A method for extracting mesoscale eddy migration paths based on RDP trajectory division and direction clustering

Abstract

The present invention proposes a method for extracting the migration path of a mesoscale vortex based on RDP trajectory division and directional clustering. By introducing the RDP algorithm and defining directional similarity, the trajectory division method of the traditional density-based clustering algorithm is optimized, which is more suitable for the selection of vortex trajectory feature points and is sensitive to the direction of the trajectory segment. At the same time, the reference evaluation QM index and the silhouette coefficient are introduced to measure the clustering effect. The results show that the sample density within the cluster of this algorithm is more compact, the classification standard is clearer, the number of misclassified noise segments is less, the clustering quality is higher, and the effect is better. This method divides vortex trajectories with similar behaviors into one category, explores the movement path of the vortex, and analyzes the movement law, in order to predict the propagation path and evolution of the vortex in a certain sea area. It has a great reference role in the research work on ocean energy conversion and biochemical cycles, and is also of great significance for better understanding the global material and energy balance.

Description

Technical field:

[0001] The present invention relates to the field of ocean-scale eddies, and in particular to a method for extracting a mesoscale eddy migration path based on RDP trajectory division and direction clustering. Background technology:

[0002] As the largest ecosystem on Earth, the ocean carries extremely rich biological resources and a huge energy conversion process. Among them, mesoscale vortices, as one of the most common dynamic phenomena in the ocean, play a key role in regulating the Earth's climate and controlling the ocean's absorption of greenhouse gases with their significant energy carrying and material transfer functions. The flow field distribution of these vortices is manifested as circling around a certain center point. According to the different directions of rotation, they are divided into cyclonic vortices and anticyclonic vortices, which have a profound impact on the marine ecological environment. In particular, their role in promoting vertical convection and horizontal mixing of seawater and carrying nutrients cannot be ignored.

[0003] With the rapid development of ocean observation technology, especially satellite remote sensing and Argo float systems, people's understanding of ocean eddies has gradually deepened. The research field not only covers the spatiotemporal distribution, internal structure and influencing factors of eddies, but also extends to the interaction between eddies and marine ecosystems and global climate change. Although there have been many research results on mesoscale eddies in the ocean, most of these studies focus on the analysis of static characteristics of eddies, such as macroscopic descriptions such as spatiotemporal distribution and movement trends, or case studies of single special eddies. However, in-depth analysis and accurate prediction of the movement laws of eddies, especially the accurate revelation of eddy movement paths, is still a challenge.

[0004] In response to the above problems, the present invention proposes a method for extracting the migration path of mesoscale eddies based on RDP trajectory division and directional clustering, aiming to explore the movement path and law of mesoscale eddies in the ocean through trajectory clustering analysis technology. This method is based on an in-depth analysis of marine remote sensing data, and divides eddy trajectories with similar behavioral characteristics into one category. On this basis, it can not only reveal the movement law of eddies, but also predict the propagation path and evolution process of eddies in a certain sea area. This research not only provides new perspectives and tools for the scientific study of ocean energy conversion and biochemical cycles, but also provides important support for understanding the global material and energy balance relationship, and has important scientific value and practical significance. Summary of the invention:

[0005] The purpose of the present invention is to address the defects of the prior art and provide a method for extracting the migration path of a mesoscale vortex based on RDP trajectory division and directional clustering. The invention aims to construct a research method suitable for clustering mesoscale vortex trajectories according to the movement characteristics of the mesoscale vortex and extract the vortex migration path.

[0006] To achieve the above object, the present invention provides the following technical solution: a method for extracting the migration path of a mesoscale vortex based on RDP trajectory division and direction clustering, and the specific method steps are as follows:

[0007] S1: Define the trajectory distance function. When clustering line sets in a two-dimensional plane, redefine the calculation method of the distance between lines. The distance is calculated by the vertical distance d ⊥ , parallel distance d || The angle distance d θ It consists of three parts;

[0008] S2: Trajectory segmentation: first, the vortex trajectory is segmented, and the Ramer-Douglas-Peucker algorithm (RDP) is used to segment the trajectory, and the adaptive parameter method is used to determine the appropriate parameter D;

[0009] S3: Trajectory segment clustering. After the trajectory is segmented, clustering is performed based on the trajectory segments. By extending the density-based point clustering algorithm, a distance function is defined and a measurement method for trajectory direction similarity is introduced to classify trajectory segments with similar behaviors in the trajectory segment set into one category.

[0010] S4: Extracting the moving path. After obtaining the clustering results, the scanning line method is used to extract the representative trajectory to describe the overall moving path of the trajectory segment within the cluster. The representative trajectory is the moving path of the vortex.

[0011] As a preferred technical solution of the present invention, defining the trajectory distance function in step S1 specifically includes the following steps:

[0012] S1-1: Set two line segments L i =s i e i and L j =s j e j , where L i For a longer line segment, L j is the shorter line segment, passing through the perpendicular distance d between the line segments ⊥ , parallel distance d || The angle distance d θ To calculate the line segment L i With L j The distance between i and e i Represents L i The starting and ending points, s j and e j Represents L j the starting and ending points;

[0013] S1-2: Calculate the foot of the perpendicular ps and p e , respectively, line segment L i Upper pair L i The vertical projection of the endpoints is calculated by the following formulas:

[0014]

[0015]

[0016] in,

[0017]

[0018]

[0019] S1-3: Define line segment L i With L j The vertical distance d ⊥ , parallel distance d || and angular distance d θ The calculation methods are:

[0020]

[0021] d || =MIN(l ||1 , l ||2 ) (6)

[0022] d θ =||L j ||×sinθ (7)

[0023] S1-4: Line segment L i With L j The distance between i , L j ) is defined as:

[0024] dist(L i , L j )=ω ⊥ ·d ⊥ (L i , L j )+ω || ·d || (L i , L j )+ω θ ·d θ (L i , L j ) (8)

[0025] Among them, ω ⊥ ,ω || and ωθ are three distance weights.

[0026] As a preferred technical solution of the present invention, the trajectory division step in step S2 is characterized by: using RDP to divide a group of trajectories Each track in The specific method is as follows:

[0027] S2-1: First, the trajectory start and end points p1 and Connect to get line segment Traverse all points to line segments on the trajectory The maximum value is recorded as dmax;

[0028] S2-2: Compare dmax with D. If dmax < D, then Considered as track TR i If dmax ≥ D, retain the coordinate point corresponding to dmax, and use this point as the boundary to divide the trajectory into two parts, and recursively repeat steps S2-1 and S2-2 for each part;

[0029] S2-3: Process all segmented trajectory parts until the maximum deviation of each part is less than the threshold D, and finally form a new trajectory segment by connecting the segmentation points;

[0030] In addition, this method uses an adaptive parameter method to determine the distance threshold D, and calculates the optimal threshold change rate k0 through the trajectory fitting curve equation (9). The angle change rate is the change rate between two adjacent points on the fitting curve in the tangent direction. The lower change rate between the pth point and the p+1th point is calculated as shown in equation (10):

[0031]

[0032]

[0033] Among them, a, b and c are the parameters of the fitting function, r p is the lower rate of change between point p and point p+1, k0 is the value of all r p The maximum value represents the most significant shape change point.

[0034] As a preferred technical solution of the present invention, the characteristics of trajectory segment clustering in step S3 are: assuming that S is a set of all line segments, parameter ε represents the threshold value of the distance between two line segments (neighborhood range), parameter MinLns represents the minimum number of line segments (minimum number of lines) that the clustering set should contain, and the following definition is required in the clustering process:

[0035] T1: Line segment L i ∈S’s neighborhood: Nε (L i )={L j ∈D|dist(L i , L j )≤ε};

[0036] T2: Core segment: When |N ε (L i )|≥MinLns, line segment L i ∈S is called the core segment;

[0037] T3: Density can be reached directly: meet L i ∈N ε (L j ) and |N ε (L j )|≥MinLns, then L i Direct density up to L j ;

[0038] T4: Density reachable: There exists a set of line segments L i , L i+1 …L j-1 , L j ∈S, if L k Direct density up to L k+1 (L k+1 is the core segment), then L i Density up to L j ;

[0039] T5: Density connection: If there is L k ∈S and L k is the core segment, so that segment L i With line segment L j Average density can reach L k , then L i Density connection L j ;

[0040] T6: Density-connected set: When a non-empty subset Satisfy a. With L j Density connection b, If L j ∈C and L j Density up to L i , then L j ∈C, then C is called a density connection set, where the parameter ε can be expressed by the information entropy method, and then the heuristic algorithm is used to determine the range of ε. The entropy calculation formula is:

[0041]

[0042] In the formula, For each given ε neighborhood range, we can know the number of line segments N in the corresponding neighborhood range of any line segment L ε (L), when H(X) reaches the minimum value, it is an optimal classification of the original data set. At this time, the ε value is the optimal neighborhood range, so the size of MlinLns is estimated. The selected parameter ε is not easy to be too small, and the parameter MlinLns is not easy to be too large.

[0043] As a preferred technical solution of the present invention, the trajectory segment clustering in step S3 introduces a method for measuring trajectory direction similarity. The method measures the similarity of the overall directions of the two trajectories by comparing the consistency of the motion direction between each point on the trajectory and its vertical projection point on the other trajectory. Specifically, the method includes the following steps:

[0044] G1: For each divided trajectory segment P, the n original trajectory points P contained between its feature points = {p1, p2, p3, ..., p n}, where p1 = (x1, y1), p2 = (x2, p2)…, p n =(x n ,y n );

[0045] G2: Calculate trajectory point p i The direction of motion is represented by the vector direction between two adjacent trajectory points (δx i ,δy i ) represents, where δx i and δy i Represent the motion direction components of the trajectory point on the x-axis and y-axis respectively. For point p i , the calculation formula is:

[0046]

[0047]

[0048] For the last point p n , its motion direction is the motion direction component δx of the previous point i-1 and δy i-1 ;

[0049] G3: By calculating and comparing the set of points on the trajectory segment and their movement directions {(δx1, δy1), (δx2, δy2), …, (δx n ,δy n )}, to measure the similarity of trajectory directions.

[0050] As a preferred technical solution of the present invention, the specific characteristics of the direction similarity in step G3 are:

[0051] H1: Two divided trajectory segments P1 and P2, assuming that there is a trajectory point p on trajectory segment P1 i , calculate p i The direction of motion (δx i ,δy i ), and find p i Projection point q on trajectory segment P2 i , and calculate q in the same way i The direction of motion (δx (i) ,δy (i) );

[0052] H2: Calculate the trajectory point p on the trajectory line P1 i The difference between the moving direction of trajectory segment P2 and the specific calculation formula is as follows:

[0053]

[0054] H3: Calculate the direction difference between track segment P1 and track segment P2. The specific calculation formula is as follows:

[0055]

[0056] Where n represents the total number of trajectory points contained in trajectory segment P1;

[0057] H4: Calculate the overall direction similarity between trajectory segment P1 and trajectory segment P2:

[0058] D r (P1, P2) = min{d TR (P1, P2),d TR (P2,P1)} (16)

[0059] Where d TR (P1, P2) represents the direction difference between the trajectory segment P1 and the trajectory segment P2; d TR (P2, P1) represents the direction difference between the trajectory segment P2 and the trajectory segment P1; D r The value range of D is [0, 2]. r The smaller it is, the higher the similarity between the directions of trajectory segment P1 and trajectory segment P2 is. The more similar their movement directions are, the more similar the movement directions of the red segment and the yellow segment obtained after division are.

[0060] As a preferred technical solution of the present invention, the specific operation steps of clustering the trajectory segments in step S3 are:

[0061] S3-1: Calculate the ε neighborhood N of each unclassified line segment L ε(L), and calculate the directional similarity between each line segment in the neighborhood and line segment L. If the directional similarity between the two line segments is D r ≤1, then keep the segment in the neighborhood. If L is confirmed as a core segment, perform the second step to expand a cluster, which now contains only N ε (L);

[0062] S3-2: Calculate the density connection set of each core segment, calculate the density reachable segments of each core segment, and add them to the current cluster. If a newly added segment is unclassified, it will be added to the queue Q for further processing because it may be a core segment, otherwise it will not be added to the queue Q;

[0063] S3-3: Check the trajectory cardinality of each cluster, and if its trajectory cardinality is less than the threshold, remove it from the associated cluster.

[0064] As a preferred technical solution of the present invention, the specific operation steps of extracting the moving path in step S4 are:

[0065] S4-1: Superimpose all line segment vectors in the same class, and the direction of the resulting vector line segment is the main direction of the class;

[0066] S4-2: Use a set of straight lines perpendicular to the main direction to scan the starting point and end point of each line segment in sequence, and record the positions where the scan lines intersect with all line segments;

[0067] S4-3: If the number of intersection points on a scan line is greater than MlinLns, calculate the average position of all intersection points on the scan line;

[0068] S4-4: Connect the average points on the scan line in order according to the main direction to obtain the characterization trajectory of this type. It should be pointed out that when two average points are adjacent to each other, smoothing is required and the latter average point is discarded.

[0069] Compared with the related prior art, the present invention has the following technical advantages and the beneficial effects of the present invention are:

[0070] Accurate trajectory extraction and cluster analysis: This invention uses advanced trajectory extraction technology combined with a directional clustering algorithm to more accurately identify and track the movement path of ocean mesoscale eddies. Compared with traditional density- or distance-based clustering methods, this method can better capture the directional characteristics of eddies, thereby improving the accuracy and efficiency of clustering.

[0071] In-depth analysis of vortex behavior characteristics: By clustering the segmented vortex trajectory segments, the present invention can reveal the detailed behavior and movement laws of the vortex, including its changing speed and direction, etc. This kind of analysis is often difficult to achieve in traditional technologies, so the present invention can provide a more in-depth and comprehensive understanding of the dynamics research and prediction of the vortex.

[0072] Wide application potential: This invention can be used not only to study mesoscale eddies in the ocean, but also to study other eddy phenomena, such as atmospheric eddies, whirlpools in rivers and lakes, etc. The universality of its analytical methods and theoretical framework provides new tools and perspectives for eddy-related research in multiple fields.

[0073] Contribution to marine environment monitoring and early warning: By accurately analyzing the movement path and behavior of vortices, the present invention helps to better understand the impact of vortices on the marine environment, ecosystem and global climate change. This has important practical significance for the protection of marine resources, monitoring of the marine environment and early warning of disasters.

[0074] Enhanced data processing capability: The present invention optimizes the data processing flow through an adaptive parameter method and a trajectory-based directional clustering algorithm, which can effectively process large-scale ocean remote sensing data sets, improve the efficiency of data analysis and the ability to process large data sets. Description of the drawings:

[0075] Figure 1 is a flow chart of the method provided by the present invention;

[0076] Figure 2 It is a demonstration of the trajectory clustering process of a specific embodiment provided by the present invention;

[0077] Figure 3 It is a schematic diagram of a line segment distance calculation formula of a specific embodiment provided by the present invention;

[0078] Figure 4 is a schematic diagram of error clustering of a specific embodiment provided by the present invention;

[0079] Figure 5 is a schematic diagram of trajectory direction similarity calculation according to a specific embodiment of the present invention;

[0080] Figure 6 It is a comparison of clustering results before and after improvement of a specific embodiment provided by the present invention;

[0081] Figure 7 It is a North Indian Ocean warm vortex clustering result of a specific embodiment provided by the present invention;

[0082] Figure 8 This is the North Indian Ocean cold vortex clustering result of a specific embodiment provided by the present invention. Specific implementation method:

[0083] The present invention is further described below in conjunction with the accompanying drawings and examples. However, the present invention can be implemented in many different ways and should not be construed as being limited to the embodiments shown; on the contrary, these embodiments provide those skilled in the art with implementation methods that meet applicable legal requirements.

[0084] Embodiment 1: According to Figure 1 As shown in the figure, the method for extracting the migration path of a mesoscale vortex based on RDP trajectory division and directional clustering is specifically composed of the following steps: The first step is to define the trajectory distance function. When clustering a line set in a two-dimensional plane, it is necessary to redefine the calculation method of the distance between lines. The distance between lines is determined by the vertical distance d ⊥ , parallel distance d || The angle distance d θ It consists of three parts. The second step is trajectory segmentation. Before clustering the trajectory, the trajectory needs to be segmented first, so that the same trajectory may belong to multiple clusters. The original trajectory will be compressed and simplified during segmentation, and the characteristics of the original trajectory will be retained, and the research granularity will be finer. This method will use the Ramer-Douglas-Peucker algorithm (RDP) to segment the vortex trajectory, and use the adaptive parameter method to determine the appropriate parameter D. The third step is trajectory segment clustering. After the vortex trajectory is segmented, clustering is performed based on the trajectory segments. Based on the density-based point clustering algorithm, this method is extended for vortex trajectory segments, defines a distance function, and introduces a measurement method for trajectory direction similarity. Trajectory segments with similar behaviors in a trajectory segment set are classified into one category. It can identify trajectories of any shape and variable behaviors. It not only considers the similar sub-trajectories of multiple trajectories, but also shows the differences between trajectories, and can effectively mine the trajectory characteristics of mesoscale vortices. The fourth step is to extract the moving path. After obtaining the clustering results, the scanning line method is used to extract the representative trajectory to describe the overall movement of the trajectory segment within the cluster. The representative trajectory is the moving path of the vortex.

[0085] This method extends the traditional DBSCAN clustering method for point data to line data. It uses the idea of ​​"partition-aggregation" and includes three stages: trajectory partitioning, trajectory segment clustering, and migration path extraction. First, a trajectory is divided into a set of segments, then the segments that meet the requirements are combined into a cluster according to the defined distance metric, and finally a representative trajectory is generated for each cluster. The specific problem is defined as: Given a set of input trajectories Each trajectory is a set of points Track TR i A sub-trajectory of is P c1P c2 …P ck (1≤c1<c2<…c k <len i ). The output is a set of line segment clusters and each line segment is clustered C i A representative trajectory of Represents a group of sub-trajectories. A sub-trajectory in a trajectory may belong to multiple different clusters. Figure 2 The overall process of trajectory clustering in the partitioning and combining framework is demonstrated.

[0086] When clustering a set of points, Euclidean distance is often used as the basis for classification. When clustering a set of lines in a two-dimensional plane, it is necessary to redefine the calculation method of the distance between lines. The distance function of a line consists of three parts: the vertical distance d ⊥ , parallel distance d || The angle distance d θ .like Figure 3 As shown, suppose there are two line segments L i =s i e i and L j =s j e j , specify the longer line segment as L i , the shorter line segment is L j , p s With p e is line segment L i Endpoint on line segment L i The projection on the right, θ is the angle between the two line segments, and the foot of the perpendicular is p s With p e It can be calculated by formula (1) and formula (2).

[0087]

[0088]

[0089] in:

[0090]

[0091]

[0092] Vertical distance d ⊥ , parallel distance d || The angle distance d θ The calculations of are shown in formula (5), formula (6) and formula (7) respectively.

[0093]

[0094] d || =MIN(l ||1 , l ||2 ) (6)

[0095] d θ =||L j ||×sinθ (7)

[0096] Finally, define the line segment L i With L j The distance between them is:

[0097] dist(L i , L j )=ω ⊥ ·d ⊥ (L i , L j )+ω || ·d || (L i , L j )+ω θ ·d θ (L i , L j ) (8)

[0098] where ω ⊥ ,ω || and ω θ There are three distance weights, which are generally 1 by default.

[0099] Before clustering the trajectory, it is necessary to segment the trajectory first, so that the same trajectory may belong to multiple clusters. The original trajectory will be compressed and simplified during segmentation, and the characteristics of the original trajectory will be retained, and the research granularity will be finer. This method will use the Ramer-Douglas-Peucker algorithm (RDP) to segment the vortex trajectory. As a classic algorithm for vector data compression, the RDP algorithm is often used to simplify paths or contours, and can segment the trajectory from the perspective of the entire trajectory. It iteratively removes points on the line while ensuring that the maximum deviation between the simplified line and the original line shape does not exceed the preset threshold. Suppose there is a trajectory The preset parameter (distance threshold) is D, and the specific implementation method is as follows:

[0100] 1. Connect the trajectory end to end to get a line segment Traverse all points to line segments on the trajectory The maximum value is recorded as dmax;

[0101] 2. Compare dmax with D. If dmax < D, then the line segment Considered as track TR iIf dmax ≥ D, keep the coordinate point corresponding to dmax, and use this point as the boundary to divide the trajectory into two parts, and repeat the above process for these two parts respectively;

[0102] 3. When all trajectory parts have been processed, connect each segmentation point in turn to form a new trajectory.

[0103] In addition, the RDP algorithm also sets a threshold D to control the compression degree of the vortex trajectory. If the value of D is low, the length of the divided trajectory segments will be shorter, and these short segments will cause the quality of clustering to deteriorate; if the value of D is high, the divided trajectory segments will ignore some obvious feature points, resulting in the failure to reflect the movement details of the vortex in the subsequent clustering and extraction of feature trajectories. Therefore, a suitable method is used to determine the D value. This method uses an adaptive parameter method to determine the parameter D. This method first calculates the optimal threshold change rate k0 through the fitting curve of the trajectory, and then identifies the point with the most significant shape change of the trajectory based on k0, which is the retained feature point, thereby achieving trajectory compression, where k0 is calculated as follows. Assume that the fitting curve equation of the trajectory is formula (9).

[0104]

[0105] Where a, b and c are the parameters of the fitting function, which control the shape of the curve. The angle change rate is defined as the rate of change between two adjacent points on the fitting curve in the tangent direction. The lower rate of change between the pth point and the p+1th point is calculated as shown in formula (10).

[0106]

[0107] The threshold change rate corresponding to the point with the largest angle change rate is the optimal threshold change rate k0. The parameter D obtained in this way can minimize the trajectory distortion while balancing the compression rate.

[0108] After the vortex trajectory is segmented, it is assumed that S is the set of all line segments, the parameter ε represents the threshold value of the distance between two line segments (neighborhood range), and the parameter MinLns represents the minimum number of line segments (minimum number of lines) that the clustering set should contain. The following definitions are required in the clustering process:

[0109] 1. Line segment L i ∈S’s neighborhood: N ε (L i )={L j ∈D|dist(L i , L j )≤ε};

[0110] 2. Core segment: When |N ε (L i )|≥MinLns, line segment Li ∈S is called the core segment;

[0111] 3. Density can be directly reached: meet L i ∈N ε (L j ) and |N ε (L j )|≥MinLns, then L i Direct density up to L j ;

[0112] 4. Density reachable: there exists a set of line segments L i , L i+1 …L j-1 , L j ∈S, if L k Direct density up to L k+1 (L k+1 is the core segment), then L i Density up to L j ;

[0113] 5. Density connection: If there is L k ∈S and L k is the core segment, so that segment L i With line segment L j Average density can reach L k , then L i Density connection L j ;

[0114] 6. Density-connected set: When a non-empty subset Satisfy a. With L j Density connection b. If L j ∈C and L j Density up to L i , then L j ∈C, then C is called a density-connected set.

[0115] The parameter ε can be expressed by the information entropy method, and then the range of ε is determined by a heuristic algorithm. The entropy can be expressed by formula (11).

[0116]

[0117] In the formula

[0118] For each given ε neighborhood range, we can know the number of line segments N in the corresponding neighborhood range of any line segment L ε(L). According to the information entropy theory, when H(X) reaches the minimum value, it is an optimal classification of the original data set. At this time, the ε value is the optimal neighborhood range, so the size of MlinLns can be estimated. The selected parameter ε is not easy to be too small, and the parameter MlinLns is not easy to be too large.

[0119] At the same time, this method also takes into account the directional characteristics of the trajectory when clustering, and introduces a measurement method for trajectory directional similarity to calculate the directional similarity between trajectories. Traditional density-based trajectory clustering algorithms mainly focus on the distance or density between trajectory segments, rather than the sequence or direction of trajectory segments. This means that even if two trajectories are completely different in direction, as long as they are close to each other in space, they may still be classified into the same cluster, such as Figure 4 As shown. The blue line segment and the green line segment are two clusters of different categories, but the line segment 1 and line segment 2 in almost opposite directions are classified into the same category, which is unreasonable. The basic idea of ​​measuring trajectory similarity is to project each point on the trajectory onto the trajectory to be measured with the trajectory, and measure the similarity of the overall direction of the trajectory by calculating the consistency of the movement direction between the trajectory point and its corresponding projection point. The projection of a point to a trajectory is defined as the position of the projection point with the shortest projection distance on the line segment when a point is vertically projected on a trajectory.

[0120] For a trajectory segment P consisting of two adjacent feature points, that is, the divided trajectory segment P, the feature points contain n original trajectory points, denoted as P = {p1, p2, p3, ..., p n}, where p1 = (x1, y1), p2 = (x2, y2) ..., p n =(x n ,y n ), the moving direction of the trajectory point is approximately represented by the vector direction between two adjacent trajectory points, then the trajectory point p i The direction of motion is expressed as (δx j ,δy i ), where δx i represents the trajectory point p i The component of the motion direction on the x-axis, δy i represents the trajectory point p i The component of motion direction on the y-axis, δx i ,δy i The calculation formulas are shown in formula (12) and formula (13).

[0121]

[0122]

[0123] From the above formula, we can see that the moving direction of the trajectory segment P can be expressed as {(δx1, δy1), (δx2, δy2), …, (δx n ,δy n )}, the directional similarity between trajectories is specifically described as:

[0124] like Figure 5 As shown in the figure, the red line segment and the yellow line segment represent the two divided trajectory segments respectively. The original trajectory is recorded as P1 and P2. Suppose there is a trajectory point p on the trajectory segment P1. i , calculate the trajectory point p according to formula (12) and formula (13) i The direction of motion (δx i ,δy i );q i represents the trajectory point p i At the projection point on the trajectory segment P2, the trajectory point q is calculated according to formula (12) and formula (13) i The direction of motion (δx (i) ,δy (i) );

[0125] Calculate the trajectory point p on the trajectory line P1 i The difference between the moving direction of trajectory segment P2 and the moving direction of trajectory segment P2 is calculated as follows:

[0126]

[0127] The directional difference between the trajectory segment P1 and the trajectory segment P2 is calculated according to formula (15).

[0128]

[0129] Wherein, n represents the total number of trajectory points included in the trajectory segment P1. According to the above steps, the direction difference between any two trajectory segments can be calculated.

[0130] The overall directional similarity between trajectory segment P1 and trajectory segment P2, that is, the directional similarity between the red line segment and the yellow line segment, is calculated as shown in formula (16).

[0131] D r (P1, P2) = min{d TR (P1, P2),d TR (P2,P1)} (16)

[0132] Where d TR (P1, P2) represents the direction difference between the trajectory segment P1 and the trajectory segment P2, d TR (P2, P1) represents the direction difference between the track segment P2 and the track segment P1. r The value range of D is [0, 2].r The smaller it is, the higher the similarity between the directions of trajectory segment P1 and trajectory segment P2 is. The more similar their movement directions are, the more similar the movement directions of the red segment and the yellow segment obtained after division are.

[0133] Based on the above definition, assuming that all trajectory segments are not classified, the density-based segment clustering algorithm can be roughly summarized into the following steps:

[0134] 1. Calculate the ε neighborhood N of each unclassified line segment L ε (L), and calculate the directional similarity between each line segment in the neighborhood and line segment L. If the directional similarity between the two line segments is D r ≤1, then keep the segment in the neighborhood. If L is confirmed as a core segment, the second step is performed to expand a cluster, which now contains only N ε (L).

[0135] 2. Calculate the density connection set of each core segment. Calculate the density reachable segments of each core segment and add them to the current cluster. If a newly added segment is unclassified, it will be added to the queue Q for further processing, because it may be a core segment, otherwise it will not be added to the queue Q.

[0136] 3. Check the trajectory cardinality of each cluster. If its trajectory cardinality is less than the threshold, it is removed from the associated cluster.

[0137] The clustering result calculated in this way has the consistency of the distance between trajectories and the direction of trajectories on the basis of the original trajectory, avoiding the deviation of the original motion state of the vortex from the desired trajectory direction due to trajectory compression, and fully improving the accuracy and performance of vortex trajectory clustering.

[0138] 4. Extract representative trajectories. For the clustering results obtained, representative trajectories need to be extracted to describe the overall movement of the trajectory segments within the cluster. The Traclus algorithm uses a scan line method to extract feature trajectories, which mainly includes three steps: first, all line segment vectors in the same class are superimposed, and the direction of the resulting vector line segment is the main direction of the class; a set of straight lines perpendicular to the main direction are used to scan the starting and end points of each line segment in turn, and the positions where the scan line intersects with all line segments are recorded; if the number of intersections on a scan line is greater than MlinLns, the average position of all intersections on the scan line is calculated; finally, the average points on the scan line are connected in order according to the main direction to obtain the representative trajectory of the class. It should be pointed out that when the positions of two average points are adjacent, smoothing is required and the latter average point is discarded.

[0139] By summarizing the clustering results, the characterization trajectory obtained is the migration path of the moving object, which can reflect the starting and ending positions of the movement process, changes in the moving direction and other information.

[0140] To verify the directional sensitivity of this method, we now test the trajectories of adjacent but different vortices. This experiment randomly selected partial trajectories of four vortices, such as Figure 6 As shown in , after extracting the feature points, the trajectory is divided and the velocity direction of the feature point is marked at the end of each line segment in chronological order as the current instantaneous direction of the trajectory segment. Figure 6 It can be seen that the 4 trajectories are divided into 10 trajectory segments, which are all classified into the same cluster when clustered using the traditional density-based clustering algorithm. After clustering using this algorithm, the trajectory segments are divided into two clusters based on direction, and the direction similarity D of the two segments in the same cluster is r ≤1, which makes the clustering result more directional while avoiding all the density-connected segments in one cluster. In extreme cases, all the segments in the density-connected set may be extracted from one trajectory. Such a cluster is meaningless because it does not have enough segments from different trajectories and is not representative, thus failing to explain the motion behavior of the extracted path.

[0141] Example 2: To verify the feasibility of this method, the number of mesoscale eddy tracks in the North Indian Ocean from January 2009 to February 2019 is used for experiments. There are 1060 warm eddy tracks and 953 cold eddy tracks. The parameters ε are 5 and 4 respectively, and the parameter MinLns is 5 and 6. Clustering results and path extraction Figure 7 , Figure 8 As shown in the figure, the blue line represents the characteristic trajectory extracted from the warm vortex clustering result, that is, the migration path of the warm vortex, and the red line represents the characteristic trajectory extracted from the cold vortex clustering result, that is, the migration path of the cold vortex. The gray line represents the original trajectory participating in the clustering, the red background represents the trajectory density of the warm vortex of the vortex, and the blue background represents the trajectory density of the cold vortex. As shown in the figure, after clustering the vortex trajectories by this method, 6 warm vortex migration paths and 6 cold vortex migration paths can be obtained, with clear trajectories and reasonable distribution.

[0142] In order to further verify the superiority of this method in processing mesoscale eddy trajectories, this method is compared with the traditional density-based trajectory clustering method. The clustering effect can be evaluated using evaluation indicators. This evaluation will use the QM indicator and silhouette coefficient.

[0143] Assumption C i represents any cluster in the clustering result, Represents the set of all noise segments, and QM is defined as the sum of the sum of squared error (Sum of Squared Error, SSE) and the noise penalty (Noise Penalty), as shown in formula (17).

[0144]

[0145] The smaller QMeasure(QM), the more compact the samples in the same cluster are after clustering, the less misclassified noise is, and the better the clustering effect is.

[0146] Assuming there are n trajectories in the total trajectory data set, the contour coefficient calculation formula for a trajectory sample is:

[0147]

[0148] Where a represents the average distance between the trajectory sample and other trajectories in the cluster, and b represents the average distance between the trajectory sample and the trajectory samples in the adjacent cluster. Therefore, the total silhouette coefficient of the entire trajectory data set is:

[0149]

[0150] The value range of the silhouette coefficient is [-1,1]. The larger the silhouette coefficient, the better the clustering effect.

[0151] In this paper, multiple groups of parameters are set within the value range of ε to evaluate the clustering results multiple times. The evaluation results are shown in Table 1.

[0152] Table 1: Comparison of trajectory clustering effect evaluation

[0153]

[0154] When using QM to evaluate the clustering results, the traditional algorithm reaches the minimum QM when ε = 5, and the algorithm reaches the minimum QM when ε = 6, and the QM value of the algorithm is always smaller than the QM value of the traditional algorithm, indicating that the sample density within the cluster of the algorithm is more compact, the classification standard is clearer, the number of misclassified noise segments is less, the clustering quality is higher, and the clustering effect is better. When using the silhouette coefficient to evaluate the clustering results, the silhouette coefficient of both the traditional algorithm and the algorithm is the largest when ε = 5, and the silhouette coefficient of the algorithm is always greater than that of the traditional algorithm. This result also proves that the samples within the cluster of the algorithm are more compact and the distance between different clusters is larger.

[0155] In summary, this method has compact sample density within the cluster, clear classification criteria, fewer misclassified noise segments, high clustering quality, good effect, and direction sensitivity.

[0156] The above embodiments only express the implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for those of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention.

Claims

1. A mesoscale eddy migration path extraction method based on RDP trajectory division and direction clustering, characterized by: The specific steps of this method are as follows: S1: Define the trajectory distance function. When clustering line sets in a two-dimensional plane, redefine the calculation method of the distance between lines. The distance is calculated by the vertical distance d ⊥ , parallel distance d || The angle distance d θ It consists of three parts; S2: Trajectory segmentation: first, the vortex trajectory is segmented, the Larmer-Douglas-Peucker algorithm is used to segment the trajectory, and the adaptive parameter method is used to determine the appropriate parameter D; S3: Trajectory segment clustering. After the trajectory is segmented, clustering is performed based on the trajectory segments. By extending the density-based point clustering algorithm, a distance function is defined and a measurement method for trajectory direction similarity is introduced to classify trajectory segments with similar behaviors in the trajectory segment set into one category. Trajectory segment clustering introduces a method to measure trajectory direction similarity. This method measures the similarity of the overall directions of two trajectories by comparing the consistency of the movement direction between each point on the trajectory and its vertical projection point on the other trajectory. The specific steps include: G1: For each trajectory segment P after division, the n original trajectory points P contained between its feature points = {p1, p2, p3, ..., p n }, where p1 = (x1, y1), p2 = (x2, y2)…, p n =(x n ,y n ); G2: Calculate trajectory point p i The direction of motion is represented by the vector direction between two adjacent trajectory points. For point p i , the calculation formula is: Among them, δx i and δy i Represent the trajectory point p i Directional components of motion on the x- and y-axes; For the last point p n , its motion direction is the motion direction component δx of the previous point i-1 and δy i-1 ; G 3: By calculating and comparing the set of points on the trajectory segment and their movement directions {(δx1, δy1), (δx2, δy2), …, (δx n ,δy n )}, to measure the similarity of trajectory directions; Among them, the specific characteristics of direction similarity are: H1: Two divided trajectory segments P1 and P2, assuming that there is a trajectory point p on trajectory segment P1 i , calculate p i direction of motion, and find p i Projection point q on trajectory segment P2 i , and calculate q in the same way i direction of movement; H2: Calculate the trajectory point p on the trajectory line P1 i The difference between the moving direction of trajectory segment P2 and the moving direction of trajectory segment P2 is calculated as follows: Among them, δx i and δy i Represent the trajectory point p i The components of the motion direction on the x-axis and y-axis, δx (i) and δy (i) Respectively represent the projection point q i Directional components of motion on the x- and y-axes; H3: Calculate the direction difference between track segment P1 and track segment P2. The specific calculation formula is as follows: Where n represents the total number of trajectory points contained in trajectory segment P1; H4: Calculate the overall direction similarity between trajectory segment P1 and trajectory segment P2: D r (P1,P2)=min{d TR (P1,P2),d tR (P2,P1)} (16) Where d TR (P1, P2) represents the direction difference between the trajectory segment P1 and the trajectory segment P2, d TR (P2, P1) represents the direction difference between the trajectory segment P2 and the trajectory segment P1, D r The value range of D is [0, 2]. r The smaller it is, the higher the direction similarity between trajectory segment P1 and trajectory segment P2 is, and the more similar their movement directions are; S4: Extracting the moving path. After obtaining the clustering results, the scanning line method is used to extract the representative trajectory to describe the overall moving path of the trajectory segment within the cluster. The representative trajectory is the moving path of the vortex.

2. The method for extracting mesoscale vortex migration paths based on RDP trajectory division and direction clustering according to claim 1, characterized in that: The trajectory division step in step S2: RDP is used to divide a set of trajectories Each track in The specific method is as follows: S2-1: First, the trajectory start and end points p1 and Connect to get line segment Traverse all points to line segments on the trajectory The maximum value is recorded as dmax; S2-2: Compare dmax with D. If dmax < D, then Considered as track TR i If dmax ≥ D, keep the coordinate point corresponding to dmax, and use this point as the boundary to divide the trajectory into two parts, and recursively repeat steps S2-1 and S2-2 for each part; S2-3: Process all segmented trajectory parts until the maximum deviation of each part is less than the threshold D, and finally form a new trajectory segment by connecting the segmentation points.

3. The method for extracting mesoscale vortex migration paths based on RDP trajectory division and direction clustering according to claim 1, characterized in that: The characteristics of trajectory segment clustering in step S3 are: assuming that S is the set of all segments, parameter ε represents the threshold of the distance between two segments, and parameter MinLns represents the minimum number of segments that the clustering set should contain. The following definitions are required in the clustering process: T1: Line segment L i ∈S’s neighborhood: N ε (L i )={L j ∈S|dist(L i , L j )≤ε}; T2: Core segment: When |N ε (L i )|≥MinLns, line segment L i ∈S is called the core segment; T3: Density can be reached directly: meet L i ∈N ε (L j ) and |N ε (L j )|≥MinLns, then L i Direct density up to L j ; T4: Density reachable: There exists a set of line segments L i , L i+1 …L j-1 , L j ∈S, if L k Direct density up to L k+1 , then we call L i Density up to L j ; T5: Density connection: If there is L k ∈S and L k is the core segment, so that segment L i With line segment L j Average density can reach L k , then L i Density connection L j ; T6: Density-connected set: When a non-empty subset satisfy L i With L j Density connection If L j ∈C and L j Density up to L i , then L j ∈C, then C is called a density connection set, where the parameter ε can be expressed by the information entropy method, and then the heuristic algorithm is used to determine the range of ε. The entropy calculation formula is: In the formula, For each given ε neighborhood range, we can know the number of line segments N in the corresponding neighborhood range of any line segment L ε (L), when H(X) reaches the minimum value, it is an optimal classification of the original data set. At this time, the ε value is the optimal neighborhood range, thereby estimating the size of MlinLns.

4. The method for extracting mesoscale vortex migration paths based on RDP trajectory division and direction clustering according to claim 1, characterized in that: The specific operation steps of trajectory segment clustering in step S3 are: S3-1: Calculate the ε neighborhood N of each unclassified line segment L ε (L), and calculate the directional similarity between each line segment in the neighborhood and line segment L. If the directional similarity between the two line segments is D r ≤1, then keep the segment in the neighborhood. If L is confirmed as a core segment, perform the second step to expand a cluster, which now contains only N ε (L); S3-2: Calculate the density connection set of each core segment, calculate the density reachable segments of each core segment, and add them to the current cluster; If a newly added line segment is unclassified, it will be added to the queue Q for further processing; S3-3: Check the trajectory cardinality of each cluster, and if its trajectory cardinality is less than the threshold, remove it from the associated cluster.

5. The method for extracting mesoscale vortex migration paths based on RDP trajectory division and direction clustering according to claim 1, characterized in that: The specific operation steps of extracting the moving path in step S4 are: S4-1: Superimpose all line segment vectors in the same class, and the direction of the resulting vector line segment is the main direction of the class; S4-2: Use a set of straight lines perpendicular to the main direction to scan the starting point and end point of each line segment in sequence, and record the positions where the scan lines intersect with all line segments; S4-3: If the number of intersection points on a scan line is greater than MlinLns, calculate the average position of all intersection points on the scan line; S4-4: Connect the average points on the scan line in order according to the main direction to obtain the characterization trajectory of this class. When two average points are close to each other, smoothing is required and the latter average point is discarded.

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