CN110781958B - OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation - Google Patents

OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation Download PDF

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CN110781958B
CN110781958B CN201911022154.XA CN201911022154A CN110781958B CN 110781958 B CN110781958 B CN 110781958B CN 201911022154 A CN201911022154 A CN 201911022154A CN 110781958 B CN110781958 B CN 110781958B
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邬群勇
项秋亮
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Fuzhou University
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Abstract

The invention relates to an OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation, which comprises the following steps: step S1, collecting the track data to be measured; step S2, extracting original flow direction data from the track data and preprocessing the original flow direction data to form an OD flow direction set F; step S3, calculating the similarity value among OD flow directions in the OD flow direction set F, constructing a maximum weight spanning tree MST of the F, and cutting the MST to obtain a plurality of subtree CTs and noise flow directions which have no similarity relation with each other; step S4, carrying out self-similarity judgment on the subtrees, organizing the flow directions in the subtrees into OD flow direction clusters to be output if the self-similarity of the subtrees meets the preset cluster output standard, otherwise, carrying out step S5; step S5: and cutting the subtrees which do not meet the output standard of the cluster by adopting an iterative optimal binary segmentation method until the cut preset subtrees meet the output standard of the cluster and are organized into OD flow direction cluster output. The invention can effectively improve the operation efficiency and reduce the calculation time.

Description

OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation
Technical Field
The invention relates to an OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation.
Background
How to mine the travel characteristics of urban residents is important to traffic planning design and management. With the rapid development and popularization of mobile positioning technology, large-data-volume geographic movement data such as human daily activity trajectory data, group migration data, vehicle trajectory data and the like are more and more easily acquired. The OD flow direction data is special mobile data, only position information of origin and Destination is reserved but actual track information is ignored, the flow direction and hot points of resident travel can be identified by clustering the vehicle OD flow direction data with large data volume level, the travel characteristics of urban residents, the space-time connection of group flow among different areas of the city and the change trend of the space-time connection can be accurately grasped, and the OD flow direction data has important significance for traffic planning design and city management.
Disclosure of Invention
In view of the above, the present invention provides an OD flow direction clustering method based on maximum spanning tree and optimal graph partitioning, which combines with the construction and cutting of the maximum weight spanning tree to partition data into a plurality of subtrees without similarity relationship, and each subtree can perform distributed processing respectively, thereby effectively improving the operation efficiency and reducing the computation time.
In order to realize the purpose, the invention adopts the following technical scheme:
an OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation comprises the following steps:
step S1, collecting the track data to be measured;
step S2, extracting the serial number of each track data, the longitude and latitude coordinate information and the time information of the O point and the D point from the track data to be detected to form original flow direction data, preprocessing all the flow direction data to form an OD flow direction set F;
step S3, calculating the similarity value among OD flow directions in the OD flow direction set F, constructing a maximum weight spanning tree MST of the F, and cutting the MST to obtain a plurality of subtree CTs and noise flow directions which have no similarity relation with each other;
step S4, self-similarity judgment is carried out on the subtree, if the self-similarity of the subtree meets the preset cluster output standard, the flow direction in the subtree is organized into OD flow direction clusters to be output, otherwise, the step S5 is carried out;
step S5: and cutting the subtrees which do not meet the output standard of the cluster by adopting an iterative optimal binary segmentation method until the cut preset subtrees meet the output standard of the cluster and are organized into OD flow direction cluster outputs.
Further, the step S3 is specifically:
step S31, calculating the similarity value among the OD flow directions in the OD flow direction set F;
step S32, regarding each flow in the flow set F as a vertex, regarding a connecting line between the two vertices as an edge, and regarding a similarity value between the flow as a weight between the vertices;
step S33, the maximum weight spanning tree MST is constructed and partitioned into subtrees and a noise flow direction.
Further, the step S31 is specifically:
the method for calculating the similarity between OD flow directions is as follows:
sim(Fi，Fj)＝1
-func(ratioO)*func(ratioD)*func(ratioTime)/23
ratioO＝dist(Oi，Oj)/disLimit
ratioD＝dist(Di，Dj)/disLimit
ratioTime＝span(timei，timej)/timeLimit
Figure BDA0002247557550000031
wherein, dist (O)i,Oj) In the direction of flow FiAnd FjDistance at point O, dist (D)i,Dj) In the direction of flow FiAnd FjDistance at point D, span (time)i,timej) In the direction of flow FiAnd FjThe time difference of getting on the train or getting off the train is manually input time parameters, the unit is minutes or hours, the distance is a spatial similarity parameter, and the calculation method comprises the following steps:
Figure BDA0002247557550000032
wherein len (F)i) In the direction of flow FiLength of (k)>3. In order to prevent the OD flow length from being too long and the spatial characteristics of the clustering result from being very fuzzy, the invention adds a limiting condition that when the flow length is more than 5000m, the DISLimit is a fixed value of 5000/k (unit: meter)
When sim (F)i，Fj)∈[0，0.875]The flow directions Fi and Fj are similar in space-time, and sim (F)i，Fj) The larger, the flow direction FiAnd FjThe higher the degree of spatiotemporal similarity.
Further, the step S33 is specifically:
s331, selecting any vertex as a construction starting point of a maximum weight spanning tree (MST);
and S332, selecting the edge with the maximum weight between the vertex in the maximum weight spanning tree and the isolated vertex, and adding the edge and the corresponding vertex into the MST.
And S333, repeating the step 2 until all the vertexes are added into the MST, and finishing the construction process of the MST.
And step S334, the edges with the weight less than 0 in the MST are broken to obtain a plurality of subtrees CT without similarity relation and noise flow direction.
Further, the self-similarity judgment is performed on the subtree, and a self-similarity function Css (CT) of the subtree CT is specifically as follows:
Figure BDA0002247557550000041
wherein, numCTThe number of vertices (flow direction) in the subtree CT.
Further, the step S5 is specifically:
step S51: constructing an undirected graph G from the vertexes in the subtree CT, and weighting values w of the edges of the undirected graphijWhen the similarity value between the vertexes is smaller than 0, no edge connection exists between the vertexes, the weight is set to be 0, and a weight matrix W is as follows:
Figure BDA0002247557550000042
where n is the number of vertices in the sub-tree CT. For any point V in undirected graph GiIts degree diDefined as the sum of the weights of all edges connected to it, i.e.
Figure BDA0002247557550000043
With the definition of each vertex degree, a degree matrix D is obtained. The degree matrix D is a diagonal matrix, i.e.
Figure BDA0002247557550000051
The normalized laplacian matrix L is calculated from the above matrices, and the calculation formula is as follows:
Figure BDA0002247557550000052
step S52: calculating the eigenvalue of the normalized Laplace matrix L, taking the second smallest eigenvalue λ2And the corresponding feature vector x2＝D-1/2α2；
Step S53: feature vector x is clustered by using k-means algorithm2Into two classes, using feature vectors x2The corresponding vertex is divided into two parts by the classification information of (2), and a subtree CT1 and a subtree CT2 which correspond to the vertex are obtained;
step S54: and respectively judging whether the subtree CT1 and the subtree CT2 meet preset cluster output standards, if so, organizing OD flow directions corresponding to all vertexes in the CT1 or the CT2 into OD flow direction clusters and outputting the OD flow direction clusters, and if not, iteratively executing a step S5.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention combines the construction and the cutting of the maximum weight spanning tree to divide the data into a plurality of subtrees without similarity relation, each subtree can respectively carry out distributed processing, the operation efficiency can be effectively improved, and the calculation time can be reduced
2. The invention combines the optimal binary segmentation method of iteration and the flow direction cluster output standard, ensures that the clustering result has sufficient intra-cluster similarity and inter-cluster heterogeneity, and ensures that the clustering result is more convincing.
Drawings
FIG. 1 is a flow diagram for the construction and cutting of a maximum spanning tree in one embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method according to an embodiment of the present invention;
FIG. 3 illustrates OD flow data in accordance with an embodiment of the present invention;
FIG. 4 shows the spatio-temporal co-clustering results of OD flow directions in an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 2, the present invention provides an OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation, including the following steps:
step S1, collecting track data to be measured;
in the embodiment, the original flow data is formed by extracting the serial number of each piece of track data, longitude and latitude coordinate information of the O point and the D point and time information from the track data of a drop-out rental car in metropolis of 11 months and 1 days in 2016;
step S2, extracting the serial number of each track data, the longitude and latitude coordinate information and the time information of the O point and the D point from the track data to be detected to form original flow direction data, preprocessing all the flow direction data to form an OD flow direction set F;
in this embodiment, all flow direction data are preprocessed to form an OD flow direction set F; the pretreatment is as follows: and taking a division map of the research area range as a base map, overlapping the original flow direction data with the map, and eliminating the OD flow direction of the O point or the D point outside the research area. The obtained OD flow data is shown in fig. 3.
Step S3, calculating the similarity value among OD flow directions in the OD flow direction set F, constructing a maximum weight spanning tree MST of the F, and cutting the MST to obtain a plurality of subtree CTs and noise flow directions which have no similarity relation with each other;
in this embodiment, the step S3 specifically includes:
step S31, calculating the similarity value among the OD flow directions in the OD flow direction set F;
in this embodiment, the step S31 specifically includes:
the method for calculating the similarity between OD flow directions is as follows:
sim(Fi，Fj)＝1
-func(ratioO)*func(ratioD)*func(ratioTime)/23
ratioO＝dist(Oi，Oj)/disLimit
ratioD＝dist(Di，Dj)/disLimit
ratioTime＝span(timei，timej)/timeLimit
Figure BDA0002247557550000071
wherein, dist (O)i,Oj) In the direction of flow FiAnd FjDistance at point O, dist (D)i,Dj) In the direction of flow FiAnd FjDistance at point D, span (time)i,timej) In the direction of flow FiAnd FjThe time difference of getting on the train or getting off the train is manually input time parameters, the unit is minutes or hours, the distance is a spatial similarity parameter, and the calculation method comprises the following steps:
Figure BDA0002247557550000072
wherein len (F)i) In the direction of flow FiLength of (k)>3. In order to prevent the spatial characteristics of the clustering result from being very fuzzy due to the excessively long flow direction length of the OD, the invention adds a limiting condition that when the flow direction length is more than 5000m, the distimit is a fixed value 5000/k (unit: meter)
When sim (F)i，Fj)∈[0，0.875]The flow directions Fi and Fj are similar in space-time, and sim (F)i，Fj) The larger, the flow direction FiAnd FjThe higher the degree of spatiotemporal similarity.
Step S32, regarding each flow in the flow set F as a vertex, regarding a connecting line between the two vertices as an edge, and regarding a similarity value between the flow as a weight between the vertices;
step S33, the maximum weight spanning tree MST is constructed and partitioned into subtrees and a noise flow direction.
In this embodiment, the step S33 specifically includes:
s331, selecting any vertex as a construction starting point of a maximum weight spanning tree (MST);
step S332, selecting the edge with the maximum weight between the vertex in the maximum weight spanning tree and the isolated vertex, and adding the edge and the corresponding vertex into the MST.
And S333, repeating the step 2 until all the vertexes are added into the MST, and finishing the construction process of the MST.
And step S334, the edges with the weight less than 0 in the MST are broken to obtain a plurality of subtrees CT without similarity relation and noise flow direction.
Step S4, self-similarity judgment is carried out on the subtree, if the self-similarity of the subtree meets the preset cluster output standard, the flow direction in the subtree is organized into OD flow direction clusters to be output, otherwise, the step S5 is carried out;
in this embodiment, the Self-Similarity of the subtree is determined by using a Self-Similarity determination function (Child Tree Self-Similarity Criterion), which is as follows:
Figure BDA0002247557550000081
wherein numCTThe number of vertices (flow direction) in the subtree CT.
The self-similarity Css (CT) of the sub-tree CT being equal to 1 means that CT satisfies the cluster-like output criterion, organizes the flow direction within CT into OD flow direction and outputs, and if not, performs step S5.
Step S5: and cutting the subtrees which do not meet the output standard of the cluster by adopting an iterative optimal binary segmentation method until the cut preset subtrees meet the output standard of the cluster and are organized into OD flow direction cluster output.
In this embodiment, the iterative optimal binary segmentation step is as follows:
1. constructing an undirected graph G from the vertexes in the subtree CT, and weighting values w of the edges of the undirected graphijFor similarity between corresponding vertices i and jAnd when the similarity value between the vertexes is less than 0, no edge is connected between the vertexes, and the weight is set to be 0. The weight matrix W is:
Figure BDA0002247557550000091
where n is the number of vertices in the sub-tree CT. For any point V in undirected graph GiIts degree diDefined as the sum of the weights of all edges connected to it, i.e.
Figure BDA0002247557550000092
With the definition of each vertex degree, a degree matrix D is obtained. The degree matrix D is a diagonal matrix, i.e.
Figure BDA0002247557550000093
The normalized laplacian matrix L is calculated from the above matrices, and the calculation formula is as follows:
Figure BDA0002247557550000094
2. calculating the eigenvalue of the normalized Laplace matrix L, taking the second smallest eigenvalue λ2And the corresponding feature vector x2＝D-1/2α2。
3. Feature vector x is clustered by using k-means algorithm2Into two classes, using feature vectors x2The corresponding vertex is divided into two parts by the classification information of (1), and a subtree CT1 and a subtree CT2 are obtained corresponding to the vertex.
4. And respectively judging whether the subtree CT1 and the subtree CT2 meet cluster output standards, if so, organizing OD flow directions corresponding to all vertexes in the CT1 or the CT2 into OD flow direction clusters and outputting the OD flow direction clusters, and if not, iteratively executing a step S4.
The above specific implementation steps and parameter settings are followed to obtain the spatial-temporal joint clustering result of the OD flow direction, showing the clustering result at all times, as shown in fig. 4. Each flow in fig. 4 has a time attribute, the time attribute of the class cluster is represented by color, and the number attribute of the class cluster is represented by thickness.
By combining the specific implementation mode and the case, the method can effectively implement space-time combined clustering on the OD flow direction data, so that the travel modes of urban residents at different moments can be extracted from disordered OD data, and reasonable suggestions are provided for urban traffic allocation and infrastructure construction.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (6)

1. An OD flow direction clustering method based on maximum spanning tree and optimal graph segmentation is characterized by comprising the following steps:
step S1, collecting the track data to be measured;
step S2, extracting the serial number of each track data, the longitude and latitude coordinate information and the time information of the O point and the D point from the track data to be detected to form original flow direction data, preprocessing all the flow direction data to form an OD flow direction set F;
step S3, calculating the similarity value among OD flow directions in the OD flow direction set F, constructing a maximum weight spanning tree MST of the F, and cutting the MST to obtain a plurality of subtree CTs and noise flow directions which have no similarity relation with each other;
step S4, self-similarity judgment is carried out on the subtree, if the self-similarity of the subtree meets the preset cluster output standard, the flow direction in the subtree is organized into OD flow direction clusters to be output, otherwise, the step S5 is carried out;
step S5: and cutting the subtrees which do not meet the output standard of the cluster by adopting an iterative optimal binary segmentation method until the cut preset subtrees meet the output standard of the cluster and are organized into OD flow direction cluster outputs.
2. The OD flow clustering method based on the maximum spanning tree and the optimal graph segmentation as claimed in claim 1, wherein the step S3 specifically comprises:
step S31, calculating the similarity value among the OD flow directions in the OD flow direction set F;
step S32, regarding each flow in the flow set F as a vertex, regarding a connecting line between the two vertices as an edge, and regarding a similarity value between the flow as a weight between the vertices;
step S33, the maximum weight spanning tree MST is constructed and partitioned into subtrees and a noise flow direction.
3. The OD flow clustering method based on the maximum spanning tree and the optimal graph segmentation as claimed in claim 2, wherein the step S31 specifically comprises:
the method for calculating the similarity between OD flow directions is as follows:
sim(Fi，Fj)＝1-func(ratioO)*func(ratioO)*func(ratioTime)/23
ratioO＝dist(Oi，Oj)/disLimit
ratioD＝dist(Di，Dj)/disLimit
ratioTime＝span(timei，timej)/timeLimit
Figure FDA0003576872940000021
wherein, dist (O)i,Oj) In the direction of flow FiAnd FjDistance at point O, dist (D)i,Dj) In the direction of flow FiAnd FjDistance at point D, span (time)i,timej) In the direction of flow FiAnd FjThe time difference of getting on the train or getting off the train is manually input time parameters, the unit is minutes or hours, the distance is a spatial similarity parameter, and the calculation method comprises the following steps:
Figure FDA0003576872940000022
wherein len (F)i) In the direction of flow FiLength of (k)>3; in order to prevent the OD flow length from being too long, the spatial characteristics of the clustering result will be very fuzzy, and a limiting condition is added, that is, when the flow length is greater than 5000m, the distimit is a fixed value of 5000/k, unit: rice;
when sim (F)i，Fj)∈[0，0.875]The flow directions Fi and Fj are similar in space-time, and sim (F)i，Fj) The larger, the flow direction is to FiAnd FjThe higher the degree of spatiotemporal similarity.
4. The OD flow clustering method based on the maximum spanning tree and the optimal graph segmentation as claimed in claim 2, wherein the step S33 specifically comprises:
s331, selecting any vertex as a construction starting point of a maximum weight spanning tree (MST);
s332, selecting the edge with the maximum weight between the peak in the maximum weight spanning tree and the isolated peak, and adding the edge and the corresponding peak into the MST;
step S333, repeating the step 2 until all the vertexes are added into the MST, and finishing the construction process of the MST;
and step S334, the edges with the weight less than 0 in the MST are broken to obtain a plurality of subtrees CT without similarity relation and noise flow direction.
5. The maximum spanning tree and optimal graph segmentation based OD flow direction clustering method of claim 4, wherein the self-similarity judgment is performed on the sub-tree, and the self-similarity function CSS (CT) of the sub-tree CT is adopted as follows:
Figure FDA0003576872940000031
wherein, numCTThe number of vertices in the subtree CT.
6. The OD flow clustering method based on the maximum spanning tree and the optimal graph segmentation as claimed in claim 1, wherein the step S5 specifically comprises:
step S51: constructing an undirected graph from the vertexes in the subtree CT, wherein the weight value w of the edge of the undirected graphijWhen the similarity value between the vertexes is less than 0, the vertexes are connected without edges, and the weight is set to be 0; the weight matrix W is:
Figure FDA0003576872940000032
wherein n is the number of vertexes in the subtree CT; for any point V in the undirected graphiIts degree diDefined as the sum of the weights of all edges connected to it, i.e.
Figure FDA0003576872940000041
Obtaining a degree matrix D by using the definition of each vertex degree; the degree matrix D is a diagonal matrix and,
namely, it is
Figure FDA0003576872940000042
The normalized laplacian matrix L is calculated from the above matrices, and the calculation formula is as follows:
Figure FDA0003576872940000043
step S52: calculating the eigenvalue of the normalized Laplace matrix L, and taking the second smallest eigenvalue lambda2And the corresponding feature vector x2＝D-1/2α2；
Step S53: using k-means clusteringNormal feature vector x2Into two classes, using feature vectors x2The corresponding vertex is divided into two parts by the classification information of (2), and a subtree CT1 and a subtree CT2 which correspond to the vertex are obtained;
step S54: and respectively judging whether the sub-tree CT1 and the sub-tree CT2 meet preset cluster output standards, if so, organizing OD flow directions corresponding to vertexes in the CT1 or the CT2 into OD flow direction clusters and outputting the OD flow directions, and if not, iteratively executing a step S5.
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