CN112070179A - Adaptive space-time trajectory clustering method based on density peak value - Google Patents

Adaptive space-time trajectory clustering method based on density peak value Download PDF

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CN112070179A
CN112070179A CN202011001436.4A CN202011001436A CN112070179A CN 112070179 A CN112070179 A CN 112070179A CN 202011001436 A CN202011001436 A CN 202011001436A CN 112070179 A CN112070179 A CN 112070179A
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陈荦
陈南宇
熊伟
钟志农
吴烨
杨岸然
贾庆仁
欧阳雪
曹竞之
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National University of Defense Technology
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Abstract

The invention belongs to the technical field of trajectory simulation, and particularly relates to a density peak-based adaptive space-time trajectory clustering method. The density peak-based adaptive space-time trajectory clustering method can reflect the time synchronism of trajectory data, a KNN algorithm is introduced into density peak clustering, a local density calculation method is redefined, the problem that the density peak clustering is sensitive to parameters is solved, meanwhile, the clustering quality is improved, a stable adaptive selection algorithm is provided on the aspect of cluster center selection, the stability and effectiveness of an ATDP algorithm are proved by theoretical analysis and an experiment result based on a real data set, a better clustering effect can be obtained under different application backgrounds, and the overall motion trend of a moving target is accurately reflected.

Description

Adaptive space-time trajectory clustering method based on density peak value
Technical Field
The invention relates to the technical field of trajectory simulation, in particular to a density peak-based adaptive space-time trajectory clustering method.
Background
The continuously developed positioning technology and mobile computing technology generate a large amount of track data with time stamps, the space-time data has rich hidden information, for example, the track data of the sailing of fishing boats can reflect the fishing modes and frequency information of fishermen in different areas, the track data of the migrating animals can reflect the overall motion trend of each species in different time periods, the hurricane landing track data can reveal the moving mode in the hurricane landing process, the track clustering is the expansion of the clustering analysis on the space-time track, the motion rules of moving targets can be analyzed by classifying the space-time objects with the same or similar attributes, the motion mode of the objects can be found, and the motion trend can be predicted, so that the method has wide application in the fields of emergency rescue, traffic planning, disaster early warning and the like.
The traditional track clustering method can be divided into a partitioning-based method, a grid-based method, a hierarchy-based method and a density-based method, for space-time track data clustering, the influence of time dimension on the similarity between tracks is not considered in most of the existing algorithms, a sliding window model is adopted to carry out incremental clustering on the tracks in fixed window time in part of the algorithms, the whole process needs to carry out clustering calculation for many times, and the time complexity is high.
In order to solve the problem of space-time trajectory clustering, the method for measuring the similarity between trajectories adds measurement on a time dimension, calculates the overall similarity between the trajectories by generating a time synchronization sub-trajectory by adopting a Hausdorff distance, performs clustering analysis on the trajectories by adopting a density peak value clustering algorithm, redefines local density by introducing a KNN algorithm in order to solve the problem of density kernel selection existing in the density peak value clustering algorithm, improves clustering performance, provides a stable and effective automatic selection method for a clustering center in order to reduce manual intervention in the clustering process, provides a representative trajectory generation algorithm in order to realize the dynamic visualization effect of a clustering result, can generate a representative trajectory with a timestamp, and fitting the representative track data by a centripetal parameterized Catmull-Rom curve to generate a smooth curve so as to better reflect the motion trend of the track.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above and/or other problems occurring in the conventional trajectory clustering method.
Therefore, the invention aims to provide a density peak-based adaptive space-time trajectory clustering method, which can reflect the time synchronism of trajectory data, introduce a KNN algorithm into density peak clustering, redefine a local density calculation method, solve the problem of parameter sensitivity of density peak clustering, improve clustering quality, provide a stable adaptive selection algorithm on the selection of a clustering center, prove the stability and effectiveness of an ATDP algorithm through theoretical analysis and an experimental result based on a real data set, obtain a better clustering effect under different application backgrounds and accurately reflect the overall motion trend of a moving target.
To solve the above technical problem, according to an aspect of the present invention, the present invention provides the following technical solutions:
a self-adaptive space-time trajectory clustering method based on density peaks comprises the following steps:
s1: inputting track data T and parameters K and q;
s2: calculating the similarity between the tracks by a Hausdorff distance measurement algorithm based on time constraint to generate a similarity matrix M;
s3: calculating the local density p from the similarity matrix MiAnd calculatei；
S4: calculating gammaiGenerating a decision graph and obtaining a decision critical point thetacSelecting a clustering center pc；
S5: obtaining the distance from each track to the clustering center through the similarity matrix M, and classifying the distance into the cluster with the minimum distance;
s6: and generating a representative track Tr by an equal interval combination method, and outputting each cluster and the representative track Tr.
As a preferred scheme of the adaptive space-time trajectory clustering method based on the density peak value, the method comprises the following steps: the pseudo code of the Hausdorff distance measurement algorithm based on the time constraint in the step S2 is as follows:
defining:
len (), obtaining the number of points in the trace point set
Inputting: track data TrA、TrBPercent of synchronization parameter q
And (3) outputting: hausdorff distance H (Tr)A,TrB)
And calculating k: k1 ═ q · (len (Tr)A)),k2＝q·(len(TrB))
forai in TrA：
At TrBTo find a distance t in the time dimensionaiNearest point bl
Generating synchronous sub-track segments NTrB＝{bl-k2,...,bl,...,bl+k2}
Figure BDA0002694470260000031
Di is reacted withminPush in set dmin
According to the formula
Figure BDA0002694470260000041
Obtaining h (Tr)A,TrB)，
for bi in TrB：
At TrATo find a distance t in the time dimensionbiNearest point al
Obtaining synchronous sub-track segments NTrA＝{al-k1，…，al，…，al+k1}
Figure BDA0002694470260000042
Di is reacted withminPush in aggregate dmin
According to the formula
Figure BDA0002694470260000043
Obtaining h (Tr)B，TrA)
According to the formula H (A, B) ═ max { H (A, B), H (B, A) }
Obtaining H (Tr)A,TrB)
return H(TrA,TrB)。
As a preferred scheme of the adaptive space-time trajectory clustering method based on the density peak value, the method comprises the following steps: in said step S3, p is calculatediThe formula of (1) is:
Figure BDA0002694470260000044
where K is the input parameter, { j1，j2…jkDenotes K points nearest to the data i, dijIs the distance between two points;
upward distanceiIs defined by calculating the minimum of the distance between data i and the data of higher density than it:
Figure BDA0002694470260000051
for the point in the data set where the local density is highest, the following formula is used:
Figure BDA0002694470260000052
as a preferred scheme of the adaptive space-time trajectory clustering method based on the density peak value, the method comprises the following steps: γ in said step S4iThe calculation formula of (a) is as follows:
γi＝pi·i
obtaining a decision critical point thetacThe calculation formula of (a) is as follows:
Figure BDA0002694470260000053
wherein, thetaiRepresenting points in the decision graph, d θiθi-1Denotes thetaiDistance from the previous point, do θiθi+1Denotes thetaiDistance from the latter point, theta when ri takes the maximum valuecDecision threshold points selected for adaptation:
θc＝max(ri)。
as a preferred scheme of the adaptive space-time trajectory clustering method based on the density peak value, the method comprises the following steps: in the step S6, inside the track cluster, the start time and the end time of the track corresponding to the clustering center are taken as boundaries, and the average value of each dimension of the track point in each time period is counted at equal intervals according to actual requirements, so as to generate the track point with the timestamp, and then the representative track Tr is formed.
Compared with the prior art: in order to solve the problem of space-time trajectory clustering, the method for measuring the similarity between trajectories adds measurement on a time dimension, calculates the overall similarity between the trajectories by generating a time synchronization sub-trajectory by adopting a Hausdorff distance, performs clustering analysis on the trajectories by adopting a density peak value clustering algorithm, redefines a local density by introducing a KNN algorithm to solve the problem of density kernel selection existing in the density peak value clustering algorithm, improves the clustering performance, can embody the time synchronization of trajectory data, redefines the local density calculation method by introducing the KNN algorithm in the density peak value clustering, solves the problem of sensitivity of the density peak value clustering to parameters, improves the clustering quality, provides a stable self-adaptive selection algorithm on the selection of the clustering center, and proves the stability and effectiveness of an ATDP algorithm by theoretical analysis and experimental results based on a real data set, the method can obtain better clustering effect under different application backgrounds and accurately reflect the overall motion trend of the moving target.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail with reference to the accompanying drawings and detailed embodiments, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise. Wherein:
FIG. 1 is a flow chart of the ATDP algorithm of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described herein, and it will be apparent to those of ordinary skill in the art that the present invention may be practiced without departing from the spirit and scope of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Next, the present invention will be described in detail with reference to the drawings, and in the detailed description of the embodiments of the present invention, the cross-sectional views illustrating the structure of the device are not enlarged partially according to the general scale for convenience of illustration, and the drawings are only examples, which should not limit the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The invention provides a density peak-based adaptive space-time trajectory clustering method, which can embody the time synchronism of trajectory data, introduces a KNN algorithm into density peak clustering, redefines a local density calculation method, solves the problem of parameter sensitivity of density peak clustering, simultaneously improves clustering quality, provides a stable adaptive selection algorithm on the selection of a clustering center, proves the stability and effectiveness of an ATDP algorithm by theoretical analysis and an experimental result based on a real data set, can obtain a better clustering effect under different application backgrounds, and accurately reflects the overall motion trend of a moving target, and please refer to FIG. 1, which comprises the following steps:
s1: inputting track data T and parameters K and q;
s2: calculating the similarity between tracks by a Hausdorff distance measurement algorithm based on time constraint to generate a similarity matrix M, wherein the pseudo code of the Hausdorff distance measurement algorithm based on time constraint is as follows:
defining:
len (), obtaining the number of points in the trace point set
Inputting: track data TrA、TrBPercent of synchronization parameter q
And (3) outputting: hausdorff distance H (Tr)A,TrB)
And calculating k: k1 ═ q · (len (Tr)A)),k2＝q·(len(TrB))
for ai in TrA：
At TrBTo find a distance t in the time dimensionaiNearest point bl
Generating synchronous sub-track segments NTrB＝{bl-k2,...,bl,...,bl+k2}
Figure BDA0002694470260000081
Di is reacted withminPush in set dmin
According to the formula
Figure BDA0002694470260000082
Obtaining h (Tr)A,TrB)，
for bi in TrB：
At TrATo find a distance t in the time dimensionbiNearest point al
Obtaining synchronous sub-track segments NTrA＝{al-k1，…，al，…，al+k1}
Figure BDA0002694470260000083
Di is reacted withminPush in aggregate dmin
According to the formula
Figure BDA0002694470260000084
Obtaining h (Tr)B，TrA)
According to the formula H (A, B) ═ max { H (A, B), H (B, A) }
Obtaining H (Tr)A,TrB)
return H(TrA,TrB)。；
S3: by a similarity matrix M
Figure BDA0002694470260000085
Calculating the local density piAnd by
Figure BDA0002694470260000086
ComputingiFor the point with the highest local density in the data set, the method is adopted
Figure BDA0002694470260000087
Computingi；
S4: by gammai＝pi·iCalculating gammaiGenerating a decision graph and processing
Figure BDA0002694470260000091
And thetac＝max(ri) Obtaining a decision critical point thetacSelecting a clustering center pc；
S5: obtaining the distance from each track to the clustering center through the similarity matrix M, and classifying the distance into the cluster with the minimum distance;
s6: generating a representative track Tr by an equal interval combination method, outputting each cluster and the representative track Tr to pass through the inside of a track cluster, taking the starting time and the ending time of a track corresponding to a clustering center as boundaries, counting the average value of each dimension of track points in each time period at equal intervals according to actual requirements, generating track points with time stamps, and then forming the representative track Tr;
example (b):
1. experimental setup:
the experimental environment is a macOS10.15 operating system, IntelCorei5@3.1GHzCPU and a 16G memory, the implementation is realized by combining Python3.7 with an NUMBA library, the experiment is divided into two parts, the first part evaluates the time complexity and effectiveness of the improved Hausdorff distance algorithm, gives the selection range of synchronous parameters through the experiment, and the second part evaluates the effectiveness of the clustering effect of the ATDP algorithm on three real data sets and compares the effectiveness with the TRACLUS track clustering algorithm. The experimental data adopts a Beidou fishing boat navigation track data set, a Starkey animal migration data set and a hurricane data set, and only longitude, latitude and time attributes of the data are reserved in the testing process.
2. Hausdorff distance algorithm experimental evaluation based on time constraint:
testing an improved Hausdorff distance algorithm using a Beidou fishing boat sailing trajectory dataset, the data being derived from the Alice cloud sky pool
The big data platform comprises 11000 fishing boat track data, and the data comprises fishing boat numbers, coordinates, speed, direction and time stamps.
2.1 selection of synchronization parameters:
the method comprises the steps of randomly extracting 500 fishing boat track data to study the influence of selection of a synchronization parameter q on algorithm performance and effectiveness, wherein the abscissa is a q value, the ordinate is a difference value between an improved algorithm result and an original algorithm result, under partial data, the calculation result of the improved algorithm is the same as the original algorithm result, and the calculation amount is reduced, because the time dimension is added in measurement of the distance between tracks, and the time dimension has special directionality which is not increased, two points with the nearest distance can be found more quickly in a synchronization threshold range corresponding to the synchronization parameter, and the synchronization parameter test can be carried out on the 500 track data, so that the improved algorithm can obtain the same calculation accuracy as the original algorithm in the range that q is less than or equal to 50.
2.2 Hausdorff distance algorithm performance evaluation based on time constraint:
the method comprises the steps of carrying out comparative evaluation on running time expenditure and a calculation result of an improved Hausdorff distance algorithm, randomly extracting 24 fishing boat navigation track data, respectively testing by using an improved algorithm, an original algorithm and a DTW algorithm, and taking a synchronization parameter q equal to 30, so that the obtained result can be obtained, the improved algorithm has less time expenditure than the other two algorithms, the original algorithm is only close to the improved algorithm in the second group of experiments, the reason is that the second group of data tracks are short in length, the improved algorithm consumes part of time expenditure when searching for the synchronization sub-track, and the DTW algorithm needs to be matched with the shortest path, so the time expenditure is much larger. In terms of calculation results, it can be found that the metric results of the three algorithms are similar for each group of data (note: for better observation, the unit of calculation result of DTW is 103), and the result of the improved algorithm is slightly higher than that of the original algorithm, because only the local closest point can be matched within the synchronization threshold range, not the global closest point, which is also the embodiment of time constraint and reflects the metric of the algorithm on the track time synchronism.
ATDP algorithm performance evaluation:
firstly, the effectiveness evaluation is carried out on the local density and self-adaptive clustering center selection method in the ATDP algorithm, then the ATDP algorithm is compared with the TRACLUS algorithm, and finally the ATDP algorithm is tested on three different real data sets.
3.1.1 local Density Nuclear evaluation:
the labeled data set is tested by adopting a Gaussian kernel (Guass), a truncation distance kernel (CutOff), a K nearest neighbor distance (KDistance) and an average nearest neighbor distance (MeanKDistance), in order to enable the experiment to be carried out without manual intervention, a constant parameter method is adopted to carry out the test in 5 data sets, parameters are set as shown in the following table, wherein p is the truncation distance percentage defined in the original algorithm, K is the nearest neighbor number K in the improved algorithm based on the KNN algorithm, q is the synchronous parameter percentage, the experimental data sets are Jain, Aggregation, Iris, parameter and Boat data sets, wherein the Boat data sets are 100 tracks randomly extracted from the Beidou data set of the navigation track of the fishing Boat, the data sets are manually labeled, and the clustering result is evaluated by using ARI (AdjdIndendex), NMI (normalized Mutual) and V-measure as clustering indexes.
Figure BDA0002694470260000111
Figure BDA0002694470260000121
Although the gaussian kernel and the truncation kernel perform well on the Aggregation data set, the clustering effect of these two local densities is not stable with constant parameters, the effect on the Flame, Iris and Boat data sets is poor, and as can be seen from the table above, the Gaussian kernel and the truncation kernel require three parameters to be input to realize clustering adaptation, the selection of the parameters and the threshold value has great influence on the clustering result, no exact and reliable selection scheme exists at present for the selection of the parameters, the clustering effect of the average nearest neighbor distance serving as the local density calculation method is more stable than that of other three local densities under the condition of constant parameters, the performance in each data set can basically meet the clustering requirement, the clustering effect in the Flame, Iris and Boat data sets is the best, the method can adapt to density peak clustering without manual intervention, and the self-adaption of the clustering process is realized.
3.2. Self-adaptive selection of clustering center effect evaluation:
another key factor influencing the clustering effect is the selection of the clustering center, and for comparing the performance of the self-adaptive clustering center selection algorithm, the clustering effect of the clustering center is selected by comparing two methods of utilizing the change rate of the gamma value and the change rate of the distance between two adjacent points in the decision diagram. And ARI, NMI and V-Measure are also adopted as performance indexes, and tests are carried out on Jain, Aggregation, Iris, frame and Boat data sets.
3.3. Comparing with a classical trajectory clustering algorithm TRACLUS algorithm:
the TRACLUS algorithm is a track clustering algorithm based on a segmentation-combination frame, which is proposed by lee and the like, the algorithm firstly segments tracks to simplify, and then combines and clusters, the clustering results of the two algorithms are compared on a hurricane data set, a Starkey animal migration data set and a Beidou fishing boat track data set, in order to avoid manual intervention in the clustering process, a fixed parameter mode is adopted for testing, wherein the parameter of the TRACLUS algorithm is set to be 40, minLns is 5, the representative track is generated by adopting a scanning line algorithm, the parameter of the ATDP algorithm is set to be 35, q is 0.1, and the specific condition of the data set is shown in a following table;
data set Number of tracks Number of tracing points
Hurrican1975-1985 361 10552
Hurrican1986-1996 368 10809
Elk1993 36 24189
Deer1993 72 61780
Boat 986 110848
The optimal path data set of hurricanes is selected from 1975 to 1985 and 1986 to 1996, and the TRACLUS and ATDP are tested, the clustering results of the two algorithms are consistent, the generated representative trajectories are approximately the same in direction, such as in Hurrian 1975-1985 data set, the trend of hurricanes from east to west to east to north is reflected, part of the trend of hurricanes from east to west moves, in Hurrian 1986-1996 data set, the TRACLUS reflects the trend of movement from east to west, the trend of movement from west to north is not obvious, and ATDP can clearly reflect the trend of movement of hurricanes from west to east to north;
the fishing boat data set is larger than the hurricane data set and the Starkey data set in scale, only one cluster is found in the track center position by the TRACLUS algorithm, obviously, the clustering result is unreasonable, parameters need to be adjusted manually, and the ATDP algorithm can find 5 clusters under the condition that experimental parameters of the two previous data sets are unchanged, so that the ATDP algorithm is higher in robustness and can adapt to clustering tasks of data sets of different scales;
the time complexity test is carried out on the TRACLUS algorithm and the ATDP algorithm in an experiment, under the condition that track indexes are not established, the time complexity of the TRACLUS algorithm is o (N) because all track segments in a data set need to be traversed and the DBSCAN algorithm is adopted for clustering2) Wherein N is the number of track segments, and the ATDP algorithm needs to establish a similarity matrix in the clustering process, so the time complexity is o (N)2) The two algorithms are shown in different data sets, in the Starkey data set, because the number of tracks is small and each track contains more track points, the TRACLUS algorithm generates a large number of track segments in the track segmentation stage, so that the time consumption is increased, and the ATDP algorithm measures the whole track, so that the actual running time is less than that of the TRACLUS algorithm.
While the invention has been described above with reference to an embodiment, various modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In particular, the various features of the disclosed embodiments of the invention may be used in any combination, provided that no structural conflict exists, and the combinations are not exhaustively described in this specification merely for the sake of brevity and resource conservation. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (5)

1. A self-adaptive space-time trajectory clustering method based on density peak is characterized by comprising the following steps:
s1: inputting track data T and parameters K and q;
s2: calculating the similarity between the tracks by a Hausdorff distance measurement algorithm based on time constraint to generate a similarity matrix M;
s3: calculating the local density p from the similarity matrix MiAnd calculatei；
S4: calculating gammaiGenerating a decision graph and obtaining a decision critical point thetacSelecting a clustering center pc；
S5: obtaining the distance from each track to the clustering center through the similarity matrix M, and classifying the distance into the cluster with the minimum distance;
s6: and generating a representative track Tr by an equal interval combination method, and outputting each cluster and the representative track Tr.
2. The adaptive spatiotemporal trajectory clustering method based on density peaks as claimed in claim 1, wherein the pseudo code of the Hausdorff distance metric algorithm based on time constraint in the step S2 is as follows:
defining:
len (), obtaining the number of points in the trace point set
Inputting: track data TrA、TrBPercent of synchronization parameter q
And (3) outputting: hausdorff distance H (Tr)A,TrB)
And calculating k: k1 ═ q · (len (Tr)A)),k2＝q·(len(TrB))
forai in TrA：
At TrBTo find a distance t in the time dimensionaiNearest point bl
Generating synchronous sub-track segments NTrB＝{bl-k2,...,bl,...,bl+k2}
Figure FDA0002694470250000021
Di is reacted withminPush in set dmin
According to the formula
Figure FDA0002694470250000022
Obtaining h (Tr)A,TrB)，
for bi in TrB：
At TrATo find a distance t in the time dimensionbiNearest point al
Obtaining synchronous sub-track segments NTrA＝{al-k1，…，al，…，al+k1}
Figure FDA0002694470250000025
Di is reacted withminPush in aggregate dmin
According to the formula
Figure FDA0002694470250000023
Obtaining h (Tr)B，TrA)
According to the formula H (A, B) ═ max { H (A, B), H (B, A) }
Obtaining H (Tr)A,TrB)
return H(TrA,TrB)。
3. The adaptive clustering method of spatiotemporal trajectories based on density peaks as claimed in claim 1, wherein p is calculated in step S3iThe formula of (1) is:
Figure FDA0002694470250000024
where K is the input parameter, { j1，j2…jkDenotes K points nearest to the data i, dijIs the distance between two points;
upward distanceiIs defined by calculating the minimum of the distance between data i and the data of higher density than it:
Figure FDA0002694470250000031
for the point in the data set where the local density is highest, the following formula is used:
Figure FDA0002694470250000032
4. the adaptive clustering method of spatiotemporal trajectories based on density peaks as claimed in claim 1, wherein γ in step S4iThe calculation formula of (a) is as follows:
γi＝pi·i
obtaining a decision critical point thetacThe calculation formula of (a) is as follows:
Figure FDA0002694470250000033
wherein, thetaiRepresenting points in the decision graph, d θiθi-1Denotes thetaiDistance from the previous point, do θiθi+1Denotes thetaiDistance from the latter point, theta when ri takes the maximum valuecDecision threshold points selected for adaptation:
θc＝max(ri)。
5. the adaptive space-time trajectory clustering method based on the density peak according to claim 1, wherein in step S6, by taking the start time and the end time of the trajectory corresponding to the clustering center as boundaries inside the trajectory cluster, the average value of each dimension of the trajectory points in each time period is counted at equal intervals according to actual requirements, thereby generating the trajectory points with the time stamps, and then forming the representative trajectory Tr.
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