Differential privacy trajectory data publishing method based on density clustering

Abstract

The invention discloses a differential privacy trajectory data publishing method based on density clustering, which belongs to the technical field of trajectory privacy, and comprises the following steps: time generalization: generalizing time attributes in a trajectory by using k-means clustering, and merging positions of similar time nodes into one group; space division: performing grouping division on trajectories belonging to a uniform timestamp in the time generalization trajectory set by using a DENCLUS clustering method; abnormal trajectory processing: forming a generalization trajectory set based on the data after space division, and identifying and deleting abnormal trajectory data in the generalization trajectory set; noise is added to the track and published, Laplace noise of differential privacy is introduced, and the track is published after the real statistical number is confused. By adopting the method, not only is the availability of the trajectory data improved, but also the privacy protection of the trajectory data is enhanced, and the security is improved.

Description

Technical Field

[0001] The present invention relates to the field of trajectory privacy technology, and in particular to a differential privacy trajectory data publishing method based on density clustering. Background Art

[0002] The application of trajectory data is crucial to modern life. Map functions and road planning commonly used in life are developed through the development of trajectory data, but the unreasonable release of trajectory data will lead to the leakage of user privacy. Li et al. proposed an NGTMA algorithm that combines bounded noise constraints and differential privacy technology to achieve high data availability. Ma et al. proposed a new trajectory privacy protection method based on random sampling differential privacy (TPRSDP), which can provide more security protection. However, the existing trajectory data release method based on differential privacy only considers the release method of static trajectory data and is not suitable for the dynamic data processing process generated by personnel flow. Secondly, the k-means clustering algorithm used in the trajectory division process is only applicable to data of specific shapes and has no noise concept, which makes the clustering process prone to large deviations. Summary of the invention

[0003] The purpose of the present invention is to provide a differential privacy trajectory data publishing method based on density clustering to solve the problems mentioned in the above background technology.

[0004] To achieve the above objectives, the present invention provides a differential privacy trajectory data publishing method based on density clustering, the steps comprising:

[0005] Temporal generalization: k-means clustering is used to generalize the temporal attributes in the trajectory, and the positions of nodes with similar time are merged into a group to obtain a temporal generalization trajectory set;

[0006] Spatial partitioning: Use the DENCLUS clustering method to group the trajectories with the same timestamp in the time generalization trajectory set to obtain the cluster center set for each timestamp;

[0007] Abnormal trajectory processing, based on the data after spatial division, a generalized trajectory set is formed, and the abnormal trajectory data in the generalized trajectory set is identified and deleted;

[0008] The trajectory is noisy and published. The original trajectory after statistical abnormal trajectory processing is generated, and a new trajectory is generated. Laplace noise of differential privacy is introduced to confuse the real statistical number before publication.

[0009] Preferably, the time generalization divides the time attribute by a predefined k value and an initial centroid to obtain k time periods, and the specific steps include:

[0010] (1) Select k value and k initial centroids;

[0011] (2) Each time point is divided into the cluster with the nearest center according to the Euclidean distance. The Euclidean distance expression is:

[0012]

[0013] Where, t i and t j represents different moments, d(t i ,t j ) represents the Euclidean distance between the two;

[0014] (3) Calculate the center of each cluster using the formula:

[0015]

[0016] In the formula, u i represents the new centroid;

[0017] (4) Iterate steps (2) and (3) until the maximum number of steps or the difference between the previous and next distances is less than the threshold, the cluster centroid approaches the destination and stops moving, and the closest time cluster set is obtained. The centroid is calculated as the generalized timestamp of the cluster, and finally k time generalized trajectory sets are formed.

[0018] Preferably, when clustering is performed in step (2), all data points (x i ,y i ,t i ) is an independent point, and all time points t i Clustering, locations with similar time points in the trajectory (x i ,y i ) are classified into the same cluster, and by generalizing the time attribute, the time is divided into k fixed time periods Δt i (i=1,2,···,k), the same time period has the same time point.

[0019] Preferably, the specific steps of dividing the space include:

[0020] The k time generalization data sets after time generalization are segmented and divided, and the segmentation results are stored in the data set D;

[0021] Based on the DENCLUS clustering algorithm, the spatial location points are clustered and the trajectory is divided into sub-trajectories. Each sub-trajectory is represented by two points, and the clustering results are stored in the data set O.

[0022] Calculate the center of each cluster and finally get the set of cluster centers for each timestamp.

[0023] Preferably, for a single time point in the time generalization dataset, the sub-trajectory has the same starting point and end point.

[0024] Preferably, the specific steps of abnormal trajectory processing include:

[0025] Compare the trajectory generated at each timestamp with the actual trajectory data;

[0026] The data of the original trajectory corresponding to the newly generated trajectory is counted. When the corresponding original trajectory data is 0, the newly generated trajectory is deleted, and finally a new trajectory set is obtained.

[0027] Preferably, the specific steps of adding noise to the trajectory and publishing it include:

[0028] Count the number of original trajectories n, the number of newly generated trajectories is n1, introduce the Laplace mechanism of differential privacy, and add Laplace noise Lap(S(F) / ε) to the number of real trajectory records;

[0029] set up represents the trajectory of noise count sorting, Ω represents the spatial area, C i express Noise, where C1>C2>···>C i ;

[0030] Starting from the set (C2, C1), use the Laplace method to calculate The amount of noise in the trajectory is located at (C i+1 ,C i )'s expected value Num i , the formula is:

[0031]

[0032] Where f(x,ε) represents the probability density function of the Laplace distribution, After the introduction of Lap(S(F) / ε) A trajectory in the noise content is (C i+1 ,C i ) interval, where The number of each trajectory in is 0;

[0033] Using differential privacy algorithm from The noise amount of different trajectories is randomly selected, and the noise amount of the randomly selected different trajectories is merged with these renewal trajectories, and the sum of the noise-added trajectory data is counted. When the total count is the same as the number of original trajectories, stop adding noise to form an output trajectory data set;

[0034] Publish the obfuscated trajectory dataset.

[0035] Therefore, the present invention adopts the above-mentioned differential privacy trajectory data publishing method based on density clustering, which has the following beneficial effects:

[0036] (1) First, the temporal attributes in the trajectory are generalized by the k-means clustering method, and then the DENCLUS density clustering algorithm is used to perform spatial division to obtain generalized trajectory data, which improves the efficiency and effect of spatial division;

[0037] (2) The abnormal data in the generalized trajectory data was filtered to improve the availability of the published data;

[0038] (3) Laplace noise is added to the trajectory data to enhance the privacy protection of the trajectory data and ensure the privacy of users.

[0039] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0041] Figure 2 Schematic diagram of a trajectory set after time generalization in an embodiment of the present invention;

[0042] Figure 3 Schematic diagram of a trajectory set after spatial division in an embodiment of the present invention;

[0043] Figure 4 This is a comparison chart of the execution time of the TPRSDP, NGTMA and DCT-DP methods with the number of clusters in Example 1 of the present invention;

[0044] Figure 5 This is a comparison chart of the execution time of the TPRSDP, NGTMA and DCT-DP methods in Example 1 of the present invention as the privacy budget ε changes;

[0045] Figure 6 This is a privacy strength protection comparison diagram when the privacy budget ε is 0.1 in Example 1 of the present invention;

[0046] Figure 7 This is a privacy strength protection comparison diagram when the privacy budget ε is 0.5 in Example 1 of the present invention;

[0047] Figure 8 This is a comparison diagram of Hausdorff distance when the privacy budget ε is 0.1 in Example 1 of the present invention;

[0048] Fig. 9 This is a comparison diagram of Hausdorff distance when the privacy budget ε is 0.2 in Example 1 of the present invention;

[0049] Fig.10 This is a comparison diagram of Hausdorff distance when the privacy budget ε is 0.5 in Example 1 of the present invention. DETAILED DESCRIPTION

[0050] Example

[0051] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0052] Reference Figure 1 , a density clustering-based differential privacy trajectory data publishing (DCT-DP) method is provided, the steps comprising:

[0053] Temporal generalization,uses k-means clustering to generalize the temporal attributes in the trajectory,,merges the positions of similar time nodes into a group, and obtains a temporal generalization trajectory set.

[0054] Spatial partitioning,DENCLUS clustering method is used to group and partition the trajectories belonging to the same timestamp in the time generalized trajectory set, and the cluster center set of each timestamp is obtained.

[0055] Abnormal trajectory processing, based on the data after spatial division, a generalized trajectory set is formed, and the abnormal trajectory data in the generalized trajectory set is identified and deleted;

[0056] The trajectory is noisy and published. The original trajectory after statistical abnormal trajectory processing is generated, and a new trajectory is generated. Laplace noise of differential privacy is introduced to confuse the real statistical number before publication.

[0057] Temporal Generalization

[0058] Temporal generalization uses the k-means clustering algorithm to divide the temporal attributes by the predefined k value and the initial centroid to obtain k time periods.

[0059] The specific steps include:

[0060] (1) Select k value and k initial centroids. To ensure the accuracy of trajectory data release, different k values ​​are selected for different situations. If the user moves fast, k needs to take a larger value, and vice versa.

[0061] (2) Each time point is divided into the cluster with the nearest center according to the Euclidean distance. In this process, all data points (x i ,y i ,t i ) is an independent point, and all time points t iClustering, locations with similar time points in the trajectory (x i ,y i ) are classified into the same cluster, and by generalizing the time attribute, the time is divided into k fixed time periods Δt i (i=1,2,···,k), the same time period has the same time point. Figure 2 , positions that are close in time are gathered into the same cluster.

[0062] The Euclidean distance expression is:

[0063]

[0064] Where, t i and t j represents different moments, d(t i ,t j ) represents the Euclidean distance between the two.

[0065] (3) Calculate the center of each cluster using the formula:

[0066]

[0067] In the formula, u i represents the new centroid.

[0068] (4) Iterate steps (2) and (3) until the maximum number of steps or the difference between the previous and next distances is less than the threshold, the cluster centroid approaches the destination and stops moving, and the closest time cluster set is obtained. The centroid is calculated as the generalized timestamp of the cluster, and finally a set of k time generalized trajectories D is formed. time_j (i=1,2,···,k).

[0069] Space Division

[0070] The spatial partitioning process is the output at each time stamp Δt i The cluster center set CP when (i=1,2,···,k) i (i=1,2,···,k), the steps include:

[0071] The k time generalization data sets after time generalization are segmented and divided, and the segmentation results are stored in the data set D.

[0072] Based on the DENCLUS clustering algorithm, the spatial location points are clustered and the trajectory is divided into sub-trajectories. The sub-trajectory is called a line segment. Each line segment is represented by two points. For a separate time point in the time generalization dataset, the starting point and the end point of the line segment are the same point. The clustering results are stored in the dataset O.

[0073] Calculate the center of each cluster and finally get the set of cluster centers for each timestamp. DENCLUS has two parameters: and minPts, determines the maximum distance between two input records, and minPts is the minimum cluster size. If the line segments k and l satisfy They are considered as neighbors. In this embodiment, the optimal The value with the smallest cluster entropy is used. For minPts, the selection is based on the use case, privacy requirements, and the size of the data set. In this embodiment, n / 100 in minPts is generally more advantageous for large clusters, which is easier to generalize and leaks less information. Figure 3 , is the trajectory set after space division, each cluster has a corresponding cluster center, and the points outside the circle are noise points.

[0074] Abnormal trajectory processing

[0075] The focus of abnormal trajectory processing is to check the newly generated trajectory data set and increase the availability of published trajectory data. i , each location point in the region is generalized into |CP i | cluster centers, then for k fixed timestamps, |CP1||CP2|···|CP k | tracks, this data covers the possibility of all track releases.

[0076] The specific steps include:

[0077] The trajectory generated at each timestamp is compared with the real trajectory data.

[0078] The data of the original trajectory corresponding to the newly generated trajectory is counted. When the corresponding original trajectory data is 0, the newly generated trajectory is deleted, and finally a new trajectory set is obtained. The optimization process is shown in Table 1.

[0079] Table 1 Abnormal trajectory processing process

[0080]

[0081] Add noise to the trajectory and publish it

[0082] After deleting the abnormal trajectories, if the trajectory set and its statistical data are directly released, there is a great risk that for a trajectory with a real trajectory record number of 1 (such as l 11 → 22 → 31 , l 12 → 21 → 31), if the attacker has certain background knowledge, it is possible to guess that the trajectory belongs to the user, resulting in information leakage. Therefore, the trajectory information needs to be obfuscated before it is published.

[0083] The specific steps include:

[0084] Count the number of original trajectories n, the number of newly generated trajectories is n1, introduce the Laplace mechanism of differential privacy, and add Laplace noise Lap(S(F) / ε) to the number of real trajectory records;

[0085] set up represents the trajectory of noise count sorting, Ω represents the spatial area, C i express Noise, where C1>C2>···>C i ;

[0086] Starting from the set (C2, C1), use the Laplace method to calculate The amount of noise in the trajectory is located at (C i+1 ,C i )'s expected value Num i , the formula is:

[0087]

[0088] Where f(x,ε) represents the probability density function of the Laplace distribution, After the introduction of Lap(S(F) / ε) A trajectory in the noise content is (C i+1 ,C i ) interval, where The number of each track is 0.

[0089] Using differential privacy algorithm from The noise amount of different trajectories randomly selected in the original trajectory dataset of these renewal trajectories is compared with the noise amount of different trajectories randomly selected in the original trajectory dataset of these renewal trajectories. Merge, count the sum of the noisy trajectory data, and when the total count is the same as the number of original trajectories, stop adding noise to form the output trajectory dataset.

[0090] The obfuscated trajectory dataset is published, and the publishing process is shown in Table 2.

[0091] Table 2 Trajectory publishing process

[0092]

[0093] Example 1

[0094] In order to verify the efficiency, privacy and data availability of the DCT-DP model, an experimental comparison was conducted with the NGTMA and TPRSDP methods. This embodiment runs on a desktop with an Intel Core i9-7960X CPUs with a 2.8GHz processor and 16G memory. The Microsoft Research'T-Drive project database was selected. This dataset counts the trajectory operation data of Beijing taxi drivers within a week in 2008. The attributes included in the dataset are: user name, time, longitude, and latitude. The trajectory data of 3,000 taxis were randomly selected from the dataset for experimental comparison.

[0095] Algorithm efficiency

[0096] The privacy protection parameter ε and the size of the trajectory data set are selected for analysis. In this embodiment, the number of clustering groups selected is 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and the privacy budget is 0, 0.2, 0.4, 0.6, 0.8. Each configuration is repeated 10 times and the average result is calculated.

[0097] Figure 4 and Figure 5 Comparison of the time consumption of NGTMA, TPRSDP and DCT-DP methods. Figure 4 It can be seen that as the number of clusters increases, the time cost of the three methods increases. Figure 5 It can be seen that when the number of clusters is constant, as the privacy budget ε increases, the privacy protection capability gradually decreases, the computational cost decreases, and the execution time of the three algorithms decreases linearly. Figure 4 and 5 It can be seen that the time cost of the DCT-DP method is much lower than that of NGTMA, but slightly higher than that of TPRSDP. The TPRSDP method selects the position sample division according to the sample rate of 0.6, which reduces the sample size and thus reduces the time cost, so it is more efficient. The DCT-DP method is relatively stable in terms of time consumption. The DCT-DP method uses the DENCLUS algorithm in the spatial division process, which will mark more noise points during the division, thereby reducing the time consumption of the iterative process. Therefore, the DCT-DP model performs better on large data sets.

[0098] Privacy

[0099] According to the definition of the differential privacy model, the privacy parameter ε is used to measure the strength of privacy protection, and a smaller ε provides a higher privacy protection strength. Mutual Information (MI) is used to measure the privacy protection degree of the DCT-DP method. Mutual information measures the degree of mutual dependence between two random variables X and Y. If X and Y are two identical variables, knowing X determines the value of Y, and vice versa; if X and Y are independent, knowing X cannot infer any information about Y, and vice versa, so the mutual information between them is zero. The definition of mutual information is as follows: Given functions x(t) and y(t), time series t=1,2,3,···,N, then the mutual information between x(t) and y(t) is defined as

[0100]

[0101] We selected privacy parameters ε = 0.1 and ε = 0.5 to analyze the changes in mutual information values ​​of the three schemes with the number of clusters. Each configuration was repeated 10 times and the average result was calculated. Figure 6 , 7 As shown. The x-axis represents the number of clusters and the y-axis represents MI. When the privacy budget is 0.1, the privacy loss of DCT-DP is 59.1% smaller than that of NGTMA and 30.1% smaller than that of TPRSDP on average. When the privacy budget is 0.5, the privacy loss of DCT-DP is 31.5% smaller than that of NGTMA and 28.1% smaller than that of TPRSDP on average. The main reason is that noise points are removed during the spatial partitioning process, and abnormal trajectories are deleted to optimize the generalized trajectory dataset, thereby reducing the impact of abnormal trajectories and improving privacy.

[0102] Availability

[0103] Hausdorff distance (HD) is used to measure the availability of data. Hausdorff distance is widely used to measure the similarity between two point sets. The point set D can be calculated relative to the point set The utility:

[0104]

[0105] in The smaller the utility (D) value, the closer the point set D is to the point set The higher the similarity, the better the data utility of the dataset D. In this embodiment, HD calculates the distance between the true count of the merged trajectory and its noise count.

[0106] We selected privacy budget ε as 0.1, 0.2, and 0.5 to analyze the three schemes, repeated each configuration 10 times, and calculated the average result. Figure 8 , 9 , 10, where the x-axis represents the number of clusters and the y-axis represents HD. Figure 8 , 9 , 10, it can be seen that the larger the value of ε, the smaller the HD, and the greater the data utility of the privacy protection algorithm. In addition, in the three sets of experimental result graphs, compared with NGTMA and TPRSDP, the proposed DCT-DP method has a smaller HD in most cases, and the curve fluctuation is relatively stable. Therefore, the data generated by the DCT-DP method has higher data utility and stable effect, while the HD value of TPRSDP fluctuates greatly and has poor stability.

[0107] Therefore, the differential privacy trajectory data publishing method based on density clustering provided in this application effectively improves the privacy and effectiveness of trajectory publishing.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A differential privacy trajectory data publishing method based on density clustering, characterized in that the steps include: Temporal generalization: k-means clustering is used to generalize the temporal attributes in the trajectory, and the positions of nodes with similar time are merged into a group to obtain a temporal generalization trajectory set; Spatial partitioning: Use the DENCLUS clustering method to group the trajectories with the same timestamp in the time generalization trajectory set to obtain the cluster center set for each timestamp; Abnormal trajectory processing, based on the data after spatial division, a generalized trajectory set is formed, and the abnormal trajectory data in the generalized trajectory set is identified and deleted; The trajectory is noisy and published. The original trajectory after statistical abnormal trajectory processing is generated, and a new trajectory is generated. Laplace noise of differential privacy is introduced to confuse the real statistical number before publication.

2. According to claim 1, a differential privacy trajectory data publishing method based on density clustering is characterized in that: The time generalization divides the time attribute by a predefined k value and an initial centroid to obtain k time periods. The specific steps include: (1) Select k value and k initial centroids; (2) Each time point is divided into the cluster with the nearest center according to the Euclidean distance. The Euclidean distance expression is: Where, t i and t j represents different moments, d(t i ,t j ) represents the Euclidean distance between the two; (3) Calculate the center of each cluster using the formula: In the formula, u i represents the new centroid; (4) Iterate steps (2) and (3) until the maximum number of steps or the difference between the previous and next distances is less than the threshold, the cluster centroid approaches the destination and stops moving, and the closest time cluster set is obtained. The centroid is calculated as the generalized timestamp of the cluster, and finally k time generalized trajectory sets are formed.

3. The method for publishing differentially private trajectory data based on density clustering according to claim 2, characterized in that: When clustering is performed in step (2), all data points (x i ,y i ,t i ) is an independent point, and all time points t i Clustering, locations with similar time points in the trajectory (x i ,y i ) are classified into the same cluster, and by generalizing the time attribute, the time is divided into k fixed time periods Δt i (i=1,2,···,k), the same time period has the same time point.

4. According to claim 3, a differential privacy trajectory data publishing method based on density clustering is characterized in that: The specific steps of the space division include: The k time generalization data sets after time generalization are segmented and divided, and the segmentation results are stored in the data set D; Based on the DENCLUS clustering algorithm, the spatial location points are clustered and the trajectory is divided into sub-trajectories. Each sub-trajectory is represented by two points, and the clustering results are stored in the data set O. Calculate the center of each cluster and finally get the set of cluster centers for each timestamp.

5. According to claim 4, a density clustering-based differential privacy trajectory data publishing method is characterized by: For a single time point in the time generalization dataset, the sub-trackline has the same starting point and end point.

6. According to claim 5, a differential privacy trajectory data publishing method based on density clustering is characterized in that: The specific steps of abnormal trajectory processing include: Compare the trajectory generated at each timestamp with the actual trajectory data; The data of the original trajectory corresponding to the newly generated trajectory is counted. When the corresponding original trajectory data is 0, the newly generated trajectory is deleted, and finally a new trajectory set is obtained.

7. According to claim 6, a differential privacy trajectory data publishing method based on density clustering is characterized in that: The specific steps of adding noise to the trajectory and publishing it include: Count the number of original trajectories n, the number of newly generated trajectories is n1, introduce the Laplace mechanism of differential privacy, and add Laplace noise Lap(S(F) / ε) to the number of real trajectory records; set up represents the trajectory of noise count sorting, Ω represents the spatial area, C i express Noise, where C1>C2>···>C i ; Starting from the set (C2, C1), use the Laplace method to calculate The amount of noise in the trajectory is located at (C i+1 ,C i )'s expected value Num i , the formula is: Where f(x,ε) represents the probability density function of the Laplace distribution, After the introduction of Lap(S(F) / ε) A trajectory in the noise content is (C i+1 ,C i ) interval, where The number of each trajectory in is 0; Using differential privacy algorithm from The noise amount of different trajectories is randomly selected, and the noise amount of the randomly selected different trajectories is merged with these renewal trajectories, and the sum of the noise-added trajectory data is counted. When the total count is the same as the number of original trajectories, stop adding noise to form an output trajectory data set; Publish the obfuscated trajectory dataset.

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