector representing node j, S representing x _i And x _j Covariance matrix between them.

5. A social graph generating method for protecting personal similarity as recited in claim 3, wherein the attribute similarity is expressed as (i, j, l) _ij ) Where i represents node i, j represents node j, l _ij Representing the associated distance of the associated nodes i and j.

6. The method for generating a social graph protecting personal similarity according to claim 1, 2, 4 or 5, wherein the step of writing the final similarity sequence into the initial social graph to generate the private social graph is specifically as follows:

dividing the initial social graph into a node set, an edge set and a node attribute set; a private social graph is generated using the final similarity sequence in place of the set of node attributes in the initial social graph.

7. A social graph generating system for protecting personal similarity, characterized in that the steps of a social graph generating method for protecting personal similarity according to any one of claims 1-6 are implemented in the running process; the system comprises an acquisition module, a calculation module, a noise adding module, a rear module and a generation module;

the acquisition module is used for acquiring an initial social graph;

the computing module is used for computing attribute similarity of the associated nodes in the initial social graph and forming an initial similarity sequence;

the noise adding module is used for carrying out noise adding processing on the initial similarity sequence to obtain a noise adding similarity sequence;

the post module is used for carrying out post processing on the noise-added similarity sequence to obtain a final similarity sequence;

the generating module is used for writing the final similarity sequence into the initial social graph to generate a private social graph.