In order to solve the problem of low accuracy of sampling irregular tracks, a time series clustering algorithm for detecting stops is proposed. Firstly, based on the data field theory, a hybrid feature density detection method considering temporal and spatial characteristics is designed. Secondly, according to the characteristic that the center density of the stop point is greater than the inlet density, the filtering and refining strategy is used to extract the stop point. In the filtration stage, the time duration and the minimum density threshold are selected as the candidate residence points. The maximum threshold is used to identify the actual residence point in the refining stage. The experimental results show that the proposed method can effectively detect the residence points on the irregular trajectories with higher accuracy and less time consumption than the existing methods

Wang, Yuqi

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Electronics Science Technology and Application (E-Journal)

-128-Electronics Science Technology and ApplicationResearch and Application of Trajectory Stop Point DetectionAlgorithm for Time Series ClusteringYuqi WangHangzhou Normal University, School of Mathematics Hangzhou, Hangzhou 311121, China.Abstract: In order to solve the problem of low accuracy of sampling irregular tracks, a time series clustering algorithm fordetecting stops is proposed. Firstly, based on the data field theory, a hybrid feature density detection method consideringtemporal and spatial characteristics is designed. Secondly, according to the characteristic that the center density of the stoppoint is greater than the inlet density, the filtering and refining strategy is used to extract the stop point. In the filtration stage,the time duration and the minimum density threshold are selected as the candidate residence points. The maximum thresholdis used to identify the actual residence point in the refining stage. The experimental results show that the proposed methodcan effectively detect the residence points on the irregular trajectories with higher accuracy and less time consumption thanthe existing methods.Keywords: Time Series Clustering; Trajectory Stopping Point; Detection AlgorithmIntroductionWith the wide application of positioning system and mobile terminal, it is more and more difficult to obtain trajectorydata. The algorithm realizes the location and tracking of the stop point through spatial segmentation and analysis of thesampling curve. The user's behavior can be recorded in these trajectory data, which can reflect the user's behavior pattern andbehavior law. However, when dealing with a large number of raw tracks, the efficiency of direct data mining is notsatisfactory. Because the traditional trajectory clustering algorithm is very sensitive to noise, it is difficult to find hiddenpatterns behind the original data.1. Concept and method1.1 Basic ConceptsDefinition 1: A trajectory is a collection of chronological location points numbered. Where,, and represent longitude,latitude, and time respectively.Definition 2: is the locus point set table, which contains two stopping points, which represents the stopping state of themoving object at a certain position, and its value isDefinition 3: According to formula (1), we can calculate the spatial distance between trajectory points.     22, jijiji yyxxppdist  （1）1.2 Density function based on data fieldBased on the idea of field theory, the interaction of matter particles and its field description method are introduced intothe abstract number field space, and each object in the space is regarded as a particle with a certain mass, and describedaround a spherical virtual data field. In this field, each point has its corresponding energy value, and the coordinatecorresponding to the point is the magnitude value of each physical quantity at the point, that is, the potential of its positionrepresents the magnitude and direction of a variable at the point [1]. Similar to the vector intensity function and scalarpotential number description of a physical field, the potential function is defined as a vector form describing a physicalVolume 10 Issue 5-129-quantity. As shown in equation (2).    nnixxiiemx2/ （2）In formula (2) : the distance required for the target to reach the field point; The quality factors that control theinteraction between objects are called impact factors.In the trajectory, the trajectory points of the residence area show a highly dense distribution in time and space, and theinteraction between these trajectory points is very obvious, resulting in a relatively high value of the potential function.Therefore, a density calculation method based on data field is proposed in this paper. Each locus point is regarded as aparticle with a certain mass, and there is a virtual field around it, and the potential function is used to measure the density ofthe locus point. The greater the potential value, the denser the locus point and the higher the probability of stopping point. Inorder to ensure the accuracy of the results, appropriate methods must be adopted for processing. By directly using thepotential function in equation (2) to calculate the density to distinguish between stops and moving points, we ignore theeffect of the time interval on the detection of stops. In fact, the sampling interval of most trajectories is indeterminate.Because some objects move around the site in each measurement, it is impossible to accurately determine whether there is aretention point at the current position when the distance change is small. For the above situation. In this paper, we introducea new distance measurement method, the time interval of an object's spot. The time interval of the object field point ismapped to 0~1 to represent the quality of the track point, which is equivalent to setting a time weight for each object tocontrol the interaction between the track points, so as to realize the differential influence of different time intervals on thetrack density. When a user arrives at a specified location, it can accurately estimate which objects exist in the target areaaccording to the distribution characteristics of all tracks near the location. Within a given period of time, the positioncoordinates of each distance measuring device are determined according to the set target time [2]. Locate the normal range ofthe device recording interval, that is, the interval with the highest frequency. Through this method, a set of better motionestimation results can be obtained, thus improving the tracking accuracy. The calculation method is shown in equation (3) xjtttxjtttxjCTfrejjfrejj＞＜ifif,11（3）In formula (3), it represents the position of the center point of the track segment; Represents the time required for trackpoints; Record the time interval for the device.Considering that the stopping points in the trajectory show a clustering distribution, and the short-range field is moreconducive to revealing the characteristics of the data distribution, this paper adopts Gaussian function to define the potentialfunction, that is, the density function. Using potential function and distance formula to discretize the data, a new parameter,the mean cluster radius, is obtained to describe the clustering property. By processing the index displacement of objects andfield points at the same time, the clustering of stop point distribution can be better demonstrated. By analyzing andcalculating the change of the data in the moving process, a stop point set generation algorithm based on the density formulais obtained. The calculation formula of density is shown in equation (4).       22 //,,11 hjidppdistuplowjijCTijieep     （4）Where: is the ratio of standard deviation to distance; When the value of the objective function is given, its range can bedetermined as needed, that is, whether there is one or more optimal locations. Is the index standard deviation; In the search-130-Electronics Science Technology and Applicationwindow, the positions represented by low and up are the lower and upper bounds respectively, which are calculated as shownin formula (5) and (6). The distance between the center and the center has a great influence on the density calculation, andthe influence of the exceeded trace points on the density calculation is negligible. hilow 3,0max  （5） hinup 3,min  （6）When the distance standard deviation value is too large, it will cause the moving track point to be incorrectly identifiedas the stop point, and when the value is too small, the stop point position will become blurred and difficult to find. Therefore,the sensitivity of the index to changes at different scales in time and direction needs to be taken into account whendetermining the position. In order to find the best value, this paper uses the inflection point as the estimated value, which isthe point with the greatest curvature and usually represents the inflection point between two states. After analyzing andcomparing the existing algorithms, an improved method is proposed to determine the threshold value and estimate theoptimal segmentation interval. Firstly, the spatial distance between adjacent trajectory points is derived and arranged in orderfrom large to small. Secondly, according to the time interval of two different moments, two straight line fitting and cubiccurve fitting are done for each key point respectively, and the curve intersection point is determined as the inflection point.Because of the high fluctuation frequency of the distance value in practical application, its smoothness is not ideal, whichbrings considerable challenges to the calculation of the inflection point. Then, the maximum-minimum normalizationtechnique is used to normalize the sequence, and the point with the most significant curvature change is taken as theinflection point.2. Stop point detection algorithm based on time series clusteringBy calculating the density of trajectory points, it can be inferred that each trajectory point is likely to become a stoppingpoint. When the distance between any two points in a given area is less than a certain threshold, there will be multiple stopsin the area, and these stops may contain important information such as moving objects or pedestrians. However, consideringthat the density value at the entrance of the stopping point is similar to the density value at the moving point, a singlebreaking value is difficult to accurately distinguish the two. In order to solve this problem, it is necessary to record andanalyze multiple trajectories in a certain period of time to obtain the number and distribution of stopping points in each area.In order to reduce unnecessary redundant operations and improve time efficiency, a new statistical calculation method can beused to determine the threshold and determine whether there are isolated aggregation points. A single trace ST is adopted,with the minimum threshold min_threshold and the maximum threshold max_threshold as the input. The same statisticalrules apply to all trajectory points in more than two consecutive time intervals. candidateidx and candidate_den are used torepresent the index and density of the current cluster respectively. The core process of candidateIDX and CANDIdate_DENis to calculate the density of each track point on the timeline and set the minimum density value to include the track pointsthat meet the conditions into the candidate stop points. If the conditions are not met, the maximum density max_threshold ofthe current cluster needs to be evaluated. If the value is greater than max_threshold, the current cluster needs to be marked asthe actual stop point [3].3. Experiment and analysisIn the process of experiment, a variety of real data sets with labels, which have different characteristics, are used tocarry out simulation experiments. See Table 1 for details.name length stops moves modeShopping trip 1 968 195 1 773 foot ,carhouse visit 1 128 285 843 foot ,carhike 9 524 932 8 592 foot , carVolume 10 Issue 5-131-short walk 120 37 93 footferry 7 612 2 651 4 961 foot , ferrydog walk 833 98 735 footConclusionIn this paper, a hybrid feature density measurement method based on spatiotemporal characteristics is proposed to dealwith various noises in the real trajectory. Based on the analysis of space and time series, the mathematical model of therelationship between regions in different time periods is established, and it is used as a hybrid feature extraction method.Aiming at the characteristic that the density of the entrance of the stop point is lower than the density of the center in atrajectory, we propose a new stop point detection algorithm based on time series clustering. On this basis, the candidateresidence points are preliminatively determined by combining regional growth method and spatial neighborhood information.A double clustering strategy is used to identify the candidate stops, and then select the actual stops from these stops. Thismethod can eliminate the false stagnation points effectively and calculate the real stagnation points accurately.References[1] Yang QY, Weng XQ. Time series clustering based on LLE and Gaussian Mixture model [J]. Computer Technologyand Development,202,32(8):33-41. (in Chinese)[2] Li HL, Lin CP. Research results keyword analysis method based on time series clustering [J]. Science ResearchManagement,202,43(1):176-183.[3] Sun XL, Zhu CC, Li MN, Liang TT, Ma CQ. Research on passenger flow prediction of urban rail transit under timeseries clustering [J]. Railway Transportation and Economics,2023,45(3):149-157. (in Chinese)

Research and Application of Trajectory Stop Point Detection Algorithm for Time Series Clustering

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Research and Application of Trajectory Stop Point Detection Algorithm for Time Series Clustering

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