Terminal area approach mode mining method based on ASM-HAC
By using the ASM-HAC method, the HAC hierarchical clustering algorithm is improved by utilizing multi-dimensional feature screening of tracks and adaptive similarity measurement. This solves the problems of misjudgment and reliance on manual intervention in the existing technology for approach pattern mining, and achieves more accurate clustering and control decision support.
Patent Information
- Application Number
- CN202511448837.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-11
- Publication Date
- 2026-02-03
AI Technical Summary
Existing methods for discovering entry patterns fail to fully utilize the multidimensional attributes of flight paths, resulting in misjudgments and an insufficient number of clusters. They also rely excessively on manual intervention and cannot effectively guide control decisions.
The ASM-HAC method was adopted, and track features were screened by Pearson correlation coefficient analysis. The HAC hierarchical clustering algorithm was improved by combining weighted Euclidean distance and Gaussian kernel function with adaptive parameters. The optimal number of clusters was determined by using the Laplacian matrix and feature gap method, and the clustering results were evaluated by combining the silhouette coefficient SC.
It achieves a balance in similarity measurement between dense and sparse areas of flight tracks, reduces human intervention, improves the accuracy and automation level of clustering results, assists controllers in understanding approach patterns, and supports safe and efficient control decisions.
Smart Images
Figure CN121456510A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of terminal area arrival pattern recognition, specifically involving a terminal area arrival pattern mining method based on ASM-HAC. Background Technology
[0002] With the increasing volume of air traffic, higher demands are being placed on the safe and efficient operation of traffic flow in terminal areas. Based on this situation, the International Civil Aviation Organization (ICAO) proposed the concept of Trajectory Based Operation (TBO), in which approach pattern mining, as the foundation of TBO air trajectory operation management, is of paramount importance.
[0003] Research on existing approach pattern mining methods reveals that, although clustering algorithms have been applied to track classification, the features used are mostly concentrated on three-dimensional positional information, failing to fully utilize the multi-dimensional attributes of tracks, such as heading angle and landing gradient. Regarding track similarity measurement, existing research focuses on identifying anomalous tracks while neglecting the heterogeneity of track distribution in time and space, leading to interference between different approach patterns and prone to misjudgments due to local shifts. Furthermore, in determining the number of clusters, the clustering scenarios in existing studies are relatively simple, often resulting in an insufficient number of clusters. The results are also heavily influenced by human intervention, relying excessively on expert subjective experience, thus weakening the data's guiding role in pattern discovery.
[0004] Therefore, there is an urgent need for a terminal area access mode fusion method to overcome the above technical problems. Summary of the Invention
[0005] Purpose of the invention: This invention proposes a terminal area entry pattern mining method based on ASM-HAC, which overcomes the problem that the original hierarchical clustering method relies too much on manual intervention to obtain the optimal number of clusters; at the same time, it fully balances the similarity measurement requirements of dense and sparse track regions.
[0006] Technical Solution: This invention provides a terminal area arrival pattern mining method based on ASM-HAC, specifically including the following steps:
[0007] S1: Pre-acquire ADS-B data from the airport terminal area;
[0008] S2: Screen track features and analyze the correlation between track features using Pearson correlation coefficient;
[0009] S3: Obtain the track distance matrix using the multidimensional dynamic time warping method under weighted Euclidean distance;
[0010] S4: Improve the Gaussian kernel function using adaptive parameters to obtain the ASM track similarity matrix;
[0011] S5: The HAC hierarchical clustering algorithm is improved by introducing the Laplacian matrix and the feature gap method. After applying it to the ASM track similarity matrix, the best track clustering result is obtained.
[0012] S6: Use the silhouette coefficient (SC) to evaluate the rationality of the optimal number of clusters.
[0013] Furthermore, the ADS-B data mentioned in step S1 is the actual flight track data recorded in the air traffic control secondary radar system, including longitude, latitude, altitude, speed, heading angle, landing gradient, landing airport, timestamp, aircraft registration number, aircraft type, and aircraft call sign.
[0014] Further, step S2 includes the following steps:
[0015] S2.1: Filter track features and select longitude, latitude, altitude, speed, heading angle and landing gradient as key features for track clustering;
[0016] S2.2: The correlation between track features is analyzed using the Pearson correlation coefficient to avoid interference from redundant information by assessing the correlation between track features; the calculation formula is:
[0017]
[0018] in, and These represent the track characteristics of two different tracks, corresponding to longitude, latitude, altitude, speed, heading angle, and descent gradient, respectively. The total number of flight tracks. This represents the number of points sampled from a single flight path. For the first track number Each sampling point in the feature The value on, and Indicates track characteristics and The global mean across all track sampling points; The range of values is , among which | |>0.7 indicates a strong correlation, 0.3<| |≤0.7 indicates moderate correlation,| |≤0.3 indicates a weak correlation;
[0019] S2.3: Analyze Pearson correlation coefficient: Determine the correlation between various track features. When the correlation coefficient is greater than the preset value, redundant features are removed.
[0020] Further, step S3 includes the following steps:
[0021] S3.1: Perform Min-Max global normalization on the six track features: longitude, latitude, altitude, heading angle, and landing gradient, and linearly map each feature to... The interval is calculated using the following formula:
[0022]
[0023] in, and The first The global minimum and maximum values of each feature in the entire track dataset. For the first The numerical values of each feature in the track dataset;
[0024] S3.2: Based on the Pearson correlation coefficient analysis results, differentiated weights were assigned to the track features, with a total weight of 1; the weights for longitude and latitude features were respectively... and The weight of high-level features is The weights of the heading angle and landing gradient features are respectively and ;
[0025] S3.3: Two sampling points between flight tracks and The formula for calculating the weighted Euclidean distance is:
[0026]
[0027] in, and These are the track sampling points. and In the Numerical values under each flight path feature The sum of weights for the track features;
[0028] S3.4: Using a multidimensional dynamic time warping algorithm, time axis offset is eliminated through elastic alignment, and the minimum cumulative distance between two tracks is solved;
[0029] S3.5: After calculating the minimum cumulative distance for all track pairs, the track distance matrix is as follows:
[0030]
[0031] in, This represents the total number of tracks in the track clustering experiment.
[0032] Furthermore, the implementation process of step S3.4 is as follows:
[0033] The cumulative distance matrix is initialized to ensure that the cumulative distance from the path's starting point to the first row / column is strictly monotonically increasing, providing a feasible solution space for dynamic programming; the calculation formula is as follows:
[0034]
[0035]
[0036]
[0037] Based on the concept of dynamic programming, we gradually construct a system by making local optimal choices, i.e., minimizing the cumulative distance of the previous step.
[0038] Construct the globally optimal path; the calculation formula is as follows:
[0039]
[0040] Starting from the endpoint, backtrack along the direction of the minimum value in the neighborhood to the starting point to obtain the optimal alignment path, which is the minimum cumulative distance between the two tracks.
[0041] Further, step S4 includes the following steps:
[0042] S4.1: By introducing an adaptive scaling parameter, the scaling parameter in the basic form of the Gaussian kernel function is improved to meet the different similarity measurement requirements of dense and sparse regions of the track, enabling the similarity calculation to dynamically adapt to the spatiotemporal heterogeneity of the track distribution; the calculation formula is as follows:
[0043]
[0044]
[0045] in, The global standard deviation is used to measure the trajectory. The average difference from all other tracks; Total number of tracks; The number of tracks within the neighborhood, in The radius of the neighborhood is used to calculate the local standard deviation of the trajectory, ultimately yielding the local adaptive scaling parameters of the trajectory. ;
[0046] S4.2: The track distance matrix is mapped to a track similarity matrix using an improved Gaussian kernel function. The formula for calculating the improved Gaussian kernel function is as follows:
[0047]
[0048] in, and Tracks that belong to the track set For the track and flight path The minimum cumulative distance, , For adaptive scaling parameters;
[0049] S4.3: When the track is in a dense area, less than 0.5 A value greater than 0.5 can enhance the sensitivity of local similarity relationships, thereby effectively distinguishing subtle motion differences between overlapping or intersecting trajectories; however, in sparse track regions, values greater than 0.5... The value can be extended to expand the decay range of the Gaussian kernel function, avoiding excessive decay of similarity due to small fluctuations in distance, and obtaining the ASM track similarity matrix.
[0050] Further, step S5 includes the following steps:
[0051] S5.1: Treat each track as an independent cluster and construct an initial deviation matrix. ;
[0052] S5.2: Select the minimum distance cluster pair ,merge and For new clusters The new cluster is calculated using the recursive formula of the average linkage method. Distance to other clusters, update the bias matrix Repeat the merging process until all tracks converge into a single cluster; the recursive calculation formula for the average linking method is as follows:
[0053]
[0054] in, and For merging pre-cluster , with cluster average distance, and This represents the number of tracks in the original cluster. The number of tracks for the new cluster. For clusters and cluster The new cluster after merging with cluster The average distance;
[0055] S5.3: Symmetrically normalize the Laplace matrix of the ASM track similarity matrix. Transformation; the calculation formula is as follows:
[0056]
[0057]
[0058] in, It is the identity matrix; to distinguish it from the distance matrix. , here adopt The representation degree matrix is defined as a diagonal matrix, where the diagonal elements are the sum of the elements in each row of the track similarity matrix;
[0059] S5.4: Solve Feature gap sequence Determine the optimal number of clusters corresponding to the location of the largest gap. The calculation formula is as follows:
[0060]
[0061]
[0062] in, for The eigenvalue sequence; the eigengap sequence The index corresponding to the first occurrence of the maximum gap in the text. That is, the optimal number of clusters. Optimal number of clusters It is 8;
[0063] S5.5: Based on the optimal number of clusters Guided pruning to obtain the best track clustering results .
[0064] Further, the contour coefficient SC mentioned in step S6 is:
[0065]
[0066] in, For the track The average distance to all other tracks within the same cluster; For the track The average distance to all tracks of the nearest outer cluster.
[0067] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are: The present invention can make full use of the characteristics exhibited by the multidimensional features of the flight track, and overcome the problem that the original hierarchical clustering method relies too much on manual intervention to obtain the optimal number of clusters; at the same time, the present invention fully balances the similarity measurement requirements of dense and sparse regions of the flight track, the clustering process is more in line with the spatiotemporal heterogeneity of the flight track distribution, and the clustering results can further assist controllers in grasping the characteristics of different approach patterns, which is conducive to making control decisions. Attached Figure Description
[0068] Figure 1 This is a flowchart of the present invention;
[0069] Figure 2 A heatmap of trajectory characteristics correlation under Pearson correlation coefficient analysis;
[0070] Figure 3 The image shows the effect of flight path clustering for arriving flights, taking Nanjing Lukou Airport, a typical busy airport terminal area in eastern China, as an example.
[0071] Figure 4 This is a comparison chart of the silhouette coefficient (SC) under different numbers of clusters. Detailed Implementation
[0072] The present invention will now be described in further detail with reference to the accompanying drawings.
[0073] This invention provides a terminal region entry pattern mining method based on ASM-HAC (Adaptive Similarity Matrix - Hierarchical Agglomerative Clustering), such as... Figure 1 As shown, the specific steps are as follows:
[0074] Step 1: Collect ADS-B (Automatic Dependent Surveillance-Broadcast) data from the terminal areas of typical busy airports in the east, taking the Nanjing Lukou Airport terminal area as an example.
[0075] ADS-B data consists of flight track data recorded by the air traffic control secondary radar system during actual operation, including more than ten types of track information such as longitude, latitude, landing airport, timestamp, aircraft registration number, aircraft type, and aircraft call sign. This embodiment collected 17,665 flight track data points from April 1st to April 30th, 2024 (30 days in total). The secondary radar scan cycle was 4 seconds, and the information for each track point included time, flight number, longitude, latitude, altitude, heading angle, speed, and landing gradient.
[0076] Step 2: Filter the track features and analyze the correlation between track features using the Pearson correlation coefficient.
[0077] Track features were selected, with longitude, latitude, altitude, speed, heading angle, and landing gradient chosen as key features for track clustering. The Pearson correlation coefficient was used to analyze the correlation between track features, and this assessment of correlation helps avoid interference from redundant information. The calculation formula is as follows:
[0078]
[0079] in, and These represent the track characteristics of two different tracks, corresponding to longitude, latitude, altitude, speed, heading angle, and descent gradient, respectively. The total number of flight tracks. This represents the number of points sampled from a single flight path. For the first track number Each sampling point in the feature The value on, and Indicates track characteristics and The global mean across all track sampling points. The range of values is ,in Strong correlation, It is moderately relevant. It is a weak correlation.
[0080] In this embodiment, the trajectory feature correlation heatmap under Pearson correlation coefficient analysis, such as... Figure 2 As shown, the descent gradient and speed characteristics exhibit a moderate correlation with a correlation coefficient of 0.96, indicating that the descent gradient can be considered a further characterization of the aircraft's flight state, reflecting different pilot operation modes. The heading angle shows a moderate correlation with altitude and speed, with correlation coefficients ranging from 0.47 to 0.48, suggesting that the aircraft is frequently guided by radar during the approach phase, leading to frequent heading angle adjustments. Altitude and speed characteristics show an extremely strong correlation with a correlation coefficient as high as 0.92. Their trends during the approach phase are highly synchronized, resulting in significant feature redundancy. The relationships between the remaining features reflect their independent parameter values; therefore, speed as a track feature is subsequently removed.
[0081] Step 3: Obtain the track distance matrix using the multidimensional dynamic time warping method under weighted Euclidean distance.
[0082] The six track features—longitude, latitude, altitude, heading angle, and landing gradient—are subjected to Min-Max global normalization, which linearly maps each feature to... The interval is calculated using the following formula:
[0083]
[0084] in, and The first The global minimum and maximum values of each feature in the entire track dataset. For the first The numerical values of each feature in the track dataset.
[0085] Based on the Pearson correlation coefficient analysis, differential weights were assigned to the track features, with a total weight of 1. The assignment results are as follows: the weights for longitude and latitude features are respectively... and Spatial location is dominant; the weight of height features is The weights of the heading angle and landing gradient features are respectively and .
[0086] Two sampling points between flight tracks and The formula for calculating the weighted Euclidean distance is:
[0087]
[0088] in, and These are the track sampling points. and In the Numerical values under each flight path feature The sum of the weights of the track features is 1. The specific assignment method of the track feature weights is as shown above.
[0089] Using a multidimensional dynamic time warping algorithm, time axis offset is eliminated through elastic alignment, and the minimum cumulative distance between two tracks is calculated:
[0090] Cumulative distance matrix initialization: This initialization ensures that the cumulative distance from the path's starting point to the first row / column is strictly monotonically increasing, providing a feasible solution space for dynamic programming. The calculation formula is as follows:
[0091]
[0092]
[0093]
[0094] Recursive filling of the cumulative distance matrix: Based on the idea of dynamic programming, a globally optimal path is gradually constructed by selecting the local optimum, i.e., the minimum cumulative distance of the previous step. The calculation formula is as follows:
[0095]
[0096] Optimal path backtracking: Starting from the endpoint, backtracking along the direction of the minimum value in the neighborhood to the starting point, and finally obtaining the optimal alignment path, which is the minimum cumulative distance between the two tracks.
[0097] After calculating the minimum cumulative distance for all track pairs, the track distance matrix is obtained as follows, where This represents the total number of tracks in the track clustering experiment.
[0098]
[0099] Step 4: Improve the Gaussian kernel function using adaptive parameters to obtain the ASM track similarity matrix.
[0100] By introducing an adaptive scaling parameter to improve the scaling parameter in the basic form of the Gaussian kernel function, different similarity measurement requirements for dense and sparse regions of the track are met, enabling the similarity calculation to dynamically adapt to the spatiotemporal heterogeneity of the track distribution. The calculation formula is as follows:
[0101]
[0102]
[0103] in, The global standard deviation is used to measure the trajectory. The average difference from all other tracks; Total number of tracks; The number of tracks within the neighborhood, in The radius of the neighborhood is used to calculate the local standard deviation of the trajectory, ultimately yielding the local adaptive scaling parameters of the trajectory. .
[0104] The track distance matrix is mapped to a track similarity matrix by using an improved Gaussian kernel function. The formula for calculating the improved Gaussian kernel function is as follows:
[0105]
[0106] in, and Tracks that belong to the track set For the track and flight path The minimum cumulative distance, , For adaptive scaling parameters.
[0107] When the flight path is in a dense area, smaller A higher value enhances the sensitivity to local similarity relationships, thus effectively distinguishing subtle motion differences in overlapping or intersecting trajectories; however, in sparse track regions, a larger value... The value can expand the decay range of the Gaussian kernel function, avoiding excessive decay of similarity due to small fluctuations in distance.
[0108] In this practical approach, based on the aforementioned improvements, the final ASM track similarity matrix is obtained, as shown in Table 1. All diagonal elements are 1, indicating that the similarity of the same track is the same. Among the off-diagonal elements, the high similarity value of 0.972647 corresponds to flights CBJ5694 and AMU128, close to the theoretical maximum value of 1, indicating that the two tracks are highly similar in spatiotemporal location, heading angle, and landing gradient, possibly stemming from the same approach procedure. Conversely, the low similarity value of 0.000057 corresponds to flights CHH7115 and AMU128, indicating significant behavioral differences between the tracks. The data in the table shows that the similarity values in the matrix span a large range (0.000057~0.972647), reflecting the strong discriminative power of the track patterns and effectively supporting the clustering task of subsequent clustering algorithms.
[0109] Table 1. Partial ASM track similarity matrix
[0110]
[0111] Step 5: Improve the HAC hierarchical clustering algorithm by introducing the Laplacian matrix and the feature gap method. Apply it to the ASM track similarity matrix to obtain the best track clustering result.
[0112] Treat each track as an independent cluster and construct an initial deviation matrix. .
[0113] Select the cluster pair with the smallest distance. ,merge and For new clusters The new cluster is calculated using the recursive formula of the average linkage method. Distance to other clusters, update the bias matrix This process is repeated until all tracks converge into a single cluster. The recursive calculation formula for the average linking method is as follows:
[0114]
[0115] in, and For merging pre-cluster , with cluster average distance, and This represents the number of tracks in the original cluster. The number of tracks for the new cluster. For clusters and cluster The new cluster after merging with cluster The average distance.
[0116] Symmetric normalized Laplace matrix of ASM track similarity matrix Transformation. The calculation formula is as follows:
[0117]
[0118]
[0119] in, It is the identity matrix; to distinguish it from the distance matrix. , here adopt The representation degree matrix is defined as a diagonal matrix, where the diagonal elements are the sum of the elements in each row of the track similarity matrix.
[0120] Solve Feature gap sequence Determine the optimal number of clusters corresponding to the location of the largest gap. The calculation formula is as follows:
[0121]
[0122]
[0123] in, for The eigenvalue sequence; the eigengap sequence The index corresponding to the first occurrence of the maximum gap in the text. That is, the optimal number of clusters. Based on the optimal cluster number Guided pruning to obtain the best track clustering results .
[0124] In this practical approach, Table 2 lists the adaptive scaling parameters for some tracks. As can be seen from the table, the adaptive scaling parameters are different for each track. The values of the adaptive scaling parameters are relatively small in areas with relatively dense tracks, and relatively large in areas with relatively sparse tracks. Using global scaling parameters cannot accurately obtain local information about the tracks, leading to errors in the similarity matrix. Furthermore, global scaling parameters require multiple experiments to improve accuracy, significantly reducing the level of automation and wasting computational resources.
[0125] Table 2 Some adaptive scaling parameters
[0126]
[0127] In this embodiment, Table 3 lists the eigenvalues and eigengap values of the tracks. The first eigenvalue is 1, and it decreases thereafter. At the point where the maximum eigenvalue decreases, the track separation is most obvious, and the eigenspace is most stable. The eigenvalue corresponding to the maximum eigengap theoretically represents the optimal number of clusters. It can be seen that the maximum eigengap is 0.3619, which is the 8th eigenvalue. Therefore, the theoretical optimal number of track clusters is 8.
[0128] Table 3 Eigenvalues and Eigengap
[0129]
[0130] In this practical approach, taking the Nanjing Lukou Airport terminal area, a typical busy airport terminal area in eastern China, as an example, the trajectory clustering effect diagram of arriving flights is shown below. Figure 3 As shown, the optimal clustering result is 8 clusters. Through visualization, it is possible to effectively distinguish different entry modes, thus achieving the purpose of this invention.
[0131] Step 6: Use the silhouette coefficient (SC) to evaluate the rationality of the optimal number of clusters.
[0132] The silhouette coefficient (SC) examines both the cohesion of a track within its own cluster and its separation from neighboring clusters. A higher SC indicates that the track is more closely aligned with its own cluster and further away from other clusters. The calculation formula is as follows:
[0133]
[0134] in, For the track The average distance to all other tracks within the same cluster; For the track The average distance to all tracks of the nearest outer cluster.
[0135] In this embodiment, a comparison chart of the silhouette coefficient (SC) under different numbers of clusters is shown, as follows: Figure 4 As shown, the ASM-HAC method proposed in this invention exhibits the optimal SC evaluation index when the number of clusters is 8, compared to other comparative methods (K-maens, DBSCAN, HAC (σ=0.3), HAC (σ=0.7)). This further verifies the rationality of the overall process of this invention. Methods HAC (σ=0.3) and HAC (σ=0.7) verify that the adaptive scaling parameter of this invention is a better choice because it adapts to the track distribution and is not a fixed value.
[0136] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.
Claims
1. A terminal area entry pattern mining method based on ASM-HAC, characterized in that, Includes the following steps: S1: Pre-acquire ADS-B data from the airport terminal area; S2: Screen track features and analyze the correlation between track features using Pearson correlation coefficient; S3: Obtain the track distance matrix using the multidimensional dynamic time warping method under weighted Euclidean distance; S4: Improve the Gaussian kernel function using adaptive parameters to obtain the ASM track similarity matrix; S5: The HAC hierarchical clustering algorithm is improved by introducing the Laplacian matrix and the feature gap method. After applying it to the ASM track similarity matrix, the best track clustering result is obtained. S6: Use the silhouette coefficient (SC) to evaluate the rationality of the optimal number of clusters.
2. The terminal area access pattern mining method based on ASM-HAC according to claim 1, characterized in that, The ADS-B data mentioned in step S1 is the actual flight track data recorded in the air traffic control secondary radar system, including longitude, latitude, altitude, speed, heading angle, landing gradient, landing airport, timestamp, aircraft registration number, aircraft type, and aircraft call sign.
3. The terminal area access pattern mining method based on ASM-HAC according to claim 1, characterized in that, Step S2 includes the following steps: S2.1: Filter track features and select longitude, latitude, altitude, speed, heading angle and landing gradient as key features for track clustering; S2.2: The Pearson correlation coefficient is used to analyze the degree of correlation between track features. By evaluating the correlation between track features, interference from redundant information can be avoided. The calculation formula is: ； in, and These represent the track characteristics of two different tracks, corresponding to longitude, latitude, altitude, speed, heading angle, and descent gradient, respectively. The total number of flight tracks. This represents the number of points sampled from a single flight path. For the first track number Each sampling point in the feature The value on, and Indicates track characteristics and Global mean across all track sampling points; S2.3: Analyze Pearson correlation coefficient: Determine the correlation between various track features. When the correlation coefficient is greater than the preset value, redundant features are removed.
4. The terminal area access pattern mining method based on ASM-HAC according to claim 3, characterized in that, The The range of values is , among which | |>0.7 indicates a strong correlation, 0.3<| |≤0.7 indicates moderate correlation,| |≤0.3 indicates a weak correlation.
5. The terminal area access pattern mining method based on ASM-HAC according to claim 1, characterized in that, Step S3 includes the following steps: S3.1: Perform Min-Max global normalization on the six track features: longitude, latitude, altitude, heading angle, and landing gradient, and linearly map each feature to... The interval is calculated using the following formula: ； in, and The first The global minimum and maximum values of each feature in the entire track dataset. For the first The numerical values of each feature in the track dataset; S3.2: Based on the Pearson correlation coefficient analysis results, differentiated weights were assigned to the track features, with a total weight of 1; the weights for longitude and latitude features were respectively... and The weight of high-level features is The weights of the heading angle and landing gradient features are respectively and ; S3.3: Two sampling points between flight tracks and The formula for calculating the weighted Euclidean distance is: ； in, and These are the track sampling points. and In the Numerical values under each flight path feature The sum of weights for the track features; S3.4: Using a multidimensional dynamic time warping algorithm, time axis offset is eliminated through elastic alignment, and the minimum cumulative distance between two tracks is solved; S3.5: After calculating the minimum cumulative distance for all track pairs, the track distance matrix is as follows: ； in, This represents the total number of tracks in the track clustering experiment.
6. The terminal area access pattern mining method based on ASM-HAC according to claim 5, characterized in that, The implementation process of step S3.4 is as follows: The cumulative distance matrix is initialized to ensure that the cumulative distance from the path's starting point to the first row / column is strictly monotonically increasing, providing a feasible solution space for dynamic programming; the calculation formula is as follows: ； ； ； Based on the concept of dynamic programming, we gradually construct a system by making local optimal choices, i.e., minimizing the cumulative distance of the previous step. Construct the globally optimal path; the calculation formula is as follows: ； Starting from the endpoint, backtrack along the direction of the minimum value in the neighborhood to the starting point to obtain the optimal alignment path, which is the minimum cumulative distance between the two tracks.
7. The terminal area access pattern mining method based on ASM-HAC according to claim 1, characterized in that, Step S4 includes the following steps: S4.1: By introducing an adaptive scaling parameter, the scaling parameter in the basic form of the Gaussian kernel function is improved to meet the different similarity measurement requirements of dense and sparse regions of the track, enabling the similarity calculation to dynamically adapt to the spatiotemporal heterogeneity of the track distribution; the calculation formula is as follows: ； ； in, The global standard deviation is used to measure the trajectory. The average difference from all other tracks; Total number of tracks; The number of tracks within the neighborhood, in The radius of the neighborhood is used to calculate the local standard deviation of the trajectory, ultimately yielding the local adaptive scaling parameters of the trajectory. ; S4.2: The track distance matrix is mapped to a track similarity matrix using an improved Gaussian kernel function. The formula for calculating the improved Gaussian kernel function is as follows: ； in, and Tracks that belong to the track set For the track and flight path The minimum cumulative distance, , For adaptive scaling parameters; S4.3: When the track is in a dense area, less than 0.5 A value greater than 0.5 can enhance the sensitivity of local similarity relationships, thereby effectively distinguishing subtle motion differences between overlapping or intersecting trajectories; however, in sparse track regions, values greater than 0.5... The value can be extended to expand the decay range of the Gaussian kernel function, avoiding excessive decay of similarity due to small fluctuations in distance, and obtaining the ASM track similarity matrix.
8. The terminal area access pattern mining method based on ASM-HAC according to claim 1, characterized in that, Step S5 includes the following steps: S5.1: Treat each track as an independent cluster and construct an initial deviation matrix. ; S5.2: Select the minimum distance cluster pair ,merge and For new clusters The new cluster is calculated using the recursive formula of the average linkage method. Distance to other clusters, update the bias matrix Repeat the merging process until all tracks converge into a single cluster; the recursive calculation formula for the average linking method is as follows: ； in, and For merging pre-cluster , with cluster average distance, and This represents the number of tracks in the original cluster. The number of tracks for the new cluster. For clusters and cluster The new cluster after merging with cluster The average distance; S5.3: Symmetrically normalize the Laplace matrix of the ASM track similarity matrix. Transformation; the calculation formula is as follows: ； ； in, It is the identity matrix; to distinguish it from the distance matrix. , here adopt The representation degree matrix is defined as a diagonal matrix, where the diagonal elements are the sum of the elements in each row of the track similarity matrix; S5.4: Solve Feature gap sequence Determine the optimal number of clusters corresponding to the location of the largest gap. The calculation formula is as follows: ； ； in, for The eigenvalue sequence; the eigengap sequence The index corresponding to the first occurrence of the maximum gap in the text. That is, the optimal number of clusters. ; S5.5: Based on the optimal cluster number Guided pruning to obtain the best track clustering results .
9. The terminal area access pattern mining method based on ASM-HAC according to claim 8, characterized in that, The optimal number of clusters It is 8.
10. The terminal area access pattern mining method based on ASM-HAC according to claim 1, characterized in that, The contour coefficient SC mentioned in step S6 is: ； in, For the track The average distance to all other tracks within the same cluster; For the track The average distance to all tracks of the nearest outer cluster.