A trajectory similarity analysis method based on trajectory compression and clustering

Abstract

The application discloses a trajectory similarity analysis method based on trajectory compression and clustering. Firstly, N reference trajectories are compressed, and some trajectory data is removed within a certain error range, so as to facilitate subsequent processing and analysis. Secondly, the range of trajectory segments participating in calculation is reduced by intercepting common trajectories and angle pre-judgment, and the reference trajectory data is clustered offline. When calculating the similarity matrix, the similarity of each two trajectories only needs to be calculated once within the error range to reduce the complexity. Finally, the representative trajectory of each cluster is found, the similarity of the to-be-matched trajectory and the representative trajectory of each cluster is calculated, and whether the to-be-matched trajectory exists in the reference trajectory database is judged. If the to-be-matched trajectory exists in the reference trajectory database, the trajectory similarity of the to-be-matched trajectory and each reference trajectory of the corresponding cluster is calculated, so that it is determined that the actual trajectory is similar to which reference trajectory, and a similarity result is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of trajectory data processing, and particularly relates to a trajectory similarity analysis method based on trajectory compression and clustering. BACKGROUND

[0002] With the increasing coverage of communication equipment, base stations can receive radio waves held by various mobile terminals, thereby converting into mobile data. Through the mobile data, researchers can obtain the approximate positions of a specific mobile terminal at different time periods, thereby generating corresponding time series data, i.e., trajectory data. In a specific communication scenario, it is necessary to analyze the trajectory similarity of a certain type of terminal, and to perform trajectory matching in a large-scale benchmark trajectory database to determine whether the captured trajectory data exists in the database.

[0003] However, it is unreasonable to directly use original trajectory data. On the one hand, the trajectory acquisition time of the benchmark trajectory database is intensive, and the amount of trajectory data is large. On the other hand, there is a large amount of data redundancy in the benchmark database, which brings huge time cost and space cost to trajectory similarity calculation. In addition, due to the large number of trajectories in the benchmark database, the calculation amount of online one-to-one matching of the actual trajectory collected cannot meet the real-time demand of engineering application. SUMMARY

[0004] To solve the limitations and defects existing in the prior art, the present application provides a trajectory similarity analysis method based on trajectory compression and clustering, comprising:

[0005] The OPW-TR algorithm is used to compress N benchmark trajectories, and the corresponding trajectory data is removed within a preset error range;

[0006] The range of trajectory segments participating in the calculation is reduced by intercepting the common trajectory and angle pre-judgment;

[0007] The DBSCAN algorithm is used to cluster the benchmark trajectory data offline, and the similarity of each two trajectories needs to be calculated only once to reduce the complexity when calculating the similarity matrix within a preset error range, and the LCSS algorithm is used for similarity calculation;

[0008] The clustering results are recorded to obtain the representative trajectory of each cluster, and the LCSS algorithm is used to calculate the similarity between the to-be-matched trajectory and the representative trajectory of each cluster;

[0009] It is judged whether the similarity between the to-be-matched trajectory and the representative trajectory of each cluster is greater than a preset similarity threshold;

[0010] If the result of the judgment is that the similarity between the to-be-matched trajectory and the representative trajectory of one of the clusters is greater than the preset similarity threshold value and is the highest, the LCSS algorithm is used to calculate the trajectory similarity between the to-be-matched trajectory and each reference trajectory of the corresponding cluster;

[0011] The trajectory similarity between the to-be-matched trajectory and each reference trajectory of the corresponding cluster is judged.

[0012] If the result of the judgment is that the trajectory similarity between the to-be-matched trajectory and some reference trajectories of the corresponding cluster is greater than the preset trajectory similarity threshold value, it is determined which reference trajectories are similar to the to-be-matched trajectory, and the similarity result is output.

[0013] Optionally, the similarity calculation formula is as follows:

[0014] S = similar trajectory segment / min(m, n)

[0015] Where S is the similarity, the dimension of the similarity matrix is N x N, N is the number of trajectories, L1 and L2 are two trajectories, trajectory L1 is divided into m segments, trajectory L1 has m+1 points, trajectory L2 is divided into n segments, and trajectory L2 has n+1 points.

[0016] Optionally, the conditions for the similarity of the trajectory segments include that the distance between the trajectory segments is greater than a preset distance threshold value, the distance threshold value is composed of a horizontal threshold value, a vertical threshold value and an angle threshold value, and the sum of the weights of the horizontal threshold value, the vertical threshold value and the angle threshold value is 1.

[0017] The calculation formula of the vertical distance between two trajectories is as follows:

[0018]

[0019] Where L1 = s, L2 = e, l is the Euclidean distance from s to L, and l is the Euclidean distance from s to L. i i i j j j ⊥1 j i ⊥2 i j

[0020] The calculation formula of the horizontal distance between two trajectories is as follows:

[0021] d || (L i ,L j )=min(l ||1 ,l​​​​​​​​​​​​||2 )

[0022] wherein p s is the foot of s j to L i , p e is the foot of e j to L i , l ||1 is the minimum Euclidean distance of p s to L i , l ||2 is the minimum Euclidean distance of p e to L i ;

[0023] The calculation formula of the angle distance of two trajectories is as follows:

[0024]

[0025] wherein θ is the intersection angle of L i and L j .

[0026] Optionally, before calculating the similarity of two trajectory segments, the angle of the two trajectory segments is calculated, and the calculation formula of the angle of the two trajectory segments is as follows:

[0027]

[0028] If the angle of the two trajectory segments is greater than 90 degrees, it is directly determined that the two trajectory segments are not similar, so as to avoid subsequent calculation.

[0029] The present application has the following beneficial effects:

[0030] The present application provides a trajectory similarity analysis method based on trajectory compression and clustering. Firstly, N reference trajectories are compressed, and some trajectory data is removed within a certain error range, so as to facilitate subsequent processing and analysis. Secondly, the range of trajectory segments participating in calculation is reduced by intercepting common trajectories and angle pre-judgment, and reference trajectory data is clustered offline. When calculating the similarity matrix, the similarity of each two trajectories within the error range only needs to be calculated once to reduce complexity. Finally, the representative trajectory of each cluster is found, the similarity of the trajectory to be matched and the representative trajectory of each cluster is calculated, and it is judged whether it exists in the reference trajectory database; if it exists, the trajectory similarity of the trajectory and each reference trajectory of the corresponding cluster is calculated, so as to determine which reference trajectories the actual trajectory is similar to, and the similarity result is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The present application provides a trajectory similarity analysis method based on trajectory compression and clustering. Firstly, N reference trajectories are compressed, and some trajectory data is removed within a certain error range, so as to facilitate subsequent processing and analysis. Secondly, the range of trajectory segments participating in calculation is reduced by intercepting common trajectories and angle pre-judgment, and reference trajectory data is clustered offline. When calculating the similarity matrix, the similarity of each two trajectories within the error range only needs to be calculated once to reduce complexity. Finally, the representative trajectory of each cluster is found, the similarity of the trajectory to be matched and the representative trajectory of each cluster is calculated, and it is judged whether it exists in the reference trajectory database; if it exists, the trajectory similarity of the trajectory and each reference trajectory of the corresponding cluster is calculated, so as to determine which reference trajectories the actual trajectory is similar to, and the similarity result is obtained.

[0032] Figure 2a This is a schematic diagram of the average compression ratio as a function of the SED threshold, provided in Embodiment 1 of the present invention.

[0033] Figure 2b This is a schematic diagram of the average SED error as a function of the SED threshold, provided in Embodiment 1 of the present invention.

[0034] Figure 2c This is a schematic diagram of the average compression time as a function of the SED threshold, provided in Embodiment 1 of the present invention.

[0035] Figure 3 This is a schematic diagram of the distance between trajectories in the trajectory similarity analysis method based on trajectory compression and clustering provided in Embodiment 1 of the present invention.

[0036] Figure 4 The flowchart shows a one-to-one comparison scheme of the trajectory similarity analysis method based on trajectory compression and clustering provided in Embodiment 1 of the present invention. Detailed Implementation

[0037] To enable those skilled in the art to better understand the technical solution of the present invention, the trajectory similarity analysis method based on trajectory compression and clustering provided by the present invention will be described in detail below with reference to the accompanying drawings.

[0038] Example 1

[0039] Figure 1 This is an overall flowchart of the trajectory similarity analysis method based on trajectory compression and clustering provided in Embodiment 1 of the present invention. Figure 1 As shown, this embodiment proposes a low-complexity trajectory similarity analysis algorithm. Its main idea is as follows: First, compress the N baseline trajectories, removing some trajectory data within a certain error range to facilitate subsequent processing and analysis. Second, reduce the range of trajectory segments involved in the calculation by extracting common trajectories and pre-judging angles. Third, cluster the baseline trajectory data offline. When calculating the similarity matrix D, within the error range, the similarity between each pair of trajectories only needs to be calculated once to reduce complexity. Finally, find the representative trajectory of each cluster, calculate the similarity between the trajectory to be matched and the representative trajectory of each cluster, and determine whether it exists in the baseline trajectory database. If it exists, calculate the trajectory similarity between the trajectory and some baseline trajectories in the corresponding cluster, thereby determining which baseline trajectories the actual trajectory is similar to and obtaining the similarity result.

[0040] As for the error measurement index of trajectory compression, the embodiment compares three common trajectory compression algorithms: interval sampling method, TD-TR (Top Down Time Ration) algorithm and OPW (Opening Window) algorithm. The trajectory compression error is measured by synchronous Euclidean distance (SED), and the calculation method of SED is as follows:

[0041] Suppose that the object moves at a constant speed between time t s and t e , the projection p′ m (x′ m ,y′ m ,t m ) of p m (x m ,y m ,t m ) on the compression segment p s p e is calculated according to the time stamp of each trajectory point, then the synchronous Euclidean distance SED (p m ) of point p i can be defined as follows:

[0042]

[0043]

[0044]

[0045] As for the comparison of trajectory compression algorithms, the embodiment compares the interval sampling method and the OPW-TR (Opening Window Time Ratio, OPW-TR) algorithm. For 2463 trajectories, the average SED of the interval sampling method is about 0.097 degrees and the average SED of OPW is about 0.0084 degrees when the compression rate is about 82%. In addition, the interval sampling method misses some key points, and part of the compressed trajectories loses the original shape characteristics.

[0046] The embodiment compares the TD-TR algorithm and the OPW-TR algorithm, Figure 2a the average compression rate provided by the embodiment one of the present application changes with the curve diagram of SED threshold value. Figure 2b the average SED error provided by the embodiment one of the present application changes with the curve diagram of SED threshold value. Figure 2c the average compression time provided by the embodiment one of the present application changes with the curve diagram of SED threshold value. Figure 2a 、 Figure 2b 、 Figure 2cThe average compression rate, average SED error, and average compression time of the TD-TR algorithm and the OPW-TR algorithm are given respectively. The common point of the two algorithms is that as the distance threshold value increases, the trajectory compression rate increases and the average SED error increases. The difference between the two algorithms is that as the distance threshold value increases, the running time of the OPW-TR algorithm is longer and the running time of the TD-TR algorithm is shorter. Under the same threshold value, the performance of the OPW-TR algorithm is better. Therefore, the OPW-TR algorithm is adopted for trajectory compression in this embodiment.

[0047] Regarding trajectory similarity calculation and trajectory clustering, the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) provided in this embodiment is one of the representative algorithms for trajectory clustering, and the basic idea is to gradually find density-related data objects to form a cluster until the data objects in its neighborhood cannot become core objects. The outstanding advantage of DBSCAN is that it can automatically identify the number of clusters and handle outliers, and has a wide range of applications.

[0048] In this algorithm, the similarity matrix D of the trajectory needs to be calculated in advance, and the dimension is N x N (N is the number of trajectories). The LCSS algorithm is adopted in this embodiment to measure the similarity between trajectories. Assuming that the trajectory L1 is divided into m segments (L1 has m+1 points) and the trajectory L2 is divided into n segments (L2 has n+1 points), the calculation method of the similarity S is as follows:

[0049] S = similar trajectory segment / min(m, n)

[0050] Among them, the condition for the similarity of the trajectory segment is that the distance of the trajectory segment is greater than the distance threshold value. The distance threshold value is composed of a horizontal threshold value, a vertical threshold value, and an angle threshold value, and the sum of the weights is 1. The calculation methods of the respective parts are as follows:

[0051] For two trajectories L i = s i e i and L j = s j e j , l ⊥1 is the Euclidean distance of s j to L i , and l ⊥2 is the same. The calculation method of the vertical distance of the two trajectories is as follows:

[0052]

[0053] p s and p e are s j and e j to L ifoot of the pendulum, l ||1 For p s To L i The minimum Euclidean distance, l ||2 For p e To L i If the minimum Euclidean distance is found, the formula for calculating the horizontal distance between the two trajectories is as follows:

[0054] d || (L i ,L j )=min(l ||1 ,l ||2 )

[0055] θ is L i and L j If the intersection angle is given, the angular distance between the two trajectories is calculated as follows:

[0056]

[0057] The time complexity of LCSS (Longest Common Subsequence) is O(N). 2 The computation speed is relatively slow. To reduce the amount of computation, this embodiment adopts the following solution:

[0058] This embodiment narrows the trajectory range. Before comparing the similarity of two trajectories, the maximum and minimum values ​​(max_lon, max_lat, min_lon, min_lat) of lon and lat for the two trajectories are calculated. The common part of the trajectory is then extracted using the relatively broad conditions of [min_lon-Δt, max_lon+Δt] and [min_lat-Δt, max_lat+Δt]. The specific steps are as follows:

[0059] The crawler traces the entire path from the beginning, finding the first point p1 that meets the constraints. Then, iterate from the end of the path, finding the first point p2 that meets the constraints. A crawler path that meets the constraints lies between p1 and p2. This is to prevent points between p1 and p2 from being deleted if they do not meet the constraints, thus maintaining the continuity of the original path. In this embodiment, Δt is set to 0.1.

[0060] This embodiment reduces computation by predicting similarity based on angle. Before calculating the similarity between two trajectory segments, the angle between them is calculated first. If the angle is greater than 90 degrees, they are directly determined to be dissimilar, avoiding subsequent calculations. This embodiment modifies the above formula as follows:

[0061]

[0062] In the distance calculation of clustering, the weights of horizontal distance, vertical distance and angle distance are equal (1 / 3). The horizontal distance, vertical distance and angle distance need to be considered comprehensively in clustering.

[0063] The flow of trajectory matching provided in the embodiment is as follows: the similarity of a to-be-matched trajectory and a representative trajectory of each cluster after clustering is calculated. If the similarity of the to-be-matched trajectory and the representative trajectory of a cluster is greater than a threshold value, and the similarity is the maximum, it is indicated that the to-be-matched trajectory belongs to the cluster. Then, the to-be-matched trajectory is compared with all trajectories in the corresponding cluster one by one. If the similarity is the maximum and greater than the threshold value, it is indicated that a similar trajectory is matched.

[0064] In the embodiment, the distance threshold value d_thr of matching is a lower threshold value. In the process of matching the actual trajectory, the reference trajectory with the highest similarity greater than d_thr is taken as the matching result. Since it is possible that an actual trajectory has the same and highest similarity with multiple reference trajectories under the premise of meeting the distance threshold value, all the results meeting the condition are saved.

[0065] In the embodiment, when the actual trajectory is matched, the direction weight of distance is set to 1 / 2 to ensure the shape similarity.

[0066] Regarding the trajectory compression and angle distance weight simulation, Figure 4 A one-to-one comparison scheme flowchart of the trajectory similarity analysis method based on trajectory compression and clustering provided in the first embodiment of the present application is shown in FIG. 1. Figure 4 As shown in FIG. 1, 2463 complete trajectories and 2463 trajectories compressed by OPW are compared with 57 actual trajectories one by one in the present embodiment. The compression method and the setting of the angle distance weight are determined by the one-to-one comparison scheme.

[0067] Under the same average compression rate (82%), the trajectories compressed by the interval sampling method and OPW (threshold value 0.061) are matched with 57 actual trajectories one by one, and the cases of the direction weight being 1 / 2 and 1 / 3 are compared.

[0068] Regarding the complete trajectory, the distance threshold value d_thr provided in the embodiment is 0.03 degrees (since the trajectory points are dense, the threshold value is small), and when the direction weight is 1 / 2, 4 similar trajectories can be found in the 57 measured trajectories; when the direction weight is 1 / 3, only 3 similar trajectories can be found.

[0069] Regarding OPW, the distance threshold value d_thr provided in the embodiment is 0.2 degrees, and when the direction weight is 1 / 2, 12 similar trajectories can be found in the 57 measured trajectories, and the 4 trajectories matched by the complete trajectory are included; when the direction weight is 1 / 3, there are 10 similar trajectories.

[0070] For the interval sampling, the distance threshold dthr = 0.2 degree is provided in the embodiment, 8 of the 57 measured trajectories can find similar trajectories, but only 2 of the matching results coincide with the complete trajectory.

[0071] The conclusion of the embodiment is as follows:

[0072] (1) Under the same distance threshold, the number of similar trajectories found by OPW is more than interval sampling and is accurate.

[0073] (2) The actual scene is more focused on the similarity of the shape feature, when the direction weight is 1 / 2, the number of actual trajectories that can find similar trajectories in the reference trajectory database is more than when the direction weight is 1 / 3.

[0074] For trajectory clustering and trajectory compression simulation, since clustering is time-consuming, the embodiment randomly selects 200 trajectories from the 2463 trajectories as clustering objects for simulation. Referring to FIG. 2, considering the average compression time, average SED error, and average compression rate, the embodiment selects the OPW compression threshold 0.012, the compression rate 63.26%, and the average SED 0.0014. The parameters MinLin = 3 and ε = 0.6 of DBSCAN clustering.

[0075] For simulation 1: the reference trajectory is clustered by the original clustering method, and the embodiment clusters the 200 trajectories compressed by OPW. Then, the 200 trajectories are used as the to-be-matched trajectories to calculate the matching accuracy. The accuracy is 93%.

[0076] For simulation 2: the reference trajectory is clustered by the optimized clustering algorithm, and the acceleration method is studied on the basis of simulation 1. The DBSCAN clustering algorithm needs to calculate a similarity matrix D in advance, with a dimension of N x N (N is the number of trajectories), and the calculation amount is extremely large. The similarity of two trajectories will be calculated twice (the results may not be exactly the same), and the difference between the two calculations is small. It can be considered to only calculate the similarity above the diagonal line of the D matrix, and then copy it to the lower diagonal line to reduce the calculation amount. The matching accuracy obtained by using this method is 92.5%.

[0077] Comparing simulation 1 and simulation 2 can know that: in the case of a slight decrease of 0.5% in matching accuracy, the accelerated clustering method is used, and the calculation amount of the D matrix is reduced by half, which is more in line with the engineering application requirements.

[0078] For simulation 3: matching with actual trajectories, on the basis of the clustering results of simulation 1 and simulation 2, 57 actual trajectories are matched.

[0079] The results show that: under the same parameter settings, the matching results obtained by using the original D matrix and the optimized D matrix are the same.

[0080] The embodiment provides a trajectory similarity analysis method based on trajectory compression and clustering. N reference trajectories are compressed, some trajectory data is removed within a certain error range, subsequent processing and analysis are facilitated, the range of trajectory segments participating in calculation is reduced through the way of intercepting common trajectories and angle pre-judgment, reference trajectory data is clustered offline, and the similarity of each two trajectories only needs to be calculated once within an error range to reduce complexity when a similarity matrix is calculated. Finally, a representative trajectory of each cluster is found, the similarity of a to-be-matched trajectory and each representative trajectory of a cluster is calculated, and it is judged whether the to-be-matched trajectory exists in the reference trajectory database; if the to-be-matched trajectory exists, the trajectory similarity of the to-be-matched trajectory and each reference trajectory of the corresponding cluster is calculated, so that it is determined which reference trajectories are similar to the actual trajectory, and a similarity result is obtained.

[0081] It can be understood that the above embodiments are only exemplary embodiments for illustrating the principles of the present application, and the present application is not limited thereto. Various modifications and improvements can be made by those skilled in the art without departing from the spirit and essence of the present application, and these modifications and improvements are also considered to be within the protection scope of the present application.

Claims

1. A trajectory similarity analysis method based on trajectory compression and clustering, characterized in that, The method comprises the following steps: Trajectory compression is performed on N reference trajectories using an OPW-TR algorithm, and corresponding trajectory data is removed within a preset error range; The range of trajectory segments participating in calculation is reduced through interception of common trajectories and angle pre-judgment; DBSCAN algorithm is used to perform offline clustering on reference trajectory data, and the similarity between each two trajectories needs to be calculated only once to reduce complexity when calculating the similarity matrix within a preset error range, and LCSS algorithm is used for similarity calculation; The clustering results are recorded to obtain a representative trajectory of each cluster, and LCSS algorithm is used to calculate the similarity between the to-be-matched trajectory and the representative trajectory of each cluster; It is judged whether the similarity between the to-be-matched trajectory and the representative trajectory of each cluster is greater than a preset similarity threshold; If the result of the judgment is that the similarity between the to-be-matched trajectory and the representative trajectory of one cluster is greater than the preset similarity threshold and is the highest, LCSS algorithm is used to calculate the trajectory similarity between the to-be-matched trajectory and each reference trajectory of the corresponding cluster; It is judged whether the trajectory similarity between the to-be-matched trajectory and each reference trajectory of the corresponding cluster is greater than a preset trajectory similarity threshold; If the result of the judgment is that the trajectory similarity between the to-be-matched trajectory and some reference trajectories of the corresponding cluster is greater than the preset trajectory similarity threshold, it is determined which reference trajectories are similar to the to-be-matched trajectory, and the similarity result is outputted; Before calculating the similarity between two trajectory segments, the angle of the two trajectory segments is calculated, and the angle calculation formula of the two trajectory segments is as follows: , wherein is the angle of intersection of the trajectory and the trajectory ; d θ denotes the angular distance; If the angle of the two trajectory segments is greater than 90 degrees, it is directly determined that the two trajectory segments are not similar, so as to avoid subsequent calculation. 2.The trajectory similarity analysis method based on trajectory compression and clustering according to claim 1, characterized in that, The similarity calculation formula is as follows: S = similar trajectory segment / min(m, n) Wherein, S is the similarity, the dimension of the similarity matrix is N x N, N is the number of trajectories, L1 and L2 are two trajectories, trajectory L1 is divided into m segments, trajectory L1 has m+1 points, trajectory L2 is divided into n segments, and trajectory L2 has n+1 points. 3.The trajectory similarity analysis method based on trajectory compression and clustering according to claim 2, characterized in that, The conditions for similarity of trajectory segments include that the distance of the trajectory segments is greater than a preset distance threshold, the distance threshold is composed of a horizontal threshold, a vertical threshold and an angle threshold, and the sum of the weights of the horizontal threshold, the vertical threshold and the angle threshold is 1; The calculation formula of the vertical distance between two trajectories is as follows: , wherein the trajectory , the trajectory , is to the Euclidean distance, is to the Euclidean distance; The calculation formula of the horizontal distance between two trajectories is as follows: , wherein is to the foot of is to the foot of is to the minimum Euclidean distance of is to the minimum Euclidean distance of

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