CN107103758B - A kind of city area-traffic method for predicting based on deep learning - Google Patents
A kind of city area-traffic method for predicting based on deep learning Download PDFInfo
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Abstract
The invention discloses a kind of city area-traffic method for predicting based on deep learning, this method predicts the magnitude of traffic flow in each region in city by extracting the Higher Dimensional Space Time feature of magnitude of traffic flow variation simultaneously, provides a kind of new thinking for Forecast of Urban Traffic Flow forecasting problem.The historical traffic of urban area each period is calculated according to the data of LPR equipment first；Then ConvLSTM and CNN design flow prediction model is utilized, and extracts the data on flows for the material time section for influencing prediction period as input training pattern；The prediction of city area-traffic flow is finally carried out using trained model.
Description
Technical field
The present invention relates to a kind of city area-traffic method for predicting based on deep learning, by using deep learning
The long memory network in short-term of convolutional neural networks and convolution in technology is realized in conjunction with the net region division methods of city road network
The prediction of city area-traffic flow belongs to the interleaving techniques application field of deep learning and intelligent transportation system.
Background technique
Intelligent transportation system (ITS) is the system that information and communication technology (ICT) is applied to road transport field, passes through friendship
The innovation of logical management mode enables people to be best understood from, more coordinates, reasonably utilizes transportation network.In recent years, intelligence
The fast development of traffic system provides effective solution scheme for the continuous growth of transportation network demand, is construction smart city
Core link.Currently, intelligent transportation system is solving urban road congestion, city capacity deployment, urban safety, city basis
It has been obtained and is widely applied on the problems such as facilities planning.
Accurate traffic flow forecasting system is the core of ITS, and people have done in traffic flow forecasting problem
A large amount of research work.These research work can substantially be divided into two classes: one kind is with the traditional mathematics physics such as mathematical statistics
Prediction model based on method, such as autoregression model (AR), ARMA model (ARIMA), history averaging model
(HA), Kalman filter model (KFM) etc.；Another kind of is the prediction model based on neural network, such as BP neural network mould
Type, stack encode (SAE), convolutional neural networks model (CNN), recurrent neural network model (RNN) etc. certainly.
Existing method or the defect of invention: 1) existing method only focuses on the traffic flow forecasting of single-point or single channel section mostly,
The volume forecasting in region is not suitable for, because point or section can not represent region；2) existing method only considers traffic mostly
Space-time of the changes in flow rate in the dependence of time dimension or the relevance of Spatial Dimension, without considering magnitude of traffic flow variation simultaneously
Feature；3) existing method only focuses on traffic flow forecasting in short-term mostly, and lacks the support to long-time method for predicting.
Summary of the invention
The object of the present invention is to provide a kind of city area-traffic method for predicting based on deep learning, by depth
Practise be applied to city area-traffic volume forecasting, using the traffic flow data of history as input, using multi-layer C onvLSTM into
Row Higher Dimensional Space Time feature extraction makees dimension-reduction treatment finally by the CNN of single layer, obtains prediction result, and this method is handed over by extracting
The Higher Dimensional Space Time feature of through-current capacity variation predicts the magnitude of traffic flow in each region in city simultaneously, is that Forecast of Urban Traffic Flow is pre-
Survey problem provides a kind of new thinking.
The historical traffic of urban area each period is calculated according to the data of LPR equipment first；Then it utilizes
ConvLSTM and CNN design flow prediction model, and the data on flows for extracting the material time section for influencing prediction period is made
To input training pattern；The prediction of city area-traffic flow is finally carried out using trained model.
Specific steps are as follows:
S1, the net region that city road network is divided into M × N, according to longitude and latitude by each LPR device map to grid regions
In domain；
S2, LPR data are pre-processed, obtain each LPR equipment each period crosses vehicle record, sets in conjunction with LPR
The standby mapping relations with net region obtain traffic flow data of each net region within each period；
S3, input of the data on flows for the material time section for influencing prediction period as traffic flow forecasting module is chosen；
S4, prediction model is constructed using the long memory network in short-term of convolution and convolutional neural networks, prediction model is instructed
Practice, chooses the smallest model of error as optimum prediction model, the pre- of city area-traffic flow is calculated by the model
Measured value.
Further, step S1 is specifically included:
S11, the net region for city road network being divided into according to longitude and latitude M × N；
S12, each LPR equipment is mapped in net region according to longitude and latitude, the LPR in net region (m, n) is set
It is standby to be denoted as L (m, n)={ L1, L2... Li.., Lk, wherein LiIndicate the number of i-th of equipment in net region (m, n), k
It indicates to share k equipment in the net region.
Further, step S2 is specifically included
S21, the critical field { L, P, τ } for extracting LPR data, wherein L indicates that device numbering, P indicate the vehicle of equipment L record
The trade mark, τ indicate the time of its record；
S22, LPR data are filtered with cleaning, deletion error, redundant data；
S23, it was divided into T period by one day, according to the processing result of S22, extracts each equipment in each time
Vehicle record is crossed in section；
S24, according to the mapping relations of LPR equipment and net region, by the vehicle record of crossing of LPR equipment, to be associated with its corresponding
In net region, obtains each LPR equipment in each net region and cross vehicle record within each period；
S25, the traffic in each period of each net region is calculated according to the LPR number of devices in each net region
Data on flows；
S26, the data on flows x of all net regions of all periods obtained in S25 is normalized, then hadIn formula, x ' is the flow after normalization, xmaxAnd xminMost for all net region flows of all periods
Big value and minimum value, the data on flows of time period t is the three-dimensional matrice in 1 channel of M row N column after normalization, is denoted as Xt∈RM×N×1。
Further, the calculation method of the traffic flow data in step S25 in each net region each period are as follows:
If a, not predicting that flow is denoted as 0 to its flow without LPR equipment in net region (m, n)；
If b, only one LPR equipment in net region (m, n), calculates this LPR equipment and cross vehicle number in time period t
As flow of the region in time period t；
If c, the number of devices more than one in net region (m, n), mistake of each LPR equipment in time period t is calculated first
The case where vehicle number is simultaneously summed, and then records same vehicle for the multiple LPR equipment being likely to occur is handled in the following way:
In net region if (m, n), LPR equipment LiAnd LjSame vehicle P is successively recorded in same time period tA, note
Recording the time is respectively τiWith τjIfThen it is considered vehicle PAIdentical strip path curve be repeatedly recorded, by above-mentioned summation
Result subtract 1；Otherwise retain former result；In formula, d (Li, Lj) it is LPR equipment Li、LjThe distance between, λ is given threshold.
Further, step S3 is specifically included:
S31, it chooses recentlyThe data on flows of section at the same time on the same day in week, is denoted as
S32, it chooses recentlyThe data on flows of its section at the same time, is denoted as
S33, it chooses recentlyThe data on flows of a period, is denoted as
S34, using the combination of above-mentioned three groups of data as input, be denoted asXtAs output, building
One sampleAll data are according to said method constructed into sample, and are divided into training set, verifying collection and test by a certain percentage
Collection.
Further, step S4 is specifically included:
S41, building prediction model, the model include 4 layers of convolution length memory network layer, 4 layers batches of specification layers and one layer in short-term
Convolutional neural networks layer；
S42, the network that prediction model is 9 layers, wherein the first 8 layers group for convolution long memory network layer in short-term and batch specification layer
It closes, i.e., each long memory network layer in short-term of convolution is followed by one batch of specification layer, each batch of specification layer is followed by a convolution length
When memory network layer, the 9th layer be single layer convolutional neural networks layer；
The long memory network layer in short-term of S43, each convolution uses 64 3 × 3 convolution kernels, is operated, is used using zero padding
Relu function is as activation primitive；
S44, convolutional neural networks use 13 × 3 convolution kernel layer by layer, are operated using zero padding, use sigmoid function
As activation primitive；
S45, prediction model objective function be mean square error function MSE, then have:
Wherein, XiIndicate real traffic,Indicate predicted flow rate, s indicates that sample number, M, N are the line number and columns of grid；
S46, being trained in training set input prediction model, collected according to verifying and choose the smallest model of MSE as most
Whole prediction model；
S47, test set is inputted in the trained model of S46, after obtaining output result, then carries out renormalization, obtains
Final urban area volume forecasting result.
After adopting the above technical scheme, compared with the background technology, the present invention, having the advantages that
1, existing method only focuses on the volume forecasting of single-point or single channel section mostly, and method proposed by the present invention is based on convolution
Length in short-term predicted with convolutional neural networks layer by memory network layer, the magnitude of traffic flow in each region and its peripheral region in city
The magnitude of traffic flow in other regions is related in domain or even entire city, and convolutional coding structure can learn a region and other weeks
The discharge relation for enclosing region can learn influence feature of the peri-urban region to the region with the intensification of the convolution number of plies；2,
Existing method only considers magnitude of traffic flow variation feature in time or spatially mostly, and the convolution in prediction technique of the present invention
Long memory network layer in short-term extracts space characteristics by convolutional coding structure, by LSTM structure acquisition time feature, and in its algorithm
Bottom combines convolutional neural networks with LSTM, can learn the high-dimensional space-time characteristic of magnitude of traffic flow variation, effective integration
Time dimension and Spatial Dimension, to substantially increase precision of prediction；
3, a convolution kernel is arranged in convolutional Neural, can make dimension-reduction treatment to high-dimensional space-time characteristic, be operated by zero padding,
The volume forecasting of city all areas may be implemented；
4, existing method only focuses on short-term traffic flow forecast mostly, and city area-traffic flow proposed by the present invention is pre-
Regional traffic flow prediction in short-term in one hour had both may be implemented by the specific list entries of selection in survey method, can also be real
Prolonged regional traffic flow prediction in existing 24 hours, one week etc.；
To sum up, therefore disclosed method is particularly suitable for the other occasion of City-level and the emphasis of festivals or holidays prison
Survey the traffic flow forecasting in region.
Detailed description of the invention
Fig. 1 is the algorithm flow chart of the city area-traffic method for predicting based on deep learning；
Fig. 2 is that city road network net region divides schematic diagram；
Fig. 3 is that the flow of time period t city area-traffic flow indicates Xt；
Fig. 4 is the schematic diagram output and input；
Fig. 5 is the schematic diagram of prediction model calculating process.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
Embodiment
As shown in Fig. 1 the algorithm flow chart of the city area-traffic method for predicting based on deep learning, it is pre-
Examining system includes magnitude of traffic flow computing module and traffic flow forecasting module based on net region.In magnitude of traffic flow computing module
In, net region division is carried out to urban road network according to longitude and latitude first, and by the license plate in section each in city road network
Identify (LPR) device map into net region；Secondly, being obtained in each equipment each period according to the data of LPR equipment
Cross vehicle record；Again, the result for merging above-mentioned two step calculates the magnitude of traffic flow in each period of each net region；Most
Afterwards, data on flows is normalized.In traffic flow forecasting module, the magnitude of traffic flow of material time section is chosen first
Input of the data as the long memory network (ConvLSTM) in short-term of convolution, when the higher-dimension changed by the e-learning magnitude of traffic flow
Empty feature；Secondly, carrying out dimension-reduction treatment to Higher Dimensional Space Time feature by convolutional neural networks (CNN)；Finally, passing through renormalization
Obtain final urban area volume forecasting result.
Specific steps are as follows:
S1, city road network is subjected to net region division, according to longitude and latitude by each LPR device map to net region
In:
S11, the net region for city road network being divided into according to longitude and latitude M × N；
S12, each LPR equipment is mapped in net region according to longitude and latitude, as the LPR in net region (m, n) is set
It is standby to be denoted as L (m, n)={ L1, L2... Li..., Lk, wherein LiIndicate the number of i-th of equipment in net region (m, n), k
It indicates to share k equipment in the net region.
S2, LPR data are pre-processed, obtain each equipment each period cross vehicle record, in conjunction with LPR equipment with
The mapping relations of net region obtain traffic flow data of each net region within each period；
S21, the critical field { L, P, τ } for extracting LPR data, wherein L indicates that device numbering, P indicate the vehicle of equipment L record
The trade mark, τ indicate the time of its record；
S22, LPR data are filtered with cleaning, deletion error, redundant data；
S23, it was divided into T period by one day, according to the processing result of S22, extracts each equipment in each time
Vehicle record is crossed in section；
S24, according to the mapping relations of LPR equipment and net region, by the vehicle record of crossing of LPR equipment, to be associated with its corresponding
In net region, obtain crossing vehicle record in each equipment each period in each net region；
S25, the magnitude of traffic flow for net region (m, n) in time period t, point or less three kinds of situations calculated:
If expression is without road network or is not traffic hot spot region, not to it without LPR equipment in net region (m, n)
Flow is predicted that flow is denoted as 0；
If only one LPR equipment in net region (m, n), calculates this equipment and cross the conduct of vehicle number in time period t
Flow of the region in time period t；
If the number of devices more than one in net region (m, n), each equipment is calculated first and crosses vehicle number in time period t
And the case where summing, same vehicle then is recorded for the multiple equipment being likely to occur, it handles in the following way:
If in grid (m, n), LI、LjSame vehicle P is successively recorded in same time period tA, the record time is respectively τi、
τj(τi、τjTo record vehicle P in the net regionAThe closest time, i.e., in time period t, to region (m, n),If(wherein, d (Li, Lj) it is equipment Li、Lj
The distance between, λ is given threshold), then it is assumed that it is vehicle PAIdentical strip path curve be repeatedly recorded, by the result of above-mentioned summation
Subtract 1, does not otherwise subtract 1；
The traffic flow data in each period of each net region is calculated according to the above method.
S26, the data on flows of obtained all net regions of all periods is subjected to unified normalized, calculated public
Formula:Wherein x ' is the flow after normalization, xmaxAnd xminFor all net region flows of all periods
Maximum value and minimum value, the data on flows of time period t is the three-dimensional matrice in 1 channel of M row N column after normalization, is denoted as Xt∈RM ×N×1。
S3, input of the data on flows for the material time section for influencing prediction period as traffic flow forecasting module is chosen:
It S31, is prediction Xt, choose nearestThe data on flows of section at the same time on the same day in week, is denoted as
It S32, is prediction Xt, choose nearestThe data on flows of its section at the same time, is denoted as
It S33, is prediction Xt, choose nearestThe data on flows of a period, is denoted as
S34, using the combination of above-mentioned three groups of data as input, be denoted asXtAs output, building
One sampleAll data are according to said method constructed into sample, and are divided into training set, verifying collection and test by a certain percentage
Collection.
S4, prediction model is constructed using the long memory network (ConvLSTM) in short-term of convolution and convolutional neural networks (CNN), it is right
Prediction model is trained, and chooses the smallest model of error as optimum prediction model, metropolitan district is calculated by the model
The predicted value of the domain magnitude of traffic flow.
S41, building prediction model, the model include the long memory network layer (ConvLSTM) in short-term of 4 layers of convolution, 4 layers batches of rule
Model layer (Batch Normalization) and one layer of convolutional neural networks layer (CNN)；
S42, the network that prediction model is 9 layers, wherein the first 8 layers combination for ConvLSTM and batch specification layer is (each
ConvLSTM layers are followed by one batch of specification layer, then connect ConvLSTM layers, so connect, constitute 8 layers of network), the 9th layer is single
The CNN of layer；
S43, each ConvLSTM layers use 64 3 × 3 convolution kernels, (zero-padding) is operated using zero padding, is made
Use relu function as activation primitive；
S44, CNN layers, using 13 × 3 convolution kernel, are operated using zero padding, use sigmoid function as activation letter
Number；
S45, prediction model objective function be mean square error function (MSE), it is as follows:
Wherein, XiIndicate real traffic,Indicate predicted flow rate, s indicates that sample number, M, N are the line number and columns of grid；
S46, being trained in training set input prediction model, collected according to verifying and choose the smallest model of MSE as most
Whole prediction model；
S47, test set is inputted in the trained model of S46, after obtaining output result, then carries out renormalization, obtains
Final prediction result.
Carry out some steps in detailed description method below with reference to specific example.
One, city road network net region divides
Fig. 2 show 18 × 18 net region of Fujian province Xiamen City Xiamen Island road network and divides schematic diagram, is set according to LPR
Each device map into net region, is obtained the LPR device numbering for including in each net region, such as net by standby longitude and latitude
LPR equipment in lattice region (m, n) is denoted as L (m, n)={ L1, L2... Li..., Lk}。
Two, the magnitude of traffic flow calculates
Period division was carried out for interval (T=24) with one hour according to the record time of LPR device data, counts grid
Region daily 24 periods each period crosses vehicle record, according to the mapping relations of LPR equipment and net region, counts net
The magnitude of traffic flow number crossed vehicle record, calculate in net region in each period by the following method in each period of lattice region
According to:
If expression is without road network or is not traffic hot spot region, not to it without LPR equipment in net region (m, n)
Flow is predicted that flow is denoted as 0；
If only one LPR equipment in net region (m, n), the vehicle number scale of crossing for calculating the equipment each period is to be somebody's turn to do
The magnitude of traffic flow in each period of region；
If the number of devices more than one in net region (m, n), is illustrated below:
Assuming that there are two equipment L in net region (m, n)1、L2, in time period t, L1Be recorded asL2Be recorded asIf(λ is threshold value, be may be set to 10), then grid
The magnitude of traffic flow of the region (m, n) in time period t is 3+2-1=4, is otherwise 5；
The magnitude of traffic flow of each region in each hour period, such as Fig. 3 can be calculated in method as described above
The city area-traffic flow for showing time period t indicates Xt, then it is normalized according to min-max standardized method.
Three, list entries is obtained
The flow of time period t and its beforeThe flow of a time step has certain continuity, with its preceding d days synchronization
Flow has certain periodicity, and before itThe flow of all synchronizations on the same day has certain similitude.To predict Xt,
It takes Enable inputInputting step-length isIt is expected that
Output is Xt, sample pair is constructed, and be training set, verifying collection and test set by 8: 1: 1 points.
By design list entries, but realize in short-term or it is long when volume forecasting.It is exemplified below:
If the urban area flow of following one hour of prediction, can be set T=24,If pre-
Urban area flow after surveying 24 hours, can be set T=24,If the city of prediction after a week
T=24 can be set in zone flow,Be illustrated in figure 4 system outputs and inputs schematic diagram.
The design and training of prediction model:
Prediction model is made of 4 layers ConvLSTM layers, 4 layers batches of specification layers and one layer of CNN layer.It is for 8 layers before network
(each ConvLSTM layers is followed by one batch of specification layer, then connects ConvLSTM layers, so for the combination of ConvLSTM and batch specification layer
Series connection constitutes 8 layers of network), the 9th layer of CNN for single layer.
Each ConvLSTM layers uses 64 3 × 3 convolution kernels, operates (zero-padding) using zero padding, uses
Relu function is as activation primitive, and ConvLSTM layers of three first layers of input and output sequence length is identical, the last layer ConvLSTM
The output sequence length of layer is 1；CNN layers use 13 × 3 convolution kernel to use using zero padding operation (zero-padding)
Sigmoid function is as activation primitive；The objective function of prediction model is mean square error function (MSE).
Fig. 5 is the schematic diagram of prediction model calculating process.Being trained in training set input prediction model, according to verifying
Collection chooses the smallest model of MSE as final prediction model, and test set is inputted in trained model, obtains output result
Afterwards, then renormalization is carried out, obtains final prediction result.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of protection of the claims
Subject to.
Claims (4)
1. a kind of city area-traffic method for predicting based on deep learning, it is characterised in that: the following steps are included:
Each car license recognition equipment LPR is mapped to net according to longitude and latitude by S1, the net region that city road network is divided into M × N
In lattice region；
S2, LPR data are pre-processed, obtain each car license recognition equipment LPR each period crosses vehicle record, in conjunction with vehicle
Board identifies the mapping relations of equipment LPR and net region, obtains magnitude of traffic flow number of each net region within each period
According to；
S3, input of the data on flows for the material time section for influencing prediction period as traffic flow forecasting module is chosen；
S4, prediction model is constructed using the long memory network in short-term of convolution and convolutional neural networks, prediction model is trained, is selected
It takes the smallest model of error as optimum prediction model, the predicted value of city area-traffic flow is calculated by the model；
Wherein, step S3 is specifically included:
S31, it chooses recentlyThe data on flows of section at the same time on the same day in week, is denoted as
S32, it chooses recentlyThe data on flows of its section at the same time, is denoted as
S33, it chooses recentlyThe data on flows of a period, is denoted as
S34, using the combination of above-mentioned three groups of data as input, be denoted asXtAs output, a sample is constructed
ThisAll data are according to said method constructed into sample, and are divided into training set, verifying collection and test set by a certain percentage；
Wherein, step S4 is specifically included:
S41, building prediction model, the model include the long memory network layer in short-term of 4 layers of convolution, 4 layers batches of specification layers and one layer of volumes
Product neural net layer；
S42, the network that prediction model is 9 layers, wherein the first 8 layers combination for convolution long memory network layer in short-term and batch specification layer,
I.e. each long memory network layer in short-term of convolution is followed by one batch of specification layer, each batch of specification layer is followed by a convolution length and remembers in short-term
Recall network layer, the 9th layer of convolutional neural networks layer for single layer；
The long memory network layer in short-term of S43, each convolution uses 64 3 × 3 convolution kernels, is operated using zero padding, uses relu letter
Number is used as activation primitive；
S44, convolutional neural networks use 13 × 3 convolution kernel layer by layer, are operated using zero padding, use sigmoid function as
Activation primitive；
S45, prediction model objective function be mean square error function MSE, then have:
Wherein, XiIndicate real traffic,Indicate predicted flow rate, s indicates that sample number, M, N are the line number and columns of grid；
S46, being trained in training set input prediction model, collected according to verifying and choose the smallest model of MSE as final pre-
Survey model；
S47, test set is inputted in the trained model of S46, after obtaining output result, then carries out renormalization, obtained final
Urban area volume forecasting result.
2. a kind of city area-traffic method for predicting based on deep learning according to claim 1, feature exist
In step S1 is specifically included:
S11, the net region for city road network being divided into according to longitude and latitude M × N；
S12, each LPR equipment is mapped in net region according to longitude and latitude, the LPR equipment in net region (m, n) is remembered
For L (m, n)={ L1, L2... Li..., Lk, wherein LiIndicate the number of i-th of equipment in net region (m, n), k is indicated
K equipment is shared in the net region.
3. a kind of city area-traffic method for predicting based on deep learning according to claim 1, feature exist
In step S2 is specifically included:
S21, the critical field { L, P, τ } for extracting LPR data, wherein L indicates that device numbering, P indicate the license plate of equipment L record
Number, τ indicates the time of its record；
S22, LPR data are filtered with cleaning, deletion error, redundant data；
S23, it was divided into T period by one day, according to the processing result of S22, extracts each equipment within each period
Cross vehicle record；
S24, according to the mapping relations of LPR equipment and net region, the vehicle record of crossing of LPR equipment is associated with its corresponding grid
In region, obtains each LPR equipment in each net region and cross vehicle record within each period；
S25, the magnitude of traffic flow in each period of each net region is calculated according to the LPR number of devices in each net region
Data；
S26, the data on flows x of all net regions of all periods obtained in S25 is normalized, then hadIn formula, x ' is the flow after normalization, xmaxAnd xminFor the maximum of all net region flows of all periods
Value and minimum value, the data on flows of time period t is the three-dimensional matrice in 1 channel of M row N column after normalization, is denoted as Xt∈RM×N×1。
4. a kind of city area-traffic method for predicting based on deep learning according to claim 3, feature exist
In the calculation method of the traffic flow data in step S25 in each net region each period are as follows:
If a, not predicting that flow is denoted as 0 to its flow without LPR equipment in net region (m, n)；
If b, only one LPR equipment in net region (m, n), calculates this LPR equipment and cross the conduct of vehicle number in time period t
Flow of the region in time period t；
If c, the number of devices more than one in net region (m, n), each LPR equipment is calculated first and crosses vehicle number in time period t
And the case where summing, same vehicle then is recorded for the multiple LPR equipment being likely to occur, it handles in the following way:
In net region if (m, n), LPR equipment LiAnd LiSame vehicle P is successively recorded in same time period tA, when recording
Between be respectively τiWith τjIfThen it is considered vehicle PAIdentical strip path curve be repeatedly recorded, by the knot of above-mentioned summation
Fruit subtracts 1；Otherwise retain former result；In formula, d (Li, Lj) it is LPR equipment Li、LjThe distance between, λ is given threshold.
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