Density clustering stay point identification method for fixed-point sparse trajectory

Abstract

The invention provides a density clustering stay point identification method for a fixed-point sparse trajectory, and the method comprises the steps: employing a self-adaptive extension density peak value clustering assisted dual-threshold stay point identification technology, firstly dividing a global threshold value based on the overall features of trajectory data, and carrying out the preliminary filtering of trajectory points; setting a local threshold value according to an AE-DPC clustering result to refine a discrimination rule so as to accurately identify a stay point; comprising the following steps; the method comprises the following steps: 1, regularly segmenting a global threshold; step 2, clustering and setting a local threshold value; step 3, identifying a dual-threshold stay point; according to the invention, on the basis of overall features of trajectory data, global threshold values are divided to preliminarily filter trajectory points; and a local threshold value can be set according to an AE-DPC clustering result so as to refine a discrimination rule and accurately identify a stay point.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of spatial information technology, and particularly to a density clustering stay point identification method for fixed-point sparse trajectories. BACKGROUND

[0002] With the rapid development of Internet of Things and communication technology, trajectory data reflecting the location and movement characteristics of mobile objects are collected in large quantities. At present, trajectory data has been widely used in natural and social sciences, urban construction and management, etc., and plays an important role in rule discovery, state prediction, decision support, etc. in the scenes of mobile object and group travel mode mining, urban planning, etc.

[0003] Early trajectory research mainly focuses on floating dense trajectories. As shown in Fig. (a) attached Figure 1 , the positioning device carried by the mobile object actively generates data, and the position movement information of the mobile object is recorded relatively continuously. Commonly used are mobile phone communication GPS trajectory data, floating car GPS trajectory data, etc. Due to the need for extensive mobile object research, as well as the inherent defects of dense trajectory positioning fine privacy leakage risk and redundant position information, fixed-point sparse trajectory based on fixed position positioning device monitoring mobile object movement is increasingly concerned by the academic circle. As shown in Fig. (b) attached Figure 1 , traffic camera data based on camera and mobile phone signaling data based on base station, etc. Fixed-point sparse trajectory only triggers the collection mechanism when the mobile object enters the monitoring device coverage range. Its discrete sampling characteristics not only can effectively avoid the generation of redundant route points, but also better balance the contradiction between data precision and privacy protection.

[0004] The identification of stay points is not only a prerequisite for trajectory analysis, but also provides data support for subsequent important research, and plays an irreplaceable role in application scenarios such as point of interest mining and mobile mode classification. For floating-point dense trajectories, data points often form clusters in the continuous space-time domain where the moving object stays. Based on this clustering characteristic, previous schemes use rule-based segmentation to determine one or more thresholds such as speed, spatial radius, supplemented by geographic semantics and travel mode, as a discriminant standard to identify stay points, or use density clustering to divide the internal boundaries of trajectory data points to distinguish between stays and passes. For example, Jiang Xiaohong et al. identified the stay points of freight trucks based on DBSCAN, Zhang Kuan et al. dynamically divided the time and speed thresholds to identify the starting points and stay points of vehicles based on hierarchical clustering, and Lu Jianfeng et al. clustered and segmented GPS trajectory data based on ST-DBSCAN to obtain stay points and moving points using constraints. In addition, considering the uneven density and complex distribution of trajectory point data, related schemes also improve the clustering algorithm. For example, HDBSCAN combines density and hierarchical clustering ideas to improve the density definition by mutual reachable distance, and achieves good results based on the advantages of MST hierarchical clustering. However, its parameters have a greater impact on performance. Ju et al. proposed ATSTC, which uses adaptive K-nearest neighbor data points to determine local density and redefine the density formula, taking into account the spatial distribution of trajectories within the adaptive K-nearest neighbor. However, there are deficiencies in the definition of density peaks. Zhao et al. proposed DPC-FWSN, which designed a weighted shared neighbor similarity allocation strategy and incorporated density differences into sample allocation.

[0005] The deficiencies of the prior art mainly include: (1) There is a fundamental difference between the characteristics of stay points in fixed-point sparse trajectories and the logic of abstracting stay positions through multi-point clustering in floating-point dense trajectories. However, there are few related research schemes, and although there is some attention to fixed-point sparse trajectories, the data and stay point feature mining are still insufficient, such as only considering the speed threshold. (2) Rule-based segmentation methods are simple and efficient, but due to the complexity of trajectory data, it is difficult to identify most stay points, and the precision is limited. Clustering algorithms improve precision through refined standards, but full-trajectory clustering methods are difficult to extend to large-scale scenarios. (3) When data density is uneven and distribution is complex, existing clustering algorithms still have deficiencies. For example, HDBSCAN combines density and hierarchical clustering ideas to improve the density definition and hierarchical clustering to achieve good results. However, its parameters have a greater impact on performance. OPTICS based on hierarchical decomposition of point density requires experience or decision diagram visualization for parameter tuning, which is suitable for small and medium-sized data. Spectral clustering (SC) and improved density peak clustering (DPC) based on graph theory often require the number of clusters to be preset, and have weak noise processing capability. SUMMARY

[0006] The present application provides a density clustering stay point recognition method for fixed-point sparse trajectory, which belongs to the scheme for fixed-point sparse trajectory, and is based on the density clustering algorithm and the adaptive extended density peak clustering (AE-DPC) assisted double-threshold stay point recognition method, and is specifically based on the overall features of the trajectory data to divide the global threshold to preliminarily filter the trajectory points, then set the local threshold according to the AE-DPC clustering result to refine the discrimination rule and accurately recognize the stay points, and finally extract the aggregated clusters of the synthetic data set and recognize the stay points in the real card hole data, so as to verify the effectiveness of the method from the synthetic and real data sets.

[0007] The present application adopts the following technical solutions.

[0008] A density clustering stay point recognition method for fixed-point sparse trajectory, which uses the adaptive extended density peak clustering (AE-DPC) assisted double-threshold stay point recognition technology, is based on the overall features of the trajectory data to divide the global threshold to preliminarily filter the trajectory points, and then set the local threshold according to the AE-DPC clustering result to refine the discrimination rule and accurately recognize the stay points, and includes the following steps. Step one, rule segmentation global threshold; Step two, clustering setting local threshold; Step three, double-threshold stay point recognition.

[0009] As shown in Figure 2 The definition of the fixed-point sparse trajectory includes: Defining a trajectory point as a spatiotemporal data collected by a monitoring device such as a camera or a base station for a moving object, which is expressed in a formula as Formula 1; Where (x, y) is the monitoring device coordinate, t is the recording time, and u is the moving object identifier; The trajectory point represents a certain appearance of the moving object, including passing and staying behaviors, and reflects the activity range of the moving object within a certain spatiotemporal radius with the point as the center. For research convenience, the trajectory point position is usually regarded as the moving object position; Defining a fixed-point sparse trajectory, the sequence of all trajectory points of the same moving object in ascending order of time is expressed in a formula as Formula 2; ; The trajectory points are recorded only when the user is near the monitoring station, and their trajectory sequences are recorded. Traj It has a sparse characteristic, that is, the actual physical movement route of the moving object is sparsely represented as a scatter sequence of coordinate points of the monitoring device; Definition 3, Dwell Point: For a specific user u, a fixed-point sparse trajectory Traj_u The trajectory points in a sequence that satisfy global and local threshold conditions with their adjacent points are expressed by the following formula: Formula 3; The former is determined by the features of all trajectory points, namely the object's main movement time and speed, while the latter is... The average time and velocity of all trajectory points within a certain spatiotemporal range, which is determined by the density clustering results. In step one, when determining whether a point is a stop point, a comprehensive analysis of thresholds such as distance, time, and speed between it and neighboring points is usually performed. Specifically, the spatiotemporal characteristics of the trajectory points are statistically analyzed by frequency, i.e., the main movement time and speed of the moving object. The elbow method is used to find the inflection point of the frequency curve to determine the discrimination rule, i.e., the global threshold. The path points are quickly filtered to obtain the preliminary stop points. The following method is used: Fixed-point trajectory In the middle, if the moving distance and speed are constant, when When the time interval is short, Considered a waypoint, it indicates that after passing through this point, it is... The record states that if the time interval between two points is relatively long, it is initially considered a stopping point; considering long distances, although a long interval does not necessarily mean a stopping point, if the speed changes of the two trajectory segments are small, it is considered... These are waypoints; during the fixed-point sparse trajectory acquisition process, if the object is in... If the object stops, there are two possible scenarios: either the object is recorded at the same location twice, or the object stops and then starts again, being recorded by the next nearby monitoring station. In both cases, the displacement distance is small, and regardless of the time interval, the speed will be close to 0 and much smaller than other trajectory segments.

[0010] Specifically, it calculates and statistically analyzes characteristics such as distance and velocity between trajectory points. (See attached image.) Figure 3 The figures shown are frequency statistics for distance, time, and speed, respectively. Regarding distance, [the data is combined with the attached...] Figure 4The spatial distribution characteristics of the cameras show that most vehicles were recorded within a distance of 1000m. In terms of time, vehicles were recorded most frequently at short intervals (approximately 5 minutes or less), indicating normal vehicle passage through the road segment. Longer intervals (approximately 30 minutes or more) indicate that vehicles were not recorded by the next adjacent camera for an extended period, possibly indicating a stop event. Regarding speed, an extreme value of 5 m / s was observed, gradually decreasing, indicating that most vehicles were traveling at a normal average speed. Therefore, this invention filters out trajectory points (global thresholds) with time intervals less than 5 minutes or speeds greater than 5 m / s, based on trajectory point characteristics; for other points, local thresholds are further considered.

[0011] In step two, trajectory points are introduced based on global threshold filtering. The identification is based on the relationship between the trajectory points and their characteristics within a certain spatiotemporal range, i.e., satisfying the above formula 3. For a "staying event" to be considered a valid event, the stay time of a moving object must be greater than both the global threshold and the average movement time of all moving objects within the range of the monitoring device, while the speed must be less than both the global threshold and the average speed within that range. Clustering is used to effectively divide the spatiotemporal range of data recorded by the monitoring device. Adaptive extended density peak clustering (AE-DPC) is performed to obtain the monitoring device, i.e., the trajectory point, at a certain moment. Within a certain spatiotemporal range centered on the object, the average time and velocity of trajectory points within that range constitute the local threshold. This refers to the amount of data collected by the monitoring equipment within a certain time window.

[0012] In step two, the monitoring device is used as the recording unit, and the flow characteristics, namely the number of moving objects passing through the device within a certain time window, are introduced as the input for clustering, and parameters are set according to the global characteristics of the flow.

[0013] Based on the above global characteristics, in order to ensure traffic differences and statistical continuity, this invention sets the peak period (7-9h, 17-19h) window to 15min and the others to 30min, with the sliding step s being 1 / 2 of the window duration; Step two involves using the AE-DPC clustering algorithm to set local thresholds for clustering; this specifically includes the following: Step S1: Construction of the initial cluster; Step S2: Expansion of the initial cluster; Step S3: Merging of extended clusters.

[0014] Step S1 defines the adaptive k-neighborhood as follows: ; By plotting a k-distance curve, the distance distribution characteristics between x_i and its neighbors are visually reflected. The curvature change of this curve, exhibiting transitional characteristics, is used to identify density differences. Based on this, the adaptive selection of the number of neighboring points k overcomes the limitation of traditional density clustering methods with fixed thresholds, such as DBSCAN, which cannot adapt to uneven density. Figure 5 As shown.

[0015] It should be noted that setting the parameter k_min avoids noise sensitivity caused by an excessively small k value, while k_max limits the search range to prevent a surge in computational costs. Together, they constrain the adaptive k-neighborhood, which essentially divides a uniform region in a complexly distributed global dataset. In step S1, the local density is also defined, specifically as follows: Formula 5; Standard deviation; Traditional density-based clustering algorithms primarily rely on distance metrics to evaluate density distribution characteristics, where distance is inversely proportional to density, and this is used to determine initial cluster centers and their influence range. Taking the DPC algorithm as an example, this method is based on the fundamental assumption that "the density of cluster centers is higher than that of their neighbors," and characterizes the density distribution characteristics of the data space by calculating local density. However, this definition ignores the distribution of data in local regions, such as... Figure 6 As shown in region (a), point A has a smaller local density (0.75) but is evenly distributed. Compared with point group B, which has a wider interval, the clustering result is more stable. Therefore, the value of the improved local density calculation is larger (0.39). For case (b), although point group A is sparser, it is easy to be regarded as an outlier in the more compact point group B. However, considering its even distribution, it can still be considered as a structurally stable category. That is, the coefficient of variation reveals the potential of point group to be clustered from the structural stability of the point group.

[0016] In step S1, the peak point is also defined, specifically as follows: ; Formula 6; ; An adaptive k-neighborhood may share the same density peak point. Since local density alone cannot capture this affiliation, a voting mechanism is introduced. The frequency with which each point is nominated as a density peak is counted, i.e., the voting score V_p. The local densities are then weighted to obtain the corrected density peak. ; .

[0017] The voting mechanism implicitly reflects the characteristics of frequently occurring monitoring equipment, while the density peak, as a key attribute of the initial cluster center, together with the adaptive k-neighborhood mechanism, reflects the clustering characteristics of the core points. This is manifested in the decreasing probability of a sample point being assigned to the cluster as the distance between the sample point and the center point increases, which reflects the density decay effect in the clustering process.

[0018] In the above steps, calculating the adaptive k-neighborhood for each point results in overlapping regions in the initial cluster, which manifests as some points... Covered by multiple clusters: First, when clusters of different densities are adjacent, the centers of sparse clusters tend to be distributed around the periphery of compact clusters; second, overlapping non-central points are usually located in the cluster boundary region. For cases of overlapping cluster centers (reflecting high inter-cluster density), cluster merging can be performed; while overlapping non-central points indicate that they are in a transitional region of density decay, such as... Figure 7 As shown, these points should have their cluster labels removed and be classified together with the initially unassigned points into a set of points to be assigned.

[0019] In step S2, the expansion of the initial cluster is defined, including cluster center contention and boundary point allocation, as follows: Step a, Cluster center contention: Define the optimal contention cluster pair, specifically as follows: ; This definition merges the cluster pairs with the closest current density, merging those with the higher density, and updates the relevant attributes to continue iterating until... ; Step b, boundary point assignment, defining the assignment degree, specifically: ; Formula 7; ; In the definition of allocation degree, for a point to be assigned, the cluster with the highest frequency, the largest density peak, and the closest distance within the adaptive k-neighborhood has the highest allocation probability. This allocation degree applies to all points to be assigned. Descending order traversal, satisfying That is, the point to be assigned and When the nearest distance is less than its internal average distance, xi Classified as When there is no change in cluster centers and the initial cluster characteristics are preserved, no related attribute updates are made after the boundary points are assigned. In this way, noise is reduced and the relationship between the points to be assigned and the clusters is taken into account. For example, for the cluster with the highest assignment degree, if the distance between the point and the cluster is greater than the average distance within the cluster, it is considered an outlier and is not assigned.

[0020] Due to the adaptive k-neighborhood calculation, even after initial cluster merging, the limited influence range of density peak points (constrained by their attenuation characteristics and neighboring peak points) can still lead to over-segmentation. Specifically, in a globally continuous and uniformly distributed group of points, the algorithm tends to produce overly fine cluster partitions, such as... Figure 8 As shown; In step S3, the clustering results are optimized through a cluster merging operation, specifically as follows: Define the merge strength, i.e. Formula 8; The neighborhood overlap is constrained by the distance between two points being less than the average distance within the two clusters. The frequency of each cluster in the adaptive k-neighborhood of all data in the cluster is calculated, and the frequency is scaled by the density similarity calculated by the ratio. The cluster pair with the largest merging strength is selected, and the set and related attributes are updated after merging until the merging strength is 0, that is, the overlap is 0.

[0021] The introduction of merging intensity takes into account the mutual penetration, influence, and similarity of the boundary points of the two clusters.

[0022] The algorithm is expressed in pseudocode as follows: In step three, a global threshold is used to initially screen the trajectory points to exclude obvious waypoints and retain significant stop points. For the remaining trajectory points, a local threshold is used for auxiliary judgment.

[0023] This invention pertains to solutions for fixed-point sparse trajectories. Addressing the complex data distribution, uneven density, discrete stop points, and group comparison characteristics of these trajectories, it proposes a dual-threshold stop point identification method assisted by Adaptive Extended Density Peak Clustering (AE-DPC) based on density clustering algorithms. Specifically, this invention first uses a global threshold to initially filter trajectory points based on the overall characteristics of the trajectory data. Second, it sets local thresholds based on the AE-DPC clustering results to refine the discrimination rules and accurately identify stop points. Finally, this invention extracts clusters from synthetic datasets and identifies stop points in real checkpoint data, validating the effectiveness of the method using both synthetic and real datasets.

[0024] When identifying dwell points in fixed-point sparse trajectories, the method of this invention has the following advantages compared to traditional methods: (1) This invention defines global threshold and local threshold. The former fully explores the characteristics of trajectory data, especially the discreteness of the dwell points and the group comparison characteristics. By using frequency statistics and finding the inflection point of the frequency curve according to the elbow method, the discrimination rule is determined, the trajectory points are quickly filtered, and the preliminary dwell points are obtained. (2) The present invention developed the AE-DPC algorithm. In view of the characteristics of uneven density and complex distribution of data, especially fixed-point sparse trajectory data, the proposed algorithm can perform clustering more accurately. Then, based on the clustering results, a local threshold is set to refine the discrimination rules and support the accurate identification of the stopping point. (3) This invention combines the advantages of rule partitioning and clustering algorithms, which can both quickly filter trajectory points and accurately identify stopping points. Attached Figure Description

[0025] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Appendix Figure 1 This is a schematic diagram of two different trajectories in an embodiment of the present invention; Appendix Figure 2 This is a schematic flowchart of the method for defining fixed-point sparse trajectories in an embodiment of the present invention; Appendix Figure 3 This is a schematic diagram of the frequency statistics of trajectory point features in an embodiment of the present invention; Appendix Figure 4 This is a schematic diagram of the spatial distribution of cameras near the main road of a major city in an embodiment of the present invention; Appendix Figure 5 This is a schematic diagram of k-distance and adaptive k-neighborhood in an embodiment of the present invention; Appendix Figure 6 This is a schematic diagram of local density in an embodiment of the present invention; Appendix Figure 7This is a schematic diagram of the overlapping coverage of the initial cluster and the attenuation of the peak point density in an embodiment of the present invention; Appendix Figure 8 This is a schematic diagram of fine clustering illustrating the effect of peak point density decay in an embodiment of the present invention; Appendix Figure 9 These are the clustering results of different algorithms on various datasets in this embodiment of the invention; Appendix Figure 10 This is a schematic diagram illustrating the meaning of clustering and the clustering results of trajectory points in a certain city at 18:00 on March 1st, in an embodiment of the present invention. Appendix Figure 11 This is a visual schematic diagram illustrating the identification of vehicle driving trajectory and stopping points in an embodiment of the present invention. Detailed Implementation

[0026] As shown in the figure, a density clustering-based stop point identification method for fixed-point sparse trajectories is presented. This method employs an adaptive extended density peak clustering (AE-DPC)-assisted dual-threshold stop point identification technique. First, based on the overall characteristics of the trajectory data, a global threshold is initially used to filter trajectory points. Then, based on the AE-DPC clustering results, a local threshold is set to refine the discrimination rules and accurately identify stop points. The method includes the following steps: Step 1: Rule-based global threshold segmentation; Step 2: Set local thresholds for clustering; Step 3: Identification of Dual Threshold Dwell Points.

[0027] like Figure 2 As shown, the definition of the fixed-point sparse trajectory includes: Define a trajectory point as a spatiotemporal data point collected by monitoring equipment such as cameras and base stations on a moving object, expressed by the formula: Formula 1; In the formula, (x,y) are the coordinates of the monitoring device, t is the recording time, and u is the identifier of the moving object; A trajectory point represents a specific occurrence of a moving object, including its passing and dwelling behaviors, reflecting its activity range within a certain spatiotemporal radius centered on that point. For ease of study, the location of the trajectory point, i.e., the device location, is usually considered as the location of the moving object. Define a fixed-point sparse trajectory, where the sequence of all trajectory points of the same moving object in ascending time order is expressed by the formula: Formula 2; ; The trajectory points are recorded only when the user is near the monitoring station, and their trajectory sequences are recorded. TrajIt has a sparse characteristic, that is, the actual physical movement route of the moving object is sparsely represented as a scatter sequence of coordinate points of the monitoring device; Definition 3, Dwell Point: For a specific user u, a fixed-point sparse trajectory Traj_u The trajectory points in a sequence that satisfy global and local threshold conditions with their adjacent points are expressed by the following formula: Formula 3; The former is determined by the features of all trajectory points, namely the object's main movement time and speed, while the latter is... The average time and velocity of all trajectory points within a certain spatiotemporal range, which is determined by the density clustering results. In step one, when determining whether a point is a stop point, a comprehensive analysis of thresholds such as distance, time, and speed between it and neighboring points is usually performed. Specifically, the spatiotemporal characteristics of the trajectory points are statistically analyzed by frequency, i.e., the main movement time and speed of the moving object. The elbow method is used to find the inflection point of the frequency curve to determine the discrimination rule, i.e., the global threshold. The path points are quickly filtered to obtain the preliminary stop points. The following method is used: Fixed-point trajectory In the middle, if the moving distance and speed are constant, when When the time interval is short, Considered a waypoint, it indicates that after passing through this point, it is... The record states that if the time interval between two points is relatively long, it is initially considered a stopping point; considering long distances, although a long interval does not necessarily mean a stopping point, if the speed changes of the two trajectory segments are small, it is considered... These are waypoints; during the fixed-point sparse trajectory acquisition process, if the object is in... If the object stops, there are two possible scenarios: either the object is recorded at the same location twice, or the object stops and then starts again, being recorded by the next nearby monitoring station. In both cases, the displacement distance is small, and regardless of the time interval, the speed will be close to 0 and much smaller than other trajectory segments.

[0028] Specifically, it calculates and statistically analyzes characteristics such as distance and velocity between trajectory points. (See attached image.) Figure 3 The figures shown are frequency statistics for distance, time, and speed, respectively. Regarding distance, [the data is combined with the attached...] Figure 4The spatial distribution characteristics of the cameras show that most vehicles were recorded within a distance of 1000m. In terms of time, vehicles were recorded most frequently at short intervals (approximately 5 minutes or less), indicating normal vehicle passage through the road segment. Longer intervals (approximately 30 minutes or more) indicate that vehicles were not recorded by the next adjacent camera for an extended period, possibly indicating a stop event. Regarding speed, an extreme value of 5 m / s was observed, gradually decreasing, indicating that most vehicles were traveling at a normal average speed. Therefore, this invention filters out trajectory points (global thresholds) with time intervals less than 5 minutes or speeds greater than 5 m / s, based on trajectory point characteristics; for other points, local thresholds are further considered.

[0029] In step two, trajectory points are introduced based on global threshold filtering. The identification is based on the relationship between the trajectory points and their characteristics within a certain spatiotemporal range, i.e., satisfying the above formula 3. For a "staying event" to be considered a valid event, the stay time of a moving object must be greater than both the global threshold and the average movement time of all moving objects within the range of the monitoring device, while the speed must be less than both the global threshold and the average speed within that range. Clustering is used to effectively divide the spatiotemporal range of data recorded by the monitoring device. Adaptive extended density peak clustering (AE-DPC) is performed to obtain the monitoring device, i.e., the trajectory point, at a certain moment. Within a certain spatiotemporal range centered on the object, the average time and velocity of trajectory points within that range constitute the local threshold. This refers to the amount of data collected by the monitoring equipment within a certain time window.

[0030] In step two, the monitoring device is used as the recording unit, and the flow characteristics, namely the number of moving objects passing through the device within a certain time window, are introduced as the input for clustering, and parameters are set according to the global characteristics of the flow.

[0031] Based on the above global characteristics, in order to ensure traffic differences and statistical continuity, this invention sets the peak period (7-9h, 17-19h) window to 15min and the others to 30min, with the sliding step s being 1 / 2 of the window duration; Step two involves using the AE-DPC clustering algorithm to set local thresholds for clustering; this specifically includes the following: Step S1: Construction of the initial cluster; Step S2: Expansion of the initial cluster; Step S3: Merging of extended clusters.

[0032] Step S1 defines the adaptive k-neighborhood as follows: ; By plotting a k-distance curve, the distance distribution characteristics between x_i and its neighbors are visually reflected. The curvature change of this curve, exhibiting transitional characteristics, is used to identify density differences. Based on this, the adaptive selection of the number of neighboring points k overcomes the limitation of traditional density clustering methods with fixed thresholds, such as DBSCAN, which cannot adapt to uneven density. Figure 5 As shown.

[0033] It should be noted that setting the parameter k_min avoids noise sensitivity caused by an excessively small k value, while k_max limits the search range to prevent a surge in computational costs. Together, they constrain the adaptive k-neighborhood, which essentially divides a uniform region in a complexly distributed global dataset. In step S1, the local density is also defined, specifically as follows: Formula 5; Standard deviation; Traditional density-based clustering algorithms primarily rely on distance metrics to evaluate density distribution characteristics, where distance is inversely proportional to density, and this is used to determine initial cluster centers and their influence range. Taking the DPC algorithm as an example, this method is based on the fundamental assumption that "the density of cluster centers is higher than that of their neighbors," and characterizes the density distribution characteristics of the data space by calculating local density. However, this definition ignores the distribution of data in local regions, such as... Figure 6 As shown in region (a), point A has a smaller local density (0.75) but is evenly distributed. Compared with point group B, which has a wider interval, the clustering result is more stable. Therefore, the value of the improved local density calculation is larger (0.39). For case (b), although point group A is sparser, it is easy to be regarded as an outlier in the more compact point group B. However, considering its even distribution, it can still be considered as a structurally stable category. That is, the coefficient of variation reveals the potential of point group to be clustered from the structural stability of the point group.

[0034] In step S1, the peak point is also defined, specifically as follows: ; Formula 6; ; An adaptive k-neighborhood may share the same density peak point. Since local density alone cannot capture this affiliation, a voting mechanism is introduced. The frequency with which each point is nominated as a density peak is counted, i.e., the voting score V_p. The local densities are then weighted to obtain the corrected density peak. ; .

[0035] The voting mechanism implicitly reflects the characteristics of frequently occurring monitoring equipment, while the density peak, as a key attribute of the initial cluster center, together with the adaptive k-neighborhood mechanism, reflects the clustering characteristics of the core points. This is manifested in the decreasing probability of a sample point being assigned to the cluster as the distance between the sample point and the center point increases, which reflects the density decay effect in the clustering process.

[0036] In the above steps, calculating the adaptive k-neighborhood for each point results in overlapping regions in the initial cluster, which manifests as some points... Covered by multiple clusters: First, when clusters of different densities are adjacent, the centers of sparse clusters tend to be distributed around the periphery of compact clusters; second, overlapping non-central points are usually located in the cluster boundary region. For cases of overlapping cluster centers (reflecting high inter-cluster density), cluster merging can be performed; while overlapping non-central points indicate that they are in a transitional region of density decay, such as... Figure 7 As shown, these points should have their cluster labels removed and be classified together with the initially unassigned points into a set of points to be assigned.

[0037] In step S2, the expansion of the initial cluster is defined, including cluster center contention and boundary point allocation, as follows: Step a, Cluster center contention: Define the optimal contention cluster pair, specifically as follows: ; This definition merges the cluster pairs with the closest current density, merging those with the higher density, and updates the relevant attributes to continue iterating until... ; Step b, boundary point assignment, defining the assignment degree, specifically: ; Formula 7; ; In the definition of allocation degree, for a point to be assigned, the cluster with the highest frequency, the largest density peak, and the closest distance within the adaptive k-neighborhood has the highest allocation probability. This allocation degree applies to all points to be assigned. Descending order traversal, satisfying That is, the point to be assigned and When the nearest distance is less than its internal average distance, xi Classified as When there is no change in cluster centers and the initial cluster characteristics are preserved, no related attribute updates are made after the boundary points are assigned. In this way, noise is reduced and the relationship between the points to be assigned and the clusters is taken into account. For example, for the cluster with the highest assignment degree, if the distance between the point and the cluster is greater than the average distance within the cluster, it is considered an outlier and is not assigned.

[0038] Due to the adaptive k-neighborhood calculation, even after initial cluster merging, the limited influence range of density peak points (constrained by their attenuation characteristics and neighboring peak points) can still lead to over-segmentation. Specifically, in a globally continuous and uniformly distributed group of points, the algorithm tends to produce overly fine cluster partitions, such as... Figure 8 As shown; In step S3, the clustering results are optimized through a cluster merging operation, specifically as follows: Define the merge strength, i.e. Formula 8; The neighborhood overlap is constrained by the distance between two points being less than the average distance within the two clusters. The frequency of each cluster in the adaptive k-neighborhood of all data in the cluster is calculated, and the frequency is scaled by the density similarity calculated by the ratio. The cluster pair with the largest merging strength is selected, and the set and related attributes are updated after merging until the merging strength is 0, that is, the overlap is 0.

[0039] The introduction of merging intensity takes into account the mutual penetration, influence, and similarity of the boundary points of the two clusters.

[0040] The algorithm is expressed in pseudocode as follows: In step three, a global threshold is used to initially screen the trajectory points to exclude obvious waypoints and retain significant stop points. For the remaining trajectory points, a local threshold is used for auxiliary judgment.

[0041] Example: This invention verifies the effectiveness of a clustering algorithm and identifies stopping points based on a publicly available simulated spatial point dataset and traffic checkpoint data from a major Chinese city. The publicly available simulated spatial point dataset is described in Appendix 1, and the clustering results are shown in Appendix 2 and Appendix 3. Figure 9As shown, in general, AE-DPC has the best overall clustering performance. It can handle clusters of arbitrary shapes with relatively uniform density, and can also accurately divide datasets with large density differences between clusters. For cases with large density differences and complex distribution, AE-DPC can achieve relatively ideal clustering results.

[0042] Based on the effectiveness of the algorithm, this invention identifies stopping points, and examples of checkpoint data are shown in Appendix Table 3.

[0043] Since the clustering results represent the spatiotemporal range of the divided trajectory points, i.e., the area centered on the monitoring equipment, their characteristics indicate the road conditions in that area. For example, if the categories include high traffic volume, short distance, long time, and slow speed, then that area is a congested road section, as shown in the attached figure. Figure 10 As shown in (a), different monitoring station colors represent different vehicle conditions, and sizes represent different traffic flows. Accurate clustering can minimize intra-cluster differences and maximize inter-cluster differences, thus providing a reliable basis for determining local thresholds. Therefore, this method uses the city's daily congestion data as a constraint to optimize the AE-DPC parameters to 4 and 16, respectively. For ease of visualization, a portion of the trajectory points at 18:00 is extracted and displayed in a two-dimensional plane, as shown in the attached figure. Figure 10 As shown in (b), different colors represent different categories.

[0044] This method uses some data with real stop labels, including 718 trajectory points of 202 private cars, and assigns cluster results to them. In order to comprehensively analyze the effectiveness of the dual threshold strategy, the clustering method uses HDBSCAN to set local thresholds for comparison; the overall process uses dynamic threshold method [6] for comparison, clustering time period af and spatial clusters 1-8, and dividing data groups a1, a2...f8. The clustering results are shown in Table 5 (the field "cluster" is the clustering category of this paper, "cluster H" is the HDBSCAN category, "cluster D" is the dynamic threshold method category, and the labels -1 and 1 indicate the starting point). The results are shown in Tables 4 and 5, and the case analysis is shown in Appendix. Figure 11 .

[0045] In summary, this method uses open-source synthetic datasets and traffic checkpoint data from a certain city for experiments to verify the effectiveness of the clustering algorithm and the clustering-assisted dual-threshold stop point identification method. Results on the synthetic dataset show that the AE-DPC algorithm performs well in clustering on uniform, non-uniform, and complex distribution datasets, significantly improving upon baseline methods in ARI, AMI, and DBCV metrics. Results on the checkpoint data show that the dual-threshold constrained fixed-point sparse trajectory stop point identification demonstrates reliability in both precision and recall. Specifically, the local threshold based on AE-DPC improves precision by 11.36% compared to the local threshold based on HDBSCAN, further validating the performance of the AE-DPC algorithm. The dual-threshold method also shows a significant advantage over the dynamic threshold method, accurately identifying stop points.

Claims

1. A density clustering method for identifying dwell points in fixed-point sparse trajectories, characterized in that: The method uses an adaptive extended density peak clustering-assisted dual-threshold stop point identification technique. First, based on the overall characteristics of the trajectory data, a global threshold is divided to initially filter trajectory points. Then, a local threshold is set according to the AE-DPC clustering results to refine the discrimination rules and accurately identify stop points. Includes the following steps; Step 1: Rule-based global threshold segmentation; Step 2: Set local thresholds for clustering; Step 3: Identification of Dual Threshold Dwell Points.

2. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 1, characterized in that: The definition of the fixed-point sparse trajectory includes: Define trajectory points as spatiotemporal data collected by monitoring devices such as cameras and base stations on a moving object, expressed by the formula: Formula 1: In the formula, (x,y) are the coordinates of the monitoring device, t is the recording time, and u is the identifier of the moving object; A trajectory point represents a specific occurrence of a moving object, including passing through and stopping behaviors, reflecting its activity range within a certain spatiotemporal radius centered on that point; Define a fixed-point sparse trajectory, where the sequence of all trajectory points of the same moving object in ascending time order is expressed by the formula: Formula 2: ； The trajectory points are recorded only when the user is near the monitoring station, and their trajectory sequences are recorded. Traj It has a sparse characteristic, that is, the actual physical movement route of the moving object is sparsely represented as a scatter sequence of coordinate points of the monitoring device; Definition 3, Dwell Point: For a specific user u, a fixed-point sparse trajectory Traj_u The trajectory points in a sequence that satisfy global and local threshold conditions with their adjacent points are expressed by the following formula: Formula 3: The former is determined by the features of all trajectory points, namely the object's main movement time and speed, while the latter is... The average time and velocity of all trajectory points within a certain spatiotemporal range, which is determined by the density clustering results.

3. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 2, characterized in that: In step one, determining whether a point is a stop point involves: statistically analyzing the spatiotemporal characteristics of the trajectory points, i.e., the main movement time and speed of the moving object; using the elbow method to find the inflection point of the frequency curve to determine the discrimination rule, i.e., the global threshold; and quickly filtering out path points to obtain preliminary stop points. The following method is used: Fixed-point trajectory In the middle, if the moving distance and speed are constant, when When the time interval is short, Considered a waypoint, it indicates that after passing through this point, it is... The record is as follows: if the time interval between two points is relatively long, it is initially considered a resting point; if the speed change between the two trajectory segments is small, it is considered... These are waypoints; during the fixed-point sparse trajectory acquisition process, if the object is in... If the object stops, there are two possible scenarios: either the object is recorded at the same location twice, or the object stops and then starts again, being recorded by the next nearby monitoring station. In both cases, the displacement distance is small, and the speed will be close to 0 and much smaller than other trajectory segments.

4. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 3, characterized in that: In step two, trajectory points are introduced based on global threshold filtering. The identification is based on the relationship between the trajectory points and their characteristics within a certain spatiotemporal range, i.e., satisfying the above formula 3. For a stationary event, this condition means that the stationary time of the moving object must be greater than both the global threshold and the average moving time of all moving objects passing through the range of the monitoring device, while the speed must be less than both the global threshold and the average speed of the range. Clustering is used to effectively divide the spatiotemporal scope of data recorded by monitoring devices. Adaptive extended density peak clustering (AE-DPC) is performed to obtain the monitoring device, i.e., the trajectory point, at a certain moment. Within a certain spatiotemporal range centered on the object, the average time and velocity of trajectory points within that range constitute the local threshold. This refers to the amount of data collected by the monitoring equipment within a certain time window.

5. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 3, characterized in that: In step two, the monitoring device is used as the recording unit, and the flow characteristics, namely the number of moving objects passing through the device within a certain time window, are introduced as the input for clustering, and parameters are set according to the global characteristics of the flow.

6. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 3, characterized in that: Step two involves using the AE-DPC clustering algorithm to set local thresholds for clustering; this specifically includes the following: Step S1: Construction of the initial cluster; Step S2: Expansion of the initial cluster; Step S3: Merging of extended clusters.

7. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 6, characterized in that: Step S1 defines the adaptive k-neighborhood as follows: ； By plotting a k-distance curve, the distance distribution characteristics between x_i and its neighboring data can be visually reflected. The transition characteristics presented by the curve and the change in its curvature can be used to identify density differences. In step S1, the local density is also defined, specifically as follows: Formula 5: Standard deviation; Traditional density clustering algorithms mainly rely on distance metrics to evaluate density distribution characteristics, where distance is inversely proportional to density, and use this to determine the initial cluster centers and their influence range; Taking the DPC algorithm as an example, this method is based on the basic assumption that "the density of the cluster center is higher than that of its neighboring points" and uses the calculation of local density to characterize the density distribution characteristics of the data space. However, this definition ignores the distribution of local data. Point A has a small local density (0.75), but it is evenly distributed. Compared with point group B, which has a wider interval, the clustering result is more stable. Therefore, the value of the improved local density calculation is larger (0.39). For case (b), although point group A is sparser, it is easy to be regarded as an outlier in the more compact point group B. However, considering its even distribution, it can still be considered as a structurally stable category. That is, the coefficient of variation reveals the potential of point group to be clustered from the structural stability of the point group. In step S1, the peak point is also defined, specifically as follows: ； Formula 6: ； An adaptive k-neighborhood may share the same density peak point. Since local density alone cannot capture this affiliation, a voting mechanism is introduced. The frequency with which each point is nominated as a density peak is counted, i.e., the voting score V_p. The local densities are then weighted to obtain the corrected density peak. ; 。 8. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 7, characterized in that: In step S2, the expansion of the initial cluster is defined, including cluster center contention and boundary point allocation, as follows: Step a, Cluster center contention: Define the optimal contention cluster pair, specifically as follows: ； This definition merges the cluster pairs with the closest current density, merging those with the higher density, and updates the relevant attributes to continue iterating until... ; Step b, boundary point assignment, defining the assignment degree, specifically: ； Formula 7: ； In the definition of allocation degree, for a point to be assigned, the cluster with the highest frequency, the largest density peak, and the closest distance within the adaptive k-neighborhood has the highest allocation probability. This allocation degree applies to all points to be assigned. Descending order traversal, satisfying That is, the point to be assigned and When the nearest distance is less than its internal average distance, x i Classified as When there is no change in cluster centers and in order to maintain the initial cluster characteristics, no related attribute updates are made after the boundary points are assigned.

9. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 7, characterized in that: In step S3, the clustering results are optimized through a cluster merging operation, specifically as follows: Define the merge strength, i.e. Formula 8: The neighborhood overlap is constrained by the distance between two points being less than the average distance within the two clusters. The frequency of each cluster in the adaptive k-neighborhood of all data in the cluster is calculated, and the frequency is scaled by the density similarity calculated by the ratio. The cluster pair with the largest merging strength is selected, and the set and related attributes are updated after merging until the merging strength is 0, that is, the overlap is 0.

10. The density clustering dwell point identification method for fixed-point sparse trajectories according to claim 3, characterized in that: In step three, a global threshold is used to initially screen the trajectory points to exclude obvious waypoints and retain significant stop points. For the remaining trajectory points, a local threshold is used for auxiliary judgment.

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