CN106295395A - The uncertain method for protecting track privacy divided based on figure - Google Patents

Abstract

The invention discloses a privacy protection method for uncertain trajectories based on graph division, which includes step (1) data preprocessing: preprocessing the original trajectory data set, so that there is intersection between uncertain trajectories in the time dimension, and each Determine that the trajectory has the same number of sampling points; step (2) construction of correlation degree: extract time feature, direction feature and distance feature from the preprocessed trajectory data, and calculate the correlation degree between different uncertain trajectories; step ( 3) Undirected graph construction: map the trajectory data set into an undirected graph, each node in the undirected graph represents a trajectory, and the weight of the edge between nodes represents the degree of association between two corresponding uncertain trajectories; Step (4) Undirected graph division: Use the greedy algorithm to divide the undirected graph to form several clusters containing k uncertain trajectories. The invention allows users to balance data information loss and privacy level according to privacy protection requirements.

Description

Privacy Preservation Method for Uncertain Trajectories Based on Graph Partitioning

technical field

The invention relates to the field of graph theory, in particular to an uncertain trajectory privacy protection method based on graph division.

Background technique

In the era of smart cities and the Internet of Things, it is easy for people to collect various data, such as location, time, speed, etc., from mobile devices such as mobile phones equipped with GPS. The collected data can provide people with location-based services (LBS), such as finding the nearest gas station, hospital, etc. Due to the low accuracy of the collection equipment or collection errors, there may be errors in the longitude and latitude collected. While location-based service LBS brings convenience to users, it also has potential safety hazards. The release of uncertain trajectory data is easy to leak the privacy of users, so the privacy processing of the release of uncertain trajectory data in offline scenarios becomes extremely important.

In the research released by the trajectory, the k-anonymity technology has become the mainstream. There have been some works based on graph partitioning to construct trajectory k-anonymity sets. It has been proved that the problem of partitioning k-node graph and constructing trajectory k-anonymous set is NP-complete. Trajectory datasets can be represented by an undirected graph, where nodes represent trajectories, and edge weights represent the degree of association between trajectories. However, their method only uses the proportion of overlapping points between trajectories to measure the similarity between trajectories, but does not consider the directional similarity. Therefore, they also consider the directional similarity of trajectories and the distance between trajectories, and propose a personalized The privacy protection method strikes a balance between data utility and privacy level. Although this method finally achieves the purpose of privacy protection, there are still some deficiencies. First of all, it does not take into account the uncertainty of the trajectory. Due to the limited accuracy of GPS acquisition equipment or acquisition errors, errors will inevitably occur. The uncertainty of trajectories will affect the calculation of the distance between trajectories and the similarity of trajectory directions; secondly, this method does not consider the similarity of trajectories in the time dimension, but processes the trajectories into time in the preprocessing stage of trajectory data. In the same interval, the time difference is eliminated, which makes the algorithm less feasible.

Therefore, the privacy protection of uncertain trajectories with low acquisition accuracy, the balance of data information loss and privacy level, has become the main research direction of those skilled in the art.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art and provide a privacy protection method for uncertain trajectories based on graph division.

The technical scheme adopted in the present invention is:

An uncertain trajectory privacy protection method based on graph partitioning, which includes the following steps:

Step (1) Data preprocessing: Preprocessing the original trajectory data set, so that there is an intersection between uncertain trajectories in the time dimension, and each uncertain trajectory has the same number of sampling points;

Step (2) Correlation degree construction: extract time feature, direction feature and distance feature from the preprocessed trajectory data, and calculate the correlation degree between different uncertain trajectories according to the time feature, direction feature and distance feature;

Step (3) Undirected graph construction: map the trajectory data set into an undirected graph, each node in the undirected graph represents a trajectory, and the weight of the edges between nodes represents the association between two corresponding uncertain trajectories Spend;

Step (4) Undirected graph division: Use the greedy algorithm to divide the undirected graph to form several clusters containing k uncertain trajectories. We sort the edges in the edge set in ascending order of weight from small to large, find out the smallest edge, take out its two end nodes and put them into the set R _i . When the number of nodes in the set R _i is less than k, never From the selected node set, select the node with the highest degree of correlation with the node in R _i , and put it into the set R _i , until the number of nodes in the set R _i meets k. After the selection, the remaining ones that are not enough to make up the set of k nodes are discarded.

Further, the number of sampling points in the step (1) is 30.

Further, the sum of the weights of the time feature, direction feature, and distance feature in the step (2) must be 1, and the weights of the three parts can be adjusted according to the user's individual needs to achieve the level of privacy protection and data availability balance between.

Further, the calculation of the degree of association between uncertain trajectories in the step (2) includes the following steps:

A, respectively calculate the uncertain radius of the two uncertain trajectories;

B, calculate the trajectory direction similarity of the uncertain trajectory;

C, calculate the trajectory distance of the uncertain trajectory;

D, calculate the trajectory time similarity of the uncertain trajectory;

E, Calculate the degree of correlation between two uncertain trajectories.

The calculation method of the uncertain radius of the uncertain trajectory in the step A is:

A1, let Tp and Tq respectively represent two uncertain trajectories that need to calculate the uncertain radius;

A2, calculate the velocity of the trajectory Tp at the i-th sampling point

in represents the longitude of the i-th sampling point of the trajectory Tp, Represents the latitude of the i-th sampling point of the trajectory Tp; Represents the longitude of the i+1 sampling point of the trajectory Tp, Represents the latitude of the i+1 sampling point of the trajectory Tp, Represents the sampling time of the i-th point of the trajectory Tp, Represents the sampling time of the i+1th point of the trajectory Tp;

A3, calculate the velocity of the trajectory Tq at the i-th sampling point

in represents the longitude of the i-th sampling point of the trajectory Tq, Represents the latitude of the i-th sampling point of the trajectory Tq; Represents the longitude of the i+1th sampling point of the trajectory Tq, Represents the latitude of the i+1 sampling point of the trajectory Tq, Represents the sampling time of the i-th point of the trajectory Tq, Represents the sampling time of the i+1th point of the trajectory Tq;

A4, calculate the uncertainty radius of the trajectory Tp at the i-th sampling point Calculate the uncertainty radius of the trajectory Tq at the i-th sampling point

The calculation method of the trajectory direction similarity of the uncertain trajectory in the step B is:

B1, calculate the expected angle cosine of the direction of the i-th sub-trajectory of the trajectory Tp and Tq:

in is the expected angle cosine of the direction of the i-th sub-trajectory of the trajectories Tp and Tq, is the direction vector of the i-th sub-trajectory of the trajectory Tp, is the direction vector of the i-th sub-trajectory of the trajectory Tq;

B2, calculate the angular variation range of the i-th sub-trajectory of the trajectory Tp and Tq in is the angular change range of the i-th sub-trajectory of the trajectory Tp, is the angle change range of the i-th sub-track of the track Tq:

order vector recorded as vector recorded as

in Indicates the longitude coordinates of the i-th sampling point of the p-th trajectory Tp, Indicates the longitude coordinates of the i+1th sampling point of the pth track, Indicates the uncertainty radius of the i+1 sampling point of the p-th trajectory Tp, Indicates the uncertainty radius of the i-th sampling point of the p-th trajectory Tp, Indicates the latitude coordinates of the i-th sampling point of the p-th trajectory Tp, Represents the latitude coordinates of the i+1 sampling point of the p-th track Tp;

Then the angle change range of the trajectory T _p on the i-th sub-trajectory Corresponding cosine value satisfy

In the same way, calculate the angle change range of the trajectory T _q on the i-th sub-trajectory cosine of

The difference in angle change between uncertain trajectory segments is available by and derived indirectly;

B3, the calculation records the directional similarity of the trajectory as S _dire [ζ,p,q],

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; \&zeta;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; \&rsqb;</span>}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&rsqb;</span>}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \&rsqb;</span>}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Where n is the number of sampling points.

In the step C, the trajectory distance is the sum of the Euclidean distance of the expected coordinates of the two sampling points and the respective uncertain radii, and the specific calculation method of the trajectory distance includes the following steps:

C1, define the Euclidean distance between the trajectory and the expected coordinates of two sampling points as Then the distance between any two trajectories corresponding to a certain trajectory segment is:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

in To calculate the uncertainty radius of the trajectory Tp at the i-th sampling point, To calculate the uncertainty radius of the trajectory Tq at the i-th sampling point;

C2, define the distance between any two trajectories as:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; \&zeta;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; minmaxD</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

The specific calculation method of the trajectory time similarity described in the step D is:

D1, order and represent the start time and end time of the trajectory Tp, respectively, and represent the start time and end time of the trajectory Tq, respectively;

D2, the trajectory time similarity S _time [p,q] of the uncertain trajectory Tp and Tq is:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

The calculation of the correlation degree of the two uncertain trajectories in the step E is obtained by the following formula:

W _pq ＝α·(1-S _time [T _p ,T _q ])+β·(1-S _dire [ζ,T _p ,T _q ])+γ·D _loc [ζ,T _p ,T _q ] (6)

where W _pq is the correlation degree between uncertain trajectories Tp and Tq, S _time [T _p , T _q ] is the time similarity between uncertain trajectories Tp and Tq, S _dire [ζ, T _p , T _q ] is the Determine the trajectory direction similarity of the trajectory Tp and Tq, D _loc [ζ,T _p ,T _q ] is the trajectory distance of the uncertain trajectory Tp and Tq, α is the time similarity of the uncertain trajectory Tp and Tq S _time [T _p ,T _q ] weight coefficient, β is the weight coefficient of the trajectory direction similarity S _dire [ζ,T _p ,T _q ] of the uncertain trajectory Tp and Tq, and γ is the trajectory distance D _loc [ ζ, T _p , T _q ] weight coefficients.

The present invention adopts the above technical scheme, uses time overlap similarity, direction similarity and distance between uncertain trajectories, measures the degree of correlation between uncertain trajectories, and maps the trajectory data set into an undirected graph, the undirected Each node in the graph represents an uncertain trajectory, and the weight of the edges between nodes represents the degree of association between two corresponding uncertain trajectories. Finally, a greedy algorithm is used to divide the undirected graph to form several clusters containing k trajectories to realize k anonymity. Preprocessing the collected original trajectory data mainly refers to the need to ensure that there is an intersection between the trajectories in the time dimension, such as jointly containing the time interval [t1, t2], and each trajectory has the same sampling The number of points, for example, there are 30 longitude and latitude sampling points;

Compared with the prior art, the effect of the present invention is that it can more comprehensively and flexibly cluster uncertain trajectories in data publishing scenarios, and realize a trade-off between privacy level and data practicability. In terms of data acquisition and processing, considering the limited accuracy of acquisition equipment and possible acquisition errors, the privacy protection of uncertain trajectories is emphasized; and in the aspect of correlation degree measurement between trajectories, the present invention considers that under the condition of uncertain trajectories, no Determine the influence of factors on the similarity of trajectory direction and the distance between trajectories, as well as the overlapping similarity between trajectories in the time dimension. The privacy protection method for uncertain trajectories can more comprehensively and flexibly cluster uncertain trajectories in data publishing scenarios, and achieve a trade-off between privacy level and data utility.

Description of drawings

The present invention will be described in further detail below in conjunction with accompanying drawing and specific embodiment;

Figure 1 is a flow chart of the privacy protection method for uncertain trajectories based on graph partitioning in the present invention

Fig. 2 is the uncertain trajectory direction diagram of the uncertain trajectory privacy protection method based on graph division in the present invention;

Fig. 3 is the distance diagram between uncertain trajectories of the uncertain trajectory privacy protection method based on graph division in the present invention;

Fig. 4 is the privacy level assessment diagram of the uncertain trajectory privacy protection method based on graph division in the present invention;

Fig. 5 is an information loss assessment diagram of the uncertain trajectory privacy protection method based on graph division in the present invention;

Fig. 6 is a graph showing the relationship between the uncertainty coefficient ζ and the information loss of the privacy protection method for uncertain trajectories based on graph partitioning in the present invention.

detailed description

As shown in one of Figures 1-6, several definitions involved in the method of the present invention are as follows:

It includes the following steps:

Step (1) Data preprocessing: preprocessing the original trajectory data set, so that there is an intersection between uncertain trajectories in the time dimension, and each uncertain trajectory has the same number of sampling points;

Step (2) Correlation degree construction: extract time feature, direction feature and distance feature from the preprocessed trajectory data, and calculate the correlation degree between different uncertain trajectories according to the time feature, direction feature and distance feature;

Step (3) Undirected graph construction: map the trajectory data set into an undirected graph, each node in the undirected graph represents a trajectory, and the weight of the edges between nodes represents the association between two corresponding uncertain trajectories Spend;

Step (4) Undirected graph division: Use the greedy algorithm to divide the undirected graph to form several clusters containing k uncertain trajectories. We sort the edges in the edge set in ascending order of weight from small to large, find out the smallest edge, take out its two end nodes and put them into the set R _i . When the number of nodes in the set R _i is less than k, never From the selected node set, select the node with the highest degree of correlation with the node in R _i , and put it into the set R _i , until the number of nodes in the set R _i meets k. After the selection, the remaining ones that are not enough to make up the set of k nodes are discarded.

Further, the number of sampling points in the step (1) is 30.

Further, the sum of the weights of the time feature, direction feature, and distance feature in the step (2) must be 1, and the weights of the three parts can be adjusted according to the individual needs of the user to achieve the level of privacy protection and data availability balance between.

Further, the calculation of the degree of association between uncertain trajectories in the step (2) includes the following steps:

A, respectively calculate the uncertain radius of the two uncertain trajectories;

B, calculate the trajectory direction similarity of the uncertain trajectory;

C, calculate the trajectory distance of the uncertain trajectory;

D, calculate the trajectory time similarity of the uncertain trajectory;

E, Calculate the degree of correlation between two uncertain trajectories.

Further, the calculation method of the uncertain radius of the uncertain trajectory in the step A is:

A1, let Tp and Tq respectively represent two uncertain trajectories that need to calculate the uncertain radius;

A2, calculate the velocity of the trajectory Tp at the i-th sampling point

in represents the longitude of the i-th sampling point of the trajectory Tp, Represents the latitude of the i-th sampling point of the trajectory Tp; Represents the longitude of the i+1 sampling point of the trajectory Tp, Represents the latitude of the i+1 sampling point of the trajectory Tp, Represents the sampling time of the i-th point of the trajectory Tp, Represents the sampling time of the i+1th point of the trajectory Tp;

A3, calculate the velocity of the trajectory Tq at the i-th sampling point

in represents the longitude of the i-th sampling point of the trajectory Tq, Represents the latitude of the i-th sampling point of the trajectory Tq; Represents the longitude of the i+1th sampling point of the trajectory Tq, Represents the latitude of the i+1 sampling point of the trajectory Tq, Represents the sampling time of the i-th point of the trajectory Tq, Represents the sampling time of the i+1th point of the trajectory Tq;

A4, calculate the uncertainty radius of the trajectory Tp at the i-th sampling point Calculate the uncertainty radius of the trajectory Tq at the i-th sampling point

Further, as shown in Figure 2, the calculation method of the trajectory direction similarity of the uncertain trajectory in the step B is:

B1, calculate the expected angle cosine of the direction of the i-th sub-trajectory of the trajectory Tp and Tq:

in is the expected angle cosine of the direction of the i-th sub-trajectory of the trajectories Tp and Tq, is the direction vector of the i-th sub-trajectory of the trajectory Tp, is the direction vector of the i-th sub-trajectory of the trajectory Tq; if the The cosine value of is less than 0, which means that the moving directions of the two sub-track segments are opposite, and the cosine value is set to 0 at this time. The change range of the direction angle cosine is [0,1]. Due to the characteristics of the cosine curve, the more similar the direction is, the larger the cosine value is, and the larger the direction difference is, the smaller the cosine value is;

B2, calculate the angular variation range of the i-th sub-trajectory of the trajectory Tp and Tq in is the angular change range of the i-th sub-trajectory of the trajectory Tp, is the angle change range of the i-th sub-track of the track Tq:

order vector recorded as vector recorded as

in Indicates the longitude coordinates of the i-th sampling point of the p-th trajectory Tp, Indicates the longitude coordinates of the i+1th sampling point of the pth track, Indicates the uncertainty radius of the i+1 sampling point of the p-th trajectory Tp, Indicates the uncertainty radius of the i-th sampling point of the p-th trajectory Tp, Indicates the latitude coordinates of the i-th sampling point of the p-th trajectory Tp, Represents the latitude coordinates of the i+1 sampling point of the p-th track Tp;

Then the angle change range of the trajectory T _p on the i-th sub-trajectory Corresponding cosine value satisfy

In the same way, calculate the angle change range of the trajectory T _q on the i-th sub-trajectory cosine of

To measure the uncertain direction similarity between trajectories T _p and T _q at the i-th trajectory segment, we define the angular change difference between uncertain trajectory segments as can be made by and derived indirectly. The range of variation is between [0, 1]. The closer to 1, the smaller the angle change between uncertain trajectory segments, and the more similar in direction and latitude between uncertain trajectory segments; the closer to 0, the less similar they are. which when If it is less than 0, it means that the angle change difference between the two trajectory segments is too large, so we set it to 0.

B3, the calculation records the directional similarity of the trajectory as S _dire [ζ,p,q],

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; \&zeta;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\frac{{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; \&rsqb;</span>}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&rsqb;</span>}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \&rsqb;</span>}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Where n is the number of sampling points.

Further, as shown in Figure 3, the trajectory distance in the step C is the sum of the Euclidean distance of the expected coordinates of the two sampling points and the respective uncertain radii, and the specific calculation method of the trajectory distance includes the following steps:

C1, define the Euclidean distance between the trajectory and the expected coordinates of two sampling points as Then the distance between any two trajectories corresponding to a certain trajectory segment is:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

in To calculate the uncertainty radius of the trajectory Tp at the i-th sampling point, To calculate the uncertainty radius of the trajectory Tq at the i-th sampling point;

C2, define the distance between any two trajectories as:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; \&zeta;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; minmaxD</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

Further, the specific calculation method of the trajectory time similarity in the step D is:

D1, order and represent the start time and end time of the trajectory Tp, respectively, and represent the start time and end time of the trajectory Tq, respectively;

D2, the trajectory time similarity S _time [p,q] of the uncertain trajectory Tp and Tq is:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span>$

Further, the calculation of the correlation degree of the two uncertain trajectories in the step E is obtained by the following formula:

W _pq ＝α·(1-S _time [T _p ,T _q ])+β·(1-S _dire [ζ,T _p ,T _q ])+γ·D _loc [ζ,T _p ,T _q ] (6)

where W _pq is the correlation degree between uncertain trajectories Tp and Tq, S _time [T _p , T _q ] is the time similarity between uncertain trajectories Tp and Tq, S _dire [ζ, T _p , T _q ] is the Determine the trajectory direction similarity of the trajectory Tp and Tq, D _loc [ζ,T _p ,T _q ] is the trajectory distance of the uncertain trajectory Tp and Tq, α is the time similarity of the uncertain trajectory Tp and Tq S _time [T _p ,T _q ] weight coefficient, β is the weight coefficient of the trajectory direction similarity S _dire [ζ,T _p ,T _q ] of the uncertain trajectory Tp and Tq, and γ is the trajectory distance D _loc [ ζ, T _p , T _q ] weight coefficients.

The present invention adopts the above technical scheme, uses time overlap similarity, direction similarity and distance between uncertain trajectories, measures the degree of correlation between uncertain trajectories, and maps the trajectory data set into an undirected graph, the undirected Each node in the graph represents an uncertain trajectory, and the weight of the edges between nodes represents the degree of association between two corresponding uncertain trajectories. Finally, a greedy algorithm is used to divide the undirected graph to form several clusters containing k trajectories to realize k anonymity. Preprocessing the collected original trajectory data mainly refers to the need to ensure that there is an intersection between the trajectories in the time dimension, such as jointly containing the time interval [t1, t2], and each trajectory has the same sampling The number of points, for example, there are 30 longitude and latitude sampling points;

Compared with the prior art, the effect of the present invention is that it can more comprehensively and flexibly cluster uncertain trajectories in a data release scenario, and realize a trade-off between privacy level and data practicability. In terms of data acquisition and processing, considering the limited accuracy of acquisition equipment and possible acquisition errors, the privacy protection of uncertain trajectories is emphasized; and in the aspect of correlation degree measurement between trajectories, the present invention considers that under the condition of uncertain trajectories, no Determine the influence of factors on the similarity of trajectory direction and the distance between trajectories, as well as the overlapping similarity between trajectories in the time dimension. The privacy protection method for uncertain trajectories can more comprehensively and flexibly cluster uncertain trajectories in data release scenarios, and achieve a trade-off between privacy level and data utility.

The above description is only an embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent transformations made by using the description of the present invention and the contents of the accompanying drawings, or directly or indirectly used in related technical fields, are all included in the same principle. The patent protection scope of the present invention.

Claims (9)

1. the uncertain method for protecting track privacy divided based on figure, it is characterised in that: it comprises the following steps:

Step (1) data prediction: initial trace data set is carried out pretreatment so that at time dimension between uncertain track On have common factor, and every uncertain track has same sampled point number；

Step (2) degree of association builds: to track data extraction time feature, direction character and distance feature after pretreatment, The degree of association between different uncertain tracks is calculated according to temporal characteristics, direction character and distance feature；

Step (3) non-directed graph builds: track data collection is mapped to a non-directed graph, each node on behalf one in this non-directed graph Track, between node, the weights on limit represent the degree of association between two corresponding uncertain tracks；

Step (4) non-directed graph divides: utilizes greedy algorithm to divide non-directed graph, forms several and contain the uncertain rail of k bar The cluster of mark.

The uncertain method for protecting track privacy divided based on figure the most according to claim 1, it is characterised in that: described step Suddenly the sampled point number of (1) is 30.

The uncertain method for protecting track privacy divided based on figure the most according to claim 1, it is characterised in that: described step Suddenly the weight sum of temporal characteristics, direction character and the distance feature in (2) is necessary for 1, can be according to the individual demand of user Adjust the weight of three parts.

The uncertain method for protecting track privacy divided based on figure the most according to claim 1, it is characterised in that: described step Suddenly in (2), the calculating of the degree of association between uncertain track comprises the following steps:

A, calculates the uncertain radius of two uncertain tracks respectively；

B, calculates the course bearing similarity of uncertain track；

C, calculates the track distance of uncertain track；

D, calculates the trajectory time similarity of uncertain track；

E, calculates the degree of association of two uncertain tracks.

The uncertain method for protecting track privacy divided based on figure the most according to claim 4, it is characterised in that: described step In rapid A, the computational methods of the uncertain radius of uncertain track are:

A1, makes Tp and Tq represent two the uncertain tracks needing to calculate uncertain radius respectively；

A2, calculates the track Tp speed at ith sample point

WhereinRepresent the longitude of track Tp the i-th sampled point,Represent the latitude of track Tp the i-th sampled point；Represent track Tp The longitude of i+1 sampled point,Represent the latitude of track Tp i+1 sampled point,Represent the sampling time of track Tp i-th,Represent the sampling time of track Tp i+1 point；

A3, calculates the track Tq speed at ith sample point

WhereinRepresent the longitude of track Tq the i-th sampled point,Represent the latitude of track Tq the i-th sampled point；Represent track Tq The longitude of i+1 sampled point,Represent the latitude of track Tq i+1 sampled point,Represent the sampling time of track Tq i-th,Represent the sampling time of track Tq i+1 point；

A4, calculates the track Tp uncertain radius at ith sample pointCalculate track Tq at ith sample point Uncertain radius

The uncertain method for protecting track privacy divided based on figure the most according to claim 5, it is characterised in that: described step In rapid B, the computational methods of the course bearing similarity of uncertain track are:

B1, calculating track Tp and Tq is at the direction expected angle cosine of the i-th cross-talk track:

$cos{\&lsqb;\mathrm{\&theta;}\&rsqb;}_{pq}^i=\frac{\stackrel{\&RightArrow;}{T_p^i\&CenterDot;}\stackrel{\&RightArrow;}{T_q^i}}{\left|\stackrel{\&RightArrow;}{T_p^i}\right|\&CenterDot;\left|\stackrel{\&RightArrow;}{T_q^i}\right|}---\left(1\right);$

WhereinFor track Tp and Tq at the direction expected angle cosine of the i-th cross-talk track,For track Tp at i-th section The direction vector of sub-trajectory,For track Tq at the direction vector of the i-th cross-talk track；

B2, calculates track Tp and the Tq angle excursion at the i-th cross-talk trackWhereinFor track Tp in the angle excursion of the i-th cross-talk track,For track Tq in the angle excursion of the i-th cross-talk track:

Order vectorIt is designated asVectorIt is designated as WhereinRepresent the longitude coordinate of the ith sample point of pth bar track Tp,Represent pth bar track i+1 sampled point Longitude coordinate,Represent the uncertain radius of pth bar track Tp i+1 sampled point,Represent that pth bar track Tp i-th is adopted The uncertain radius of sampling point,Represent the latitude coordinate of pth bar track Tp ith sample point,Represent pth bar track Tp i-th The latitude coordinate of+1 sampled point；

Then track T_pAngle excursion on the i-th cross-talk trackCorresponding cosine valueMeet

In like manner calculate track T_qAngle excursion on the i-th cross-talk trackCosine value

Angle change difference between uncertain orbit segment isCan be byWithIndirect Go out；

B3, calculates and the directional similarity of track is designated as S_dire[ζ, p, q],

$S_{dire}\&lsqb;\mathrm{\&zeta;},p,q\&rsqb;=\frac{\underset{i=1}{\overset{n-1}{\&Sigma;}}\left(\frac{{\&lsqb;cos\mathrm{\&theta;}\&rsqb;}_{pq}^i+cos({\&lsqb;{\mathrm{\&theta;}}_2\&rsqb;}_p^i-{\&lsqb;{\mathrm{\&theta;}}_3\&rsqb;}_q^i)}{2}\right)}{n-1}---\left(2\right)$

Wherein n is sampled point number.

The uncertain method for protecting track privacy divided based on figure the most according to claim 6, it is characterised in that: described step In rapid C, track distance is Euclidean distance and respective uncertain radius sum, the tool of track distance of two sampled point expectation coordinates Body computational methods comprise the following steps:

C1, the Euclidean distance of two sampled point expectation coordinates of definition track distance is designated asRight in the most any two tracks Should the distance between a certain orbit segment be:

$D_{pq}^{pa}\&lsqb;i\&rsqb;={\mathrm{\&delta;}}_p^i+{\mathrm{\&delta;}}_q^i+D_{pq}^{center}---\left(3\right),$

WhereinFor calculating the track Tp uncertain radius at ith sample point,For calculating track Tq at ith sample point Uncertain radius；

C2, the distance defining any two tracks is:

$D_{loc}\&lsqb;\mathrm{\&zeta;},p,q\&rsqb;={\mathrm{minmaxD}}_{pq}^{pa}\&lsqb;i\&rsqb;(i=1,2,...,n-1)---\left(4\right).$

The uncertain method for protecting track privacy divided based on figure the most according to claim 7, it is characterised in that: described step Described in rapid D, the circular of trajectory time similarity is:

D1, orderWithRepresent initial time and the end time of track Tp respectively,WithRepresent track Tq's respectively Initial time and end time；

The trajectory time similarity S of D2, uncertain track Tp and Tq_time[p, q] is:

$S_{time}\&lsqb;p,q\&rsqb;=\frac{min(t_p^{end},t_q^{end})-max(t_p^{beg},t_q^{beg})}{max(t_p^{end},t_q^{end})-min(t_p^{beg},t_q^{beg})}---\left(5\right).$

The uncertain method for protecting track privacy divided based on figure the most according to claim 8, it is characterised in that: described step The calculating of the degree of association of two uncertain tracks in rapid E is obtained by below equation:

W_pq=α (1-S_time[T_p,T_q])+β·(1-S_dire[ζ,T_p,T_q])+γ·D_loc[ζ_,T_p,T_q] (6)

Wherein W_pqFor the degree of association between uncertain track Tp and Tq, S_time[T_p,T_q] it is the time phase of uncertain track Tp and Tq Like property, S_dire[ζ,T_p,T_q] it is the course bearing similarity of uncertain track Tp and Tq, D_loc[ζ,T_p,T_q] it is uncertain track Tp With the track distance of Tq, α is the chronotaxis S of uncertain track Tp and Tq_time[T_p,T_q] weight coefficient, β is uncertain The course bearing similarity S of track Tp and Tq_dire[ζ,T_p,T_q] weight coefficient, γ be uncertain track Tp and Tq track away from From D_loc[ζ,T_p,T_q] weight coefficient.