Ship trajectory clustering method fusing multi-dimensional features
By integrating multi-dimensional features and the DBSCAN algorithm, combined with VIKOR optimization, the problems of single similarity measurement and manual calibration in existing ship trajectory clustering are solved, achieving more accurate and stable clustering results and improving the reliability of navigation pattern recognition and adaptability in complex scenarios.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WUHAN UNIV OF TECH
- Filing Date
- 2026-02-09
- Publication Date
- 2026-05-19
AI Technical Summary
Existing ship trajectory clustering methods rely on a single similarity metric, which cannot fully identify the multi-dimensional features of the trajectory. Clustering parameters need to be manually calibrated, resulting in unstable results and a lot of noise, which cannot provide reliable support for subsequent navigation mode applications.
A multi-dimensional feature measurement method integrating geographical distance similarity, directional similarity, and cumulative common subsequence similarity is adopted. Combined with the DBSCAN clustering algorithm, the optimal clustering parameters are determined through VIKOR multi-criteria optimization to achieve automatic calibration.
It significantly improves clustering accuracy and robustness, the clustering results are more in line with actual navigation patterns, reduces noise, increases the number of effective clusters, and provides a reliable data foundation to support applications such as trajectory prediction and risk assessment.
Smart Images
Figure CN122065064A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of ship navigation and trajectory data processing technology, specifically relating to a ship trajectory clustering method that integrates multi-dimensional features. Background Technology
[0002] With the widespread adoption of Automatic Identification Systems (AIS), massive amounts of ship trajectory data have provided a foundation for research related to maritime navigation safety. Trajectory clustering, as a core technology for navigation pattern recognition, is a key prerequisite for applications such as ship trajectory prediction and collision avoidance.
[0003] Existing ship trajectory clustering methods are mainly divided into three categories: trajectory-based, trajectory-segment-based, and trajectory-point-based, all relying on a single trajectory similarity metric. Among these, trajectory-based methods tend to ignore local features, trajectory-segment-based methods are susceptible to noise interference, and trajectory-point-based methods struggle to extract complete path features. Furthermore, traditional clustering algorithms like DBSCAN only support a single similarity metric, failing to meet the comprehensive recognition requirements of multi-dimensional trajectory features. In addition, existing clustering parameters such as neighborhood thresholds and the number of core points require manual calibration, which is inefficient and makes it difficult to obtain optimal clustering results, leading to unstable clustering quality and hindering reliable support for subsequent navigation mode applications. Summary of the Invention
[0004] The main objective of this invention is to provide a ship trajectory clustering method that integrates multi-dimensional features, thereby solving the problems of single similarity measurement and the need for manual calibration of clustering parameters.
[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention provides a method for clustering ship trajectories by integrating multi-dimensional features, the method comprising: Obtain ship trajectories, each trajectory represented as a sequence of latitude and longitude coordinates including timestamps; Calculate the multi-dimensional similarity features between any two ship trajectories, including geographical distance similarity, directional similarity, and cumulative common subsequence similarity; Based on the multi-dimensional similarity features between ship trajectories, the DBSCAN clustering algorithm is used to cluster ship trajectories by setting different combinations of clustering parameters; The evaluation criteria for the clustering results of ship trajectories are determined, including the intra-cluster standard and the number of noisy trajectories; wherein, the intra-cluster standard is based on the comprehensive similarity between ship trajectories to approximate the standard deviation of trajectories in the cluster, and the comprehensive similarity is determined by combining geographical distance similarity, directional similarity and cumulative common subsequence similarity; Based on different combinations of clustering parameters and corresponding evaluation criteria for clustering results, the optimal combination of clustering parameters for the DBSCAN clustering algorithm is determined using the VIKOR multi-criteria optimization method. Based on the multi-dimensional similarity features between ship trajectories and the determined optimal clustering parameter combination, the DBSCAN clustering algorithm is used to complete ship trajectory clustering.
[0006] Following the above technical solution, the method for calculating geographical distance similarity is as follows: Determine the latitude and longitude coordinate range of the ship's trajectory: ; ; In the formula, For trajectory The range of longitude coordinates For trajectory The range of latitudinal coordinates, and Trajectories The Latitude and longitude coordinates, This represents the number of latitude and longitude coordinates of the trajectory. Estimating the similarity between coordinate ranges using Jacard similarity: ; In the formula, Denotes the Jacquard similarity between finite sets A and B; Applying Jacard similarity to latitude and longitude, and defining the geographic distance similarity (GRS) between any two ship tracks as the average value along the latitude and longitude: ; In the formula, For trajectory and trajectory Geographical distance similarity; For trajectory The range of longitude coordinates For trajectory The range of latitudinal coordinates.
[0007] Following the above technical solution, the method for calculating directional similarity is as follows: Based on the starting point O and ending point D of the ship's trajectory, the ship's trajectory is represented as an OD vector; The directional similarity between two ship trajectories is calculated using the cosine values of the two OD vectors and mapped to the interval [0, 1].
[0008] Following the above technical solution, the mapping method is as follows: ; In the formula, For trajectory and trajectory directional similarity, For trajectory and trajectory The cosine values of the two OD vectors.
[0009] Following the above technical solution, the method for calculating the cumulative common subsequence similarity is as follows: Based on a preset matching threshold, the matching rule for the midpoint of any two ship trajectories is determined, resulting in a common subsequence; let... For trajectory The Middle If there are 3 common subsequences, then the trajectory The Middle The lengths of the common subsequences are: ; In the formula, For trajectory The Middle The length of the common subsequence For trajectory The Middle The number of points in the common subsequence. and For trajectory The Middle Two consecutive points in a common subsequence The Euclidean distance between two consecutive points; Then any two ship trajectories and The cumulative common subsequence similarity is as follows: ; In the formula, For trajectory and trajectory The cumulative common subsequence similarity, for i and j , This represents the number of common subsequences in the trajectory. Let be the length of the trajectory.
[0010] Following the above technical solution, the DBSCAN clustering algorithm is used to cluster ship trajectories, as detailed below: Based on geographical distance similarity, directional similarity, and cumulative common subsequence similarity, a comprehensive neighborhood is constructed to determine trajectory adjacency, and corresponding neighborhood thresholds and minimum trajectory number thresholds are preset. Among them, the neighborhood threshold includes the geographic distance similarity neighborhood threshold. Orientation similarity neighborhood threshold and cumulative common subsequence similarity neighborhood threshold ; If the geographical distance similarity, direction similarity, and cumulative common subsequence similarity between two ship trajectories satisfy their respective neighborhood thresholds, then the two ship trajectories are determined to be adjacent to each other within the comprehensive neighborhood. The DBSCAN clustering algorithm clusters trajectories based on their adjacency relationships within the comprehensive neighborhood and the minimum number of trajectories threshold. The ship trajectories are divided into core trajectories, boundary trajectories, and noise trajectories, and ship trajectory clustering is completed. The clustering parameter combination includes geographic distance similarity neighborhood threshold. Orientation similarity neighborhood threshold Cumulative common subsequence similarity neighborhood threshold and minimum number of trajectories threshold .
[0011] Following the above technical solution, the intra-class standard approximates the standard deviation of trajectories in clustering based on the comprehensive similarity, as follows: Assuming that the DBSCAN clustering algorithm is used to cluster the ship trajectories, there are a total of K The cluster, the first k Cluster Ck The number of trajectories is Nk Then cluster Ck center for: ; In the formula, For trajectory and trajectory The overall similarity; The intra-class standard is: ; In the formula, For intra-class standards, For trajectory and trajectory center The overall similarity.
[0012] Based on the above technical solution, the comprehensive similarity determination method is as follows: ; In the formula, For trajectory and trajectory The overall similarity For trajectory and trajectory Geographical distance similarity, For trajectory and trajectory directional similarity, For trajectory and trajectory The cumulative common subsequence similarity.
[0013] In a second aspect, the present invention provides a computer device / apparatus / system, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first aspect.
[0014] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the method described in the first aspect.
[0015] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: This invention constructs a comprehensive similarity by integrating multi-dimensional features such as geographical distance, navigation direction, and accumulated common subsequences. This overcomes the limitations of traditional methods that rely on a single metric, significantly improving clustering accuracy and making the results more closely resemble real navigation patterns. Simultaneously, it introduces a parameter self-calibration method based on VIKOR multi-criteria decision-making, achieving automatic optimization of clustering parameters and solving the problems of low efficiency and unstable results associated with manual parameter tuning. Furthermore, by extending the DBSCAN algorithm to adapt to multi-dimensional similarity, it enhances the algorithm's robustness in complex scenarios, providing a more reliable data foundation for subsequent applications such as trajectory prediction and risk assessment. Attached Figure Description
[0016] Figure 1 This is a flowchart illustrating a method for clustering ship trajectories that integrates multi-dimensional features according to an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating a geographical distance similarity calculation method according to an embodiment of the present invention; Figure 3 This is a schematic diagram of matching points and common subsequences on a ship trajectory according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the clustering results and cluster centers according to an embodiment of the present invention. Detailed Implementation
[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments provided by this invention without inventive effort are within the scope of protection of this invention.
[0018] Obviously, the accompanying drawings described below are merely some examples or embodiments of the present invention. Those skilled in the art can apply the present invention to other similar scenarios based on these drawings without any inventive effort. Furthermore, it is understood that although the efforts made in this development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this invention, modifications to design, manufacturing, or production based on the technical content disclosed in this invention are merely conventional technical means and should not be construed as insufficient disclosure of the present invention.
[0019] In this invention, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this invention may be combined with other embodiments without conflict.
[0020] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "a," "an," "an," "the," and similar words used in this invention do not indicate quantity limitation and may indicate singular or plural. The terms "comprising," "including," "having," and any variations thereof used in this invention are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or modules (units) is not limited to the listed steps or units, but may also include steps or units not listed, or may include other steps or units inherent to these processes, methods, products, or devices. The terms "connected," "linked," "coupled," and similar words used in this invention are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "A plurality" used in this invention refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships may exist; for example, "A and / or B" can represent: A alone, A and B simultaneously, and B alone. The character " / " generally indicates that the preceding and following objects have an "or" relationship. The terms "first," "second," and "third" used in this invention are merely to distinguish similar objects and do not represent a specific ordering of the objects.
[0021] Existing trajectory clustering methods use a single similarity metric, which cannot comprehensively identify multi-dimensional features such as the geospatial distribution of the trajectory, navigation direction, and overlapping sub-segments, resulting in significant deviations between the clustering results and actual navigation patterns. The traditional DBSCAN algorithm only supports a single distance parameter, making it unsuitable for multi-dimensional similarity fusion scenarios, leading to incomplete recognition of both overall and local trajectory features. Clustering parameters rely on manual calibration, which is inefficient and makes it difficult to obtain optimal solutions, resulting in problems such as high clustering noise and insufficient effective cluster numbers.
[0022] This invention aims to solve the aforementioned technical problems of existing ship trajectory clustering. Addressing the shortcomings of a single similarity metric, this invention constructs a multi-dimensional feature calculation method that integrates geographical interval similarity, directional similarity, and cumulative common sub-segment similarity to comprehensively identify the overall and local features of the trajectory. To address the difficulty of adapting the traditional DBSCAN algorithm to multi-dimensional similarity fusion scenarios, the core neighborhood of the DBSCAN algorithm is expanded to make it compatible with the clustering requirements of multi-dimensional similarity fusion. Furthermore, to address the issue of clustering parameters relying on manual calibration, a parameter self-calibration method based on VIKOR multi-criteria optimization is adopted to determine the optimal clustering parameters, ultimately solving the problems of excessive noise, insufficient number of effective clusters, and inconsistency with actual navigation patterns in the clustering results.
[0023] like Figure 1 As shown, this invention provides a ship trajectory clustering method that integrates multi-dimensional features. The method includes: Obtain ship trajectories, each trajectory represented as a sequence of latitude and longitude coordinates including timestamps; Calculate the multi-dimensional similarity features between any two ship trajectories, including geographical distance similarity, directional similarity, and cumulative common subsequence similarity; Based on the multi-dimensional similarity features between ship trajectories, the DBSCAN clustering algorithm is used to cluster ship trajectories by setting different combinations of clustering parameters; The evaluation criteria for the clustering results of ship trajectories are determined, including the intra-cluster standard and the number of noisy trajectories; wherein, the intra-cluster standard is based on the comprehensive similarity between ship trajectories to approximate the standard deviation of trajectories in the cluster, and the comprehensive similarity is determined by combining geographical distance similarity, directional similarity and cumulative common subsequence similarity; Based on different combinations of clustering parameters and corresponding evaluation criteria for clustering results, the optimal combination of clustering parameters for the DBSCAN clustering algorithm is determined using the VIKOR multi-criteria optimization method. Based on the multi-dimensional similarity features between ship trajectories and the determined optimal clustering parameter combination, the DBSCAN clustering algorithm is used to complete ship trajectory clustering.
[0024] Specifically, the method consists of two parts: (1) multi-feature trajectory similarity; and (2) clustering parameter optimization.
[0025] (1) Multi-feature trajectory similarity.
[0026] In this invention, a ship's trajectory is represented as a sequence of latitude and longitude coordinates including timestamps, i.e., any trajectory. :{( ), ..., ( ), ..., ( )};in , and Representing longitude coordinates, latitude coordinates, and trajectory respectively. The r The recording time of each sample. In the subsection, three sub-indicators will be explained first, and then a comprehensive measure will be given.
[0027] ① Geographic Range Similarity (GRS): When two trajectories are in the same area, they will overlap to some extent along the latitude and longitude directions. The average percentage of overlap can be used as an indicator to measure the location similarity between the origin and destination (OD). Figure 2 As shown, a trajectory The coordinate range can be divided into two directions: latitude and longitude, denoted as . and , calculated from the minimum and maximum values of the coordinates along the path, respectively, are expressed as: ; ; In the formula, For trajectory The range of longitude coordinates (represented by an interval from the minimum to the maximum longitude value). For trajectory The range of latitudinal coordinates, and Trajectories The Latitude and longitude coordinates, This represents the number of latitude and longitude coordinates of the trajectory.
[0028] Then, the similarity between coordinate ranges is estimated using Jacardi similarity. Initially, Jacardi similarity was designed to estimate the similarity between two finite sets A and B, expressed as: ; In the formula, Let A represent the Jacardian similarity between finite sets A and B.
[0029] Subsequently, we applied the Jacard similarity to the latitude and longitude directions and then... and trajectory The GRS is defined as their average value. The GRS value ranges from 0 to 1, and the calculation formula is as follows: ; In the formula, For trajectory and trajectory Geographical distance similarity; For trajectory The range of longitude coordinates For trajectory The range of latitudinal coordinates.
[0030] ② Directional Similarity (DS): To calculate the directional similarity between different trajectories, we represent each trajectory as an OD vector. Then, we use the cosine of the two OD vectors to calculate the directional similarity between the two trajectories, such as... Figure 2 As shown. Next, the calculated values are mapped to values between [0, 1], as follows: ; ; In this context, O and D correspond to the first and last samples in the trajectory, respectively. The value of DS is between 0 and 1, where 0 and 1 represent completely opposite and the same direction, respectively.
[0031] ③ Cumulative Common Sub-Sequence Similarity (CCSS): Multiple common sub-sequences exist between any two trajectories, and the longest common sub-sequence similarity (LCSS) is the most commonly used feature metric. In LCSS, the similarity between two trajectories is represented by the portion of the shorter trajectory covered by the longest common sub-sequence. Therefore, when one trajectory is completely contained within another, the longest common sub-sequence between the two trajectories equals the shorter trajectory, and their similarity is set to 1, meaning they are completely similar. This can lead to limitations in LCSS, especially when the lengths of several common sub-sequences are close to the longest possible length. In LCSS, the longest common sub-sequence of trajectories is the longest continuous sequence of matching points, and LCSS represents the proportion of the longest common sub-sequence on the shorter trajectory. Its application is limited when multiple matching segments exist between trajectories.
[0032] To overcome this shortcoming, we made some improvements to LCSS and proposed CCSS. Similar to LCSS, the first step of CCSS is to apply a given matching threshold... δDetermine the matching rules for points in two trajectories. If the spatial distance between the two points is less than... δ If they are true, then they are considered a match. Indeed, for trajectories... Any matching point in the trajectory There may be multiple matching points. For example, as shown in Figure 3, the matching points... With the two points in Tj and Matching.
[0033] All matching points in a trajectory constitute the set of common subsequences of that trajectory. Let... For trajectory The first in A common subsequence, Figure 3 There are 2 common subsequences. Therefore, the trajectory The Middle The lengths of the common subsequences are: ; In the formula, For trajectory The Middle The length of the common subsequence For trajectory The Middle The number of points in the common subsequence. and For trajectory The Middle Two consecutive points in a common subsequence Let be the Euclidean distance between two consecutive points.
[0034] Different trajectories are often of unequal length, sometimes with significant differences, which can lead to inappropriate clustering due to short trajectories, as mentioned earlier. To avoid this, we set the similarity as the average of the common subsequences corresponding to two trajectories, rather than simply selecting the shorter trajectory.
[0035] For trajectory trajectory There are two common subsequences, as defined in CCSS: ; In the formula, For trajectory and trajectory The cumulative common subsequence similarity, for i and j , This represents the number of common subsequences in the trajectory. Let be the length of the trajectory. The value is between 0 and 1.
[0036] ④ Comprehensive Similarity (CS): Combining the advantages of GRS, DS, and CCSS, a comprehensive similarity method is proposed to simultaneously identify multiple features of a trajectory, as follows: ; In the formula, It is a trajectory and trajectory The overall similarity between them. CS is calculated in two cases. First, if... or This means that the two trajectories are either very far apart because they do not overlap in latitude and longitude, or they are in completely opposite directions. Therefore, we simply set CS to 0 to represent dissimilarity. Otherwise, we would additionally calculate CCSS based on subsequence characteristics to distinguish detailed similarities. To simultaneously consider direction, OD position, and subsequence characteristics, we define CS as a combination of GRS, DS, and CCSS. Generally, GRS and DS exhibit similarity at the macro level, while CCSS is more detailed at the micro level. Therefore, we consider GRS and DS as the "macro" part and CCSS as the "micro" part. Finally, CS is calculated as the average of the two parts.
[0037] (2) Clustering parameter optimization.
[0038] The DBSCAN algorithm typically requires determining two parameters. ε and MinPts; where, ε The maximum radius of the neighborhood of a core point is controlled by MinPts, which represents the minimum number of points in the neighborhood when a point is identified as a core point. Therefore, the core point... ε The neighborhood must contain at least MinPts points. However, only one is set. ε The various similarity levels proposed in Part 1 cannot be applied, therefore, it is necessary to... ε Further expansion is needed. Secondly, since the clustering object is a trajectory, this chapter will change MinPts to MinTrs for better context. This algorithm is based on the DBSCAN algorithm for trajectory data, expanding the core neighborhood with a single distance parameter into a comprehensive neighborhood constructed with multiple similarity measures, which can comprehensively identify the overall and local features of the trajectory.
[0039] Corresponding to the three proposed similarity metrics, namely GRS, DS, and CCSS, three corresponding neighborhood thresholds are established: Geographic Distance Similarity Neighborhood Threshold. Orientation similarity neighborhood threshold and cumulative common subsequence similarity neighborhood threshold When all three neighborhood threshold ranges mentioned above are simultaneously satisfied, it is called the comprehensive neighborhood of the trajectory.
[0040] Specifically, since each cluster category in DBSCAN is defined as the largest set of density-connected clusters, the original trajectory data can be divided into three categories: core trajectories, boundary trajectories, and noisy trajectories. Core trajectories have a comprehensive neighborhood number greater than MinTrs, boundary trajectories are within the comprehensive neighborhood of core trajectories but do not satisfy the condition that their number of trajectories is greater than MinTrs, and other trajectories are defined as noise trajectories. Based on the proposed multi-feature trajectory similarity metrics GRS, DS, and CCSS, trajectories grouped into the same cluster in the clustering results exhibit the following characteristics: ① There exists at least one core trajectory whose number of trajectories in its comprehensive neighborhood is greater than or equal to MinTrs; ② The boundary trajectory is connected to the core trajectory, and the number of trajectories in its comprehensive neighborhood is less than MinTrs; ③ The trajectories have a large overlap, and the cumulative overlap ratio is greater than 10%. ; ④ These trajectories have roughly the same starting and ending points in the same direction.
[0041] Because the increase in clustering parameters makes it difficult to achieve optimal clustering results through manual adjustment, the clustering results need to be optimized. The optimized clustering parameter combinations include geographic distance, similarity, and neighborhood threshold. Orientation similarity neighborhood threshold Cumulative common subsequence similarity neighborhood threshold and minimum number of trajectories threshold .
[0042] In the DBSCAN algorithm, parameters ε `MinPts` and `MinPts` specify the maximum radius of the neighborhood and the minimum number of trajectories in the core trajectory neighborhood, respectively. In this paper, we estimate the parameters based on the performance of a real-world application, namely historical AIS trajectory extraction. On the one hand, historical AIS trajectory extraction requires the clustering output to be sufficiently explicit to identify frequently used routes. On the other hand, it is necessary to consider more trajectories to improve the reliability of the extraction. Therefore, we designed two criteria to represent these two requirements respectively: the intra-class criterion (WC) and the number of noisy trajectories (NT).
[0043] For sequential data, the WC exponent represents the concentration of data samples within each cluster; minimizing WC yields the most concentrated clustering result. When the number of clusters equals the number of samples, WC = 0, and each cluster consists of only one sample. In this case, all samples can be considered noise. Furthermore, the smaller the NT, the more samples are in each cluster with a given number of clusters. Therefore, these two criteria are conflicting in practice. Clustering results should balance the two criteria of WC and NT, and provide a solution that balances them, which inspires us to view it as a multi-criteria decision-making (MCDM) problem.
[0044] To find the optimal trade-off clustering result, a method is needed to solve the MCDM problem. Two widely used methods for solving the MCDM problem are VIKOR and TOPSIS (Order Preference Technique for Similarity to Ideal Solution). These methods share similar principles: they both select the optimal candidate based on functions representing proximity to the positive ideal solution (PIS) and distance from the negative ideal solution (NIS). In the TOPSIS method, proximity and distance are directly calculated based on Euclidean distance. Despite its simplicity, the TOPSIS ranking index is independent of the separation weights of the candidates based on PIS and NIS. In other words, the relative importance of the two separations remains an open question. This shortcoming certainly limits the applicability of TOPSIS. Unlike the above strategies, the VIKOR method maximizes group utility and minimizes individual regret when calculating proximity and distance. That is, the VIKOR method not only obtains the optimal solution that is closest to the ideal solution at the overall index level but also reduces the impact of individual index biases on the results. Therefore, it has high stability and reliability, and was chosen in this study to find the best trade-off clustering results.
[0045] Cluster Result Criterion: A within-like criterion is defined to approximate the standard deviation of trajectories within a cluster. Since the mean of the trajectory objects cannot be calculated, it cannot be computed in a general way. Therefore, we first approximate this mean by considering the center of the trajectory set in each cluster. Assume there are a total of... K A cluster, denoted as C 1, C 2, ..., Ck , ..., CK , No. k Cluster Ck The sample size is Nk Then, clusters Ck The center is denoted as , can be defined as: ; Therefore, WC is defined as follows: ; In the formula, For intra-class standards, For trajectory and trajectory center The overall similarity.
[0046] Based on the previously proposed WC and NT metrics, clustering results can be evaluated and used as a basis for adjusting clustering parameters. However, these performance metrics usually cannot be optimal simultaneously, so seeking a compromise solution is necessary. VIKOR can be considered a ranking method to address this issue.
[0047] Parameter optimization based on VIKOR: The VIKOR method is a technique applicable to the internal implementation of MCDM. It introduces a multi-criteria ranking metric based on a specific measure of proximity to the ideal solution. Assumptions For the ideal solution, This represents the feasible solution that is closest to the ideal solution. Furthermore, compromise refers to an agreement reached through mutual concessions. The multi-criteria metric for compromise ranking evolved from the Lp-metric used as an aggregation function in compromise planning methods, as shown below: , ; in, u =1,2,…,U and v =1, 2, ..., V represent the criteria and alternatives for parameter combinations in the DBSCAN algorithm, respectively. Criteria u Weights This indicates its relative importance. yes Alternative criterion functions value, and These are the best and worst values of all criterion functions, respectively.
[0048] In the VIKOR method, use (as shown in the following formula) )and (as shown in the following formula) Use ) to define the sorting metric. The obtained solution maximizes group utility (majority principle), using The obtained solution minimizes individual regret.
[0049] The main steps of VIKOR are as follows: Step 1: Determine the optimal value for all criterion functions and worst Value: ; Step 2: Calculation and value: ; ; Step 3: Calculate the value V = 1, 2, ..., V is as follows: ; in, , , , , λ This is the weight of the majority of standard strategies (or the maximum group utility). This paper sets this weight to 0.5.
[0050] Step 4: According to Sort the alternatives in ascending order. Based on the minimum measurement, the following two conditions are met: A trade-off solution for alternative (a′) is proposed: c1. Acceptable advantages: ; Among them, a′′ is the second-ranked alternative in the ranking table based on Q; c2. Acceptable stability of decision: The other option a′ must also be based on the best ranking of G and / or H.
[0051] Therefore, the optimal combination of clustering parameters was determined, and ship trajectory clustering was completed accordingly. Figure 4 As shown.
[0052] In summary, this invention improves clustering accuracy. Through multi-dimensional feature fusion, it can more comprehensively identify ship navigation patterns compared to traditional single-similarity clustering methods. The matching degree between clustering results and actual port routes is significantly improved, the number of effective clusters increases, and the number of noise clusters decreases. Simultaneously, parameter calibration is highly efficient, achieving self-calibration of clustering parameters without manual intervention, solving the problems of low efficiency and unstable results in traditional methods, and ensuring optimal clustering results. Furthermore, its algorithm adaptability is enhanced, extending the DBSCAN algorithm to adapt to multi-dimensional similarity, breaking through the limitation of traditional clustering algorithms supporting only a single feature, and improving the robustness of clustering in complex navigation scenarios. Its application value is significant; the navigation patterns obtained from clustering provide a reliable data foundation for subsequent ship trajectory prediction and collision risk assessment, indirectly improving maritime navigation safety.
[0053] Furthermore, the present invention also provides a computer device / apparatus / system, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method.
[0054] The present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.
[0055] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more blocks of the flowchart illustrations and / or block diagrams.
[0056] These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more blocks in a block diagram.
[0057] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable data processing apparatus to produce a computer-implemented process, thereby providing steps for implementing the functions specified in one or more flowcharts and / or one or more blocks in a block diagram.
[0058] It should be noted that, depending on the implementation needs, the various steps / components described in this invention can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.
[0059] Those skilled in the art will readily understand that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for clustering ship trajectories by integrating multi-dimensional features, characterized in that, The method includes: Obtain ship trajectory; Calculate the multi-dimensional similarity features between any two ship trajectories, including geographical distance similarity, directional similarity, and cumulative common subsequence similarity; Based on the multi-dimensional similarity features between ship trajectories, the DBSCAN clustering algorithm is used to cluster ship trajectories by setting different combinations of clustering parameters; The evaluation criteria for the clustering results of ship trajectories are determined, including the intra-cluster standard and the number of noisy trajectories; wherein, the intra-cluster standard is based on the comprehensive similarity between ship trajectories to approximate the standard deviation of trajectories in the cluster, and the comprehensive similarity is determined by combining geographical distance similarity, directional similarity and cumulative common subsequence similarity; Based on different combinations of clustering parameters and corresponding evaluation criteria for clustering results, the optimal combination of clustering parameters for the DBSCAN clustering algorithm is determined using the VIKOR multi-criteria optimization method. Based on the multi-dimensional similarity features between ship trajectories and the determined optimal clustering parameter combination, the DBSCAN clustering algorithm is used to complete ship trajectory clustering.
2. The ship trajectory clustering method integrating multi-dimensional features according to claim 1, characterized in that, The method for calculating geographical distance similarity is as follows: Determine the latitude and longitude coordinate range of the ship's trajectory: ； ； In the formula, For trajectory The range of longitude coordinates For trajectory The range of latitudinal coordinates, and Trajectories The Latitude and longitude coordinates, This represents the number of latitude and longitude coordinates of the trajectory. Estimating the similarity between coordinate ranges using Jacard similarity: ； In the formula, Denotes the Jacquard similarity between finite sets A and B; Applying Jacard similarity to latitude and longitude, and defining the geographic distance similarity (GRS) between any two ship tracks as the average value along the latitude and longitude: ； In the formula, For trajectory and trajectory Geographical distance similarity; For trajectory The range of longitude coordinates For trajectory The range of latitudinal coordinates.
3. The ship trajectory clustering method integrating multi-dimensional features according to claim 1, characterized in that, The method for calculating directional similarity is as follows: Based on the starting point O and ending point D of the ship's trajectory, the ship's trajectory is represented as an OD vector; The directional similarity between two ship trajectories is calculated using the cosine values of the two OD vectors and mapped to the interval [0, 1].
4. The ship trajectory clustering method integrating multi-dimensional features according to claim 3, characterized in that, The mapping method is as follows: ； In the formula, For trajectory and trajectory directional similarity, For trajectory and trajectory The cosine values of the two OD vectors.
5. The ship trajectory clustering method integrating multi-dimensional features according to claim 1, characterized in that, The cumulative common subsequence similarity is calculated as follows: Based on a preset matching threshold, the matching rule for the midpoint of any two ship trajectories is determined, resulting in a common subsequence; let... For trajectory The Middle If there are 3 common subsequences, then the trajectory The Middle The lengths of the common subsequences are: ； In the formula, For trajectory The Middle The length of the common subsequence For trajectory The Middle The number of points in the common subsequence. and For trajectory The Middle Two consecutive points in a common subsequence is the Euclidean distance between two consecutive points; Then any two ship trajectories and The cumulative common subsequence similarity is as follows: ； In the formula, For trajectory and trajectory The cumulative common subsequence similarity, for i and j , This represents the number of common subsequences in the trajectory. Let be the length of the trajectory.
6. The ship trajectory clustering method integrating multi-dimensional features according to claim 1, characterized in that, The DBSCAN clustering algorithm is used to cluster ship trajectories, as detailed below: Based on geographical distance similarity, directional similarity, and cumulative common subsequence similarity, a comprehensive neighborhood is constructed to determine trajectory adjacency, and corresponding neighborhood thresholds and minimum trajectory number thresholds are preset. Among them, the neighborhood threshold includes the geographic distance similarity neighborhood threshold. Orientation similarity neighborhood threshold and cumulative common subsequence similarity neighborhood threshold ; If the geographical distance similarity, direction similarity, and cumulative common subsequence similarity between two ship trajectories satisfy their respective neighborhood thresholds, then the two ship trajectories are determined to be adjacent to each other within the comprehensive neighborhood. The DBSCAN clustering algorithm clusters trajectories based on their adjacency relationships within the comprehensive neighborhood and the minimum number of trajectories threshold. The ship trajectories are divided into core trajectories, boundary trajectories, and noise trajectories, and ship trajectory clustering is completed. The clustering parameter combination includes geographic distance similarity neighborhood threshold. Orientation similarity neighborhood threshold Cumulative common subsequence similarity neighborhood threshold and minimum number of trajectories threshold .
7. The ship trajectory clustering method integrating multi-dimensional features according to claim 1, characterized in that, The intra-class standard approximates the standard deviation of trajectories in the cluster based on the comprehensive similarity, as follows: Assuming that the DBSCAN clustering algorithm is used to cluster the ship trajectories, there are a total of K The cluster, the first k Cluster Ck The number of trajectories is Nk Then cluster Ck center for: ； In the formula, For trajectory and trajectory The overall similarity; The intra-class standard is: ； In the formula, For intra-class standards, For trajectory and trajectory center The overall similarity.
8. The ship trajectory clustering method integrating multi-dimensional features according to claim 1, characterized in that, The comprehensive similarity determination method is as follows: ； In the formula, For trajectory and trajectory Overall similarity For trajectory and trajectory Geographical distance similarity, For trajectory and trajectory directional similarity, For trajectory and trajectory The cumulative common subsequence similarity.
9. A computer device / equipment / system, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 8.
10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 8.