CN105788261A - Road traffic space data compression method based on PCA and LZW coding - Google Patents

Abstract

Provided is a road traffic space data compression method based on PCA and LZW coding. The road traffic space data compression method comprises the steps that: a road traffic characteristic reference sequence is established based on road traffic data of different road segments under a same modal and in a same space; a road traffic road segment set having correlation is selected based on PCA; a reference road segment is selected, and data of the reference road segment is regarded as road traffic reference data of the space; historical data of other road segments under the same modal and in the same space is extracted to serve as training data, and an optimal threshold value of spatial road traffic difference data is determined on the basis the road traffic reference data under the same modal and in the same space; data of other road segments in the space is extracted to serve as real-time data; road traffic difference data is obtained on the basis of the traffic reference data under the same modal and in the same space; compression of road traffic space data is realized based on LZW coding; and finally, reconstruction of the road traffic space data is realized based on an LZW decoding technology. The road traffic space data compression method provided by the invention simplifies the calculation and effectively accelerates the processing speed.

Description

A kind of road traffic spatial data compression method of Based PC A and LZW coding

Technical field

The invention belongs to highway traffic data process field, relate to analysis and the compression of highway traffic data, be the compression method of a kind of highway traffic data.

Background technology

Along with the development of intelligent transportation system data acquisition technology, based on the intelligent transportation data that continuous acquisition obtains, field of traffic is about to face mass data problem, it is necessary to it is carried out effective data compression, just can carry out processing, analyze and storing.

The internal characteristics of traffic flow data specifically includes that periodicity, similarity, dependency etc..There is the spatial and temporal association of complexity between the traffic flow of approach way, often similarity is higher, and same traffic flow shows extremely strong dependency and periodicity in time.These similaritys show there is substantial amounts of redundancy in data.

Based on the feature of traffic flow similarity, existing multiple method is applied in highway traffic data compression field at present.Specifically include that PCA (PCA), independent component analysis (ICA), predictive coding and dictionary encoding series process, based on small echo (bag) method such as alternative approach, artificial neural network.It mainly utilizes the thought of transform domain, highway traffic data carries out multi-scale transform and carries out relevant treatment, it is achieved the compression of data, and obtaining good effect.

The big multipair Traffic Net data of existing highway traffic data compression method carry out data compression, study less to the data compression method in relevant road segments time series.

Summary of the invention

In order to overcome the deficiency that algorithm is complicated, processing speed is relatively low of existing highway traffic data compression method, the present invention provides a kind of road traffic spatial data compression method simplifying calculating, effective Based PC A and the LZW coding improving processing speed.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of in the road traffic spatial data compression method of PCA and LZW coding, comprise the following steps:

1) based under same mode, spatially the highway traffic data of different sections of highway set up road traffic features reference sequences；Based PC A method, chooses the road traffic section set with dependency, and its process is as follows:

Extracting the road traffic historical data in s bar section from reason traffic characteristic reference sequences, the collection data in every section are r, and transform it into the matrix of s × r, are designated as: A_sⅹr；

Matrix A_sⅹrThe average of jth row is:

$a_j=\frac{1}{s}\underset{i=1}{\overset{s}{\mathrm{\Σ}}}{A}_{i,j}---\left(1\right)$

Based on a_j, it is thus achieved that A_sⅹrNormalization matrix SA_sⅹr:

${\mathrm{SA}}_{i,j}=(A_{i,j}-a_j){\left(\underset{i=1}{\overset{s}{\mathrm{\Σ}}}{\left(A_{i,j}-a_j\right)}^2\right)}^{-\frac{1}{2}}---\left(2\right)$

The covariance matrix CSA of normalization matrix SA is:

$CSA=\frac{1}{s-1}({\mathrm{SA}}^T*SA)---\left(3\right)$

Obtain the eigenvalue D and characteristic vector V of covariance matrix CSA, then D=[λ₁,λ₂…λ_r]；λ₁≥λ₂≥…≥λ_r；Characteristic of correspondence vector is: V=[v₁,v₂…v_r]；

Choose λ₁, λ₂The projection matrix VA that characteristic of correspondence vector is constituted_r×2=[v₁,v₂], based on projection matrix and normalized training matrix, ask for A_sⅹrMain constituent matrix A PC_r×2:

APC_s×2=SA_sⅹr×VA_r×2(4)

Based on APC_s×2, two dimensional surface draws the distribution in s bar section, the distribution density of point represents corresponding road section strength of correlation, by correlation analysis, sets threshold value δ, selects the dependency p+1 bar section more than δ, and its process is as follows:

Wherein, i, j represents i-th respectively, j bar section, 0 < i < s, 0 < j < s；Represent relevance function；

2) selection reference section, and using its data as road traffic benchmark data spatially；Extract under same mode, the historical data in spatially other section, as training data, based on road traffic benchmark data under same mode, spatially, it is determined that the optimal threshold of space road traffic difference data, its process is as follows:

S_i(m*Δt,M_gh)=ST_i(m*Δt,M_gh)-SB(m*Δt,M_gh)(6)

e_i(m,M_gh)=[S_i(Δt,M_gh)S_i(2*Δt,M_gh)...S_i(m*Δt,M_gh)](7)

${\mathrm{he}}_i(m,M_{gh})=\left\{\begin{array}{cc}0,& e_i(m,M_{gh})<E_i(m,M_{gh})\\ e_i(m,M_{gh}),& e_i(m,M_{gh})>E_i(m,M_{gh})\end{array}\right.---\left(8\right)$

pe_i(n,M_gh)=w (he_i(m,M_gh))(9)

pe_i(n,M_gh)=[S_i'(1,M_gh)S_i'(2,M_gh)...S_i'(n,M_gh)](10)

Wherein, Δ t is the collection period of road traffic state data；(m* Δ t) is m-th road traffic state data collection cycle, and 0≤m≤N, N represents the quantity of the transport information gathered every day；I (1≤i≤p) represents i-th section；ST_i(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in (m* Δ t) moment i section；SB (m* Δ t, M_gh) represent mode M_ghUnder, the benchmark data in (m* Δ t) moment benchmark section；S_i(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the training data in (m* Δ t) moment i section and the benchmark data in benchmark section；e_i(m, M_gh) represent mode M_ghUnder, Δ t is to the difference data of the benchmark data in training data and the benchmark section in (m* Δ t) period i section；he_i(m, M_gh) represent mode M_ghUnder, Δ t process to (m* Δ t) period threshold after the difference data of benchmark data in training data and benchmark section in i section；E_i(m, M_gh) represent mode M_ghUnder, the threshold value chosen to (m* Δ t) period i section of Δ t；pe_i(n, M_gh) represent mode M_ghUnder, Δ t is to result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；S_i' (n, M_gh) for mode M_ghUnder, Δ t is to nth data in result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；M represents at mode M_ghUnder, Δ t is to the quantity in the i section before (m* Δ t) duration compression with the difference data in benchmark section；N represents at mode M_ghUnder, Δ t is to the road traffic quantity after (m* Δ t) duration compression；W represents that LZW encodes；Compression ratio is

3) data in spatially other section are extracted, as real time data；Mode M_ghUnder, based on road traffic benchmark data spatially, obtain road traffic difference data, its general expression is as follows:

MS_j(m*Δt,M_gh)=SM_j(m*Δt,M_gh)-SB(m*Δt,M_gh)(11)

err_j(m,M_gh)=[MS_j(Δt,M_gh)MS_j(2*Δt,M_gh)...MS_j(m*Δt,M_gh)](12)

Wherein, j (1≤i≤p) represents j-th strip section；SM_j(m* Δ t, M_gh) represent mode M_ghUnder, the real time data in (m* Δ t) moment j section；MS_j(m* Δ t, M_gh) for mode M_ghUnder, the difference data of the real time data in (m* Δ t) moment j section and the benchmark data in benchmark section；err_j(m, M_gh) for mode M_ghUnder, Δ t is to the difference data of the benchmark data in real time data and the benchmark section in (m* Δ t) period j section；

4) realize the compression of road traffic spatial data based on LZW coding, its process is as follows:

The optimal threshold that the difference data in i section with benchmark section is trained is incorporated into same mode M_gh, j section and benchmark section difference data in, encode in conjunction with LZW, it is achieved the compression of j section and benchmark section difference data, its general expression is as follows:

${\mathrm{herr}}_j(m*\mathrm{\&Delta;}t,M_{gh})=\left\{\begin{array}{cc}0,& {\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh})<E_{opt}\left(M_{gh}\right)\\ {\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh}),& {\mathrm{err}}_j(m,M_{gh})>E_{opt}\left(M_{gh}\right)\end{array}\right.---\left(13\right)$

herrs_p(m*Δt,M_gh)=[herr₁(m*Δt,M_gh)herr₂(Δt,M_gh)...herr_p'(m*Δt,M_gh)](14)

perr_p'(m*Δt,M_gh)=w (herrs_p(m*Δt,M_gh))(15)

perr_p'(m*Δt,M_gh)=[MS₁(m*Δt,M_gh)MS₂(m*Δt,M_gh)...MS_p'(m*Δt,M_gh)](16)

Wherein, E_opt(M_gh) represent the optimal threshold trained；herr_j(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the benchmark data in the real time data in j section and benchmark section after (m* Δ t) moment threshold process；M represents mode M_ghUnder, Δ t is to the quantity in j section before (m* Δ t) duration compression with the difference data in benchmark section；herrs_p(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of (m* Δ t) moment p bar section difference data；Perr_p’(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of difference data after the compression of (m* Δ t) moment p bar section；MS_j' (m* Δ t, M_gh) represent mode M_ghUnder, quantity after the compression of the difference data in (m* Δ t) moment j section；P ' represents the quantity after (m* Δ t) moment LZW coding；Compression ratio is:

Further, described compression method also comprises the steps:

5) based on LZW decoding technique, it is achieved road traffic spatial data reconstructs, and its process is as follows:

The difference data in p bar section Yu benchmark section being reconstructed, in conjunction with benchmark data, it is achieved the decompression of p bar section real time data, its general expression is as follows:

dperr_p(m*Δt,M_gh)=w'(perr_p'(m*Δt,M_gh))(17)

dperr_j(m,M_gh)=w'(perr_j(Tn,M_gh))(18)

CSM_j(m,M_gh)=SB (m, M_gh)+dperr_j(m,M_gh)(19)

Wherein, w ' represents the decoding of LZW；dperr_p(m* Δ t, M_gh) represent mode M_ghUnder, the difference data in (m* Δ t) moment decoded p section and benchmark section；CSM_p(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in p bar section of (m* Δ t) moment reconstruct.

The technology of the present invention is contemplated that: owing to the trip requirements of traffic participant, travel time and space have certain regularity, therefore the road traffic state of relevant road segments has very strong dependency on similar timing node, namely the road traffic state change curve of relevant road segments has certain similarity.Therefore the present invention is based on the feature of the spatial coherence of road traffic system, it is compressed for relevant road segments road traffic spatial data.It is primarily based on PCA method, selects the section set with dependency；Secondly selection reference section and dependency section, and using its data as road traffic benchmark data spatially and training data；Then its difference data is obtained, it is determined that the optimal threshold of road traffic space interpolation data；Further, obtain the real time data of other relevant road segments, based on road traffic benchmark data, obtain its difference data；Finally, based on LZW coding and decoding technology, compression and the reconstruct of road traffic space interpolation data are realized respectively.

Beneficial effects of the present invention is mainly manifested in: simplification calculates, effectively improves processing speed.

Accompanying drawing explanation

Fig. 1 is based on the flow chart of the road traffic spatial data compression method of PCA and LZW coding.

Fig. 2 is the flow chart of reconstructing method.

Detailed description of the invention

Below in conjunction with accompanying drawing, the invention will be further described.

See figures.1.and.2, a kind of road traffic spatial data compression method based on LZW coding, comprise the steps:

1) based under same mode, spatially the highway traffic data of different sections of highway set up road traffic features reference sequences；Based PC A method, chooses the road traffic section set with dependency, and its process is as follows:

Extracting the road traffic historical data in s bar section from reason traffic characteristic reference sequences, the collection data in every section are r, and transform it into the matrix of s × r, are designated as: A_sⅹr。

Matrix A_sⅹrThe average of jth row is:

$a_j=\frac{1}{s}\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{A}_{i,j}---\left(1\right)$

Based on a_j, it is thus achieved that A_sⅹrNormalization matrix SA_sⅹr:

${\mathrm{SA}}_{i,j}=(A_{i,j}-a_j){\left(\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{\left(A_{i,j}-a_j\right)}^2\right)}^{-\frac{1}{2}}---\left(2\right)$

The covariance matrix CSA of normalization matrix SA is:

$CSA=\frac{1}{s-1}({\mathrm{SA}}^T*SA)---\left(3\right)$

Obtain the eigenvalue D and characteristic vector V of covariance matrix CSA, then D=[λ₁,λ₂…λ_r]；λ₁≥λ₂≥…≥λ_r；Characteristic of correspondence vector is: V=[v₁,v₂…v_r]；

Choose λ₁, λ₂The projection matrix VA that characteristic of correspondence vector is constituted_r×2=[v₁,v₂], based on projection matrix and normalized training matrix, ask for A_sⅹrMain constituent matrix A PC_r×2:

APC_s×2=SA_sⅹr×VA_r×2(4)

Based on APC_s×2, two dimensional surface draws the distribution in s bar section, the distribution density of point represents corresponding road section strength of correlation, by correlation analysis, sets threshold value δ, selects the dependency p+1 bar section more than δ, and its process is as follows:

Wherein, i, j represents i-th respectively, j bar section, 0 < i < s, 0 < j < s；Represent relevance function；

2) selection reference section, and using its data as road traffic benchmark data spatially；Extract under same mode, the historical data in spatially other section, as training data, based on road traffic benchmark data under same mode, spatially, it is determined that the optimal threshold of space road traffic difference data, its process is as follows:

S_i(m*Δt,M_gh)=ST_i(m*Δt,M_gh)-SB(m*Δt,M_gh)(6)

e_i(m,M_gh)=[S_i(Δt,M_gh)S_i(2*Δt,M_gh)...S_i(m*Δt,M_gh)](7)

${\mathrm{he}}_i(m,M_{gh})=\left\{\begin{array}{cc}0,& e_i(m,M_{gh})<E_i(m,M_{gh})\\ e_i(m,M_{gh}),& e_i(m,M_{gh})>E_i(m,M_{gh})\end{array}\right.---\left(8\right)$

pe_i(n,M_gh)=w (he_i(m,M_gh))(9)

pe_i(n,M_gh)=[S_i'(1,M_gh)S_i'(2,M_gh)...S_i'(n,M_gh)](10)

Wherein, Δ t is the collection period of road traffic state data；(m* Δ t) is m-th road traffic state data collection cycle, and 0≤m≤N, N represents the quantity of the transport information gathered every day；I (1≤i≤p) represents i-th section；ST_i(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in (m* Δ t) moment i section；SB (m* Δ t, M_gh) represent mode M_ghUnder, the benchmark data in (m* Δ t) moment benchmark section；S_i(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the training data in (m* Δ t) moment i section and the benchmark data in benchmark section；e_i(m, M_gh) represent mode M_ghUnder, Δ t is to the difference data of the benchmark data in training data and the benchmark section in (m* Δ t) period i section；he_i(m, M_gh) represent mode M_ghUnder, Δ t process to (m* Δ t) period threshold after the difference data of benchmark data in training data and benchmark section in i section；E_i(m, M_gh) represent mode M_ghUnder, the threshold value chosen to (m* Δ t) period i section of Δ t；pe_i(n, M_gh) represent mode M_ghUnder, Δ t is to result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；S_i' (n, M_gh) for mode M_ghUnder, Δ t is to nth data in result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；M represents at mode M_ghUnder, Δ t is to the quantity in the i section before (m* Δ t) duration compression with the difference data in benchmark section；N represents at mode M_ghUnder, Δ t is to the road traffic quantity after (m* Δ t) duration compression；W represents that LZW encodes；Compression ratio is

3) data in spatially other section are extracted, as real time data；Mode M_ghUnder, based on road traffic benchmark data spatially, obtain road traffic difference data, its general expression is as follows:

MS_j(m*Δt,M_gh)=SM_j(m*Δt,M_gh)-SB(m*Δt,M_gh)(11)

err_j(m,M_gh)=[MS_j(Δt,M_gh)MS_j(2*Δt,M_gh)...MS_j(m*Δt,M_gh)](12)

Wherein, j (1≤i≤p) represents j-th strip section；SM_j(m* Δ t, M_gh) represent mode M_ghUnder, the real time data in (m* Δ t) moment j section；MS_j(m* Δ t, M_gh) for mode M_ghUnder, the difference data of the real time data in (m* Δ t) moment j section and the benchmark data in benchmark section；err_j(m, M_gh) for mode M_ghUnder, Δ t is to the difference data of the benchmark data in real time data and the benchmark section in (m* Δ t) period j section.

4) realize the compression of road traffic spatial data based on LZW coding, its process is as follows:

The optimal threshold that the difference data in i section with benchmark section is trained is incorporated into same mode M_gh, j section and benchmark section difference data in, encode in conjunction with LZW, it is achieved the compression of j section and benchmark section difference data, its general expression is as follows:

${\mathrm{herr}}_j(m*\mathrm{\&Delta;}t,M_{gh})=\left\{\begin{array}{cc}0,& {\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh})<E_{opt}\left(M_{gh}\right)\\ {\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh}),& {\mathrm{err}}_j(m,M_{gh})>E_{opt}\left(M_{gh}\right)\end{array}\right.---\left(13\right)$

herrs_p(m*Δt,M_gh)=[herr₁(m*Δt,M_gh)herr₂(Δt,M_gh)...herr_p'(m*Δt,M_gh)](14)

perr_p'(m*Δt,M_gh)=w (herrs_p(m*Δt,M_gh))(15)

perr_p'(m*Δt,M_gh)=[MS₁(m*Δt,M_gh)MS₂(m*Δt,M_gh)...MS_p'(m*Δt,M_gh)](16)

Wherein, E_opt(M_gh) represent the optimal threshold trained；herr_j(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the benchmark data in the real time data in j section and benchmark section after (m* Δ t) moment threshold process；M represents mode M_ghUnder, Δ t is to the quantity in j section before (m* Δ t) duration compression with the difference data in benchmark section；herrs_p(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of (m* Δ t) moment p bar section difference data；Perr_p’(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of difference data after the compression of (m* Δ t) moment p bar section；MS_j' (m* Δ t, M_gh) represent mode M_ghUnder, (the m* Δ t) moment, j section difference data compression after quantity；P ' represents the quantity after (m* Δ t) moment LZW coding；Compression ratio is:

5) based on LZW decoding technique, it is achieved road traffic spatial data reconstructs, and its process is as follows:

The difference data in p bar section Yu benchmark section being reconstructed, in conjunction with benchmark data, it is achieved the decompression of p bar section real time data, its general expression is as follows:

dperr_p(m*Δt,M_gh)=w'(perr_p'(m*Δt,M_gh))(17)

dperr_j(m,M_gh)=w'(perr_j(Tn,M_gh))(18)

CSM_j(m,M_gh)=SB (m, M_gh)+dperr_j(m,M_gh)(19)

Wherein, w ' represents the decoding of LZW；dperr_p(m* Δ t, M_gh) represent mode M_ghUnder, the difference data in (m* Δ t) moment decoded p section and benchmark section；CSM_p(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in p bar section of (m* Δ t) moment reconstruct.

Example: the road traffic spatial data compression method of a kind of Based PC A and LZW coding, comprises the following steps:

1) based under same mode, spatially the highway traffic data of different sections of highway set up road traffic features reference sequences；Based PC A method, chooses the road traffic section set with dependency, and its process is as follows:

This test using section, 6, Beijing, weekend (18,19,25,26) same test point measured discharge data four day June in 2011 (sampling interval was for 2 minutes) as sample sequence, shown in road section information table 1.

Table 1

Extracting the road traffic historical data in 6 sections from reason traffic characteristic reference sequences, the collection data in every section are 720, and transform it into the matrix of s × r, and namely s is 6, r is 720, is designated as: A_sⅹr。

Matrix A_sⅹrThe average of jth row is:

$a_j=\frac{1}{s}\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{A}_{i,j}---\left(1\right)$

Based on a_j, it is thus achieved that A_sⅹrNormalization matrix SA_sⅹr:

${\mathrm{SA}}_{i,j}=(A_{i,j}-a_j){\left(\underset{i=1}{\overset{s}{\mathrm{\&Sigma;}}}{\left(A_{i,j}-a_j\right)}^2\right)}^{-\frac{1}{2}}---\left(2\right)$

The covariance matrix CSA of normalization matrix SA is:

$CSA=\frac{1}{s-1}({\mathrm{SA}}^T*SA)---\left(3\right)$

Obtain the eigenvalue D and characteristic vector V of covariance matrix CSA, then D=[λ₁,λ₂…λ_r]；λ₁≥λ₂≥…≥λ_r；Characteristic of correspondence vector is: V=[v₁,v₂…v_r]。

Choose λ₁, λ₂The projection matrix VA that characteristic of correspondence vector is constituted_r×2=[v₁,v₂], based on projection matrix and normalized training matrix, ask for A_sⅹrMain constituent matrix A PC_r×2:

APC_s×2=SA_sⅹr×VA_r×2(4)

Based on APC_s×2, two dimensional surface draws the distribution in s bar section, the distribution density of point represents corresponding road section strength of correlation.By correlation analysis, setting threshold value δ, select the dependency p+1 bar section more than δ, its process is as follows:

Wherein, i, j represents i-th respectively, j bar section, 0 < i < s, 0 < j < s；Represent relevance function；

2) selection reference section, and using its data as road traffic benchmark data spatially；Extract under same mode, the historical data in spatially other section, as training data, based on road traffic benchmark data under same mode, spatially, it is determined that the optimal threshold of space road traffic difference data, its process is as follows:

S_i(m*Δt,M_gh)=ST_i(m*Δt,M_gh)-SB(m*Δt,M_gh)(6)

e_i(m,M_gh)=[S_i(Δt,M_gh)S_i(2*Δt,M_gh)...S_i(m*Δt,M_gh)](7)

${\mathrm{he}}_i(m,M_{gh})=\left\{\begin{array}{cc}0,& e_i(m,M_{gh})<E_i(m,M_{gh})\\ e_i(m,M_{gh}),& e_i(m,M_{gh})>E_i(m,M_{gh})\end{array}\right.---\left(8\right)$

pe_i(n,M_gh)=w (he_i(m,M_gh))(9)

pe_i(n,M_gh)=[S_i'(1,M_gh)S_i'(2,M_gh)...S_i'(n,M_gh)](10)

Wherein, Δ t is the collection period of road traffic state data；(m* Δ t) is m-th road traffic state data collection cycle, and 0≤m≤N, N represents the quantity of the transport information gathered every day；I (1≤i≤p) represents i-th section；ST_i(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in (m* Δ t) moment i section；SB (m* Δ t, M_gh) represent mode M_ghUnder, the benchmark data in (m* Δ t) moment benchmark section；S_i(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the training data in (m* Δ t) moment i section and the benchmark data in benchmark section；e_i(m, M_gh) represent mode M_ghUnder, Δ t is to the difference data of the benchmark data in training data and the benchmark section in (m* Δ t) period i section；he_i(m, M_gh) represent mode M_ghUnder, Δ t process to (m* Δ t) period threshold after the difference data of benchmark data in training data and benchmark section in i section；E_i(m, M_gh) represent mode M_ghUnder, the threshold value chosen to (m* Δ t) period i section of Δ t；pe_i(n, M_gh) represent mode M_ghUnder, Δ t is to result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；S_i' (n, M_gh) for mode M_ghUnder, Δ t is to nth data in result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；M represents at mode M_ghUnder, Δ t is to the quantity in the i section before (m* Δ t) duration compression with the difference data in benchmark section；N represents at mode M_ghUnder, Δ t is to the road traffic quantity after (m* Δ t) duration compression；W represents that LZW encodes；Compression ratio is

3) data in spatially other section are extracted, as real time data；Mode M_ghUnder, based on road traffic benchmark data spatially, obtain road traffic difference data, its general expression is as follows:

MS_j(m*Δt,M_gh)=SM_j(m*Δt,M_gh)-SB(m*Δt,M_gh)(11)

err_j(m,M_gh)=[MS_j(Δt,M_gh)MS_j(2*Δt,M_gh)...MS_j(m*Δt,M_gh)](12)

Wherein, j (1≤i≤p) represents j-th strip section；SM_j(m* Δ t, M_gh) represent mode M_ghUnder, the real time data in (m* Δ t) moment j section；MS_j(m* Δ t, M_gh) for mode M_ghUnder, the difference data of the real time data in (m* Δ t) moment j section and the benchmark data in benchmark section；err_j(m, M_gh) for mode M_ghUnder, Δ t is to the difference data of the benchmark data in real time data and the benchmark section in (m* Δ t) period j section.

4) realize the compression of road traffic spatial data based on LZW coding, its process is as follows:

The optimal threshold that the difference data in i section with benchmark section is trained is incorporated into same mode M_gh, j section and benchmark section difference data in, encode in conjunction with LZW, it is achieved the compression of j section and benchmark section difference data, its general expression is as follows:

${\mathrm{herr}}_j(m*\mathrm{\&Delta;}t,M_{gh})=\left\{\begin{array}{cc}0,& {\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh})<E_{opt}\left(M_{gh}\right)\\ {\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh}),& {\mathrm{err}}_j(m,M_{gh})>E_{opt}\left(M_{gh}\right)\end{array}\right.---\left(13\right)$

herrs_p(m*Δt,M_gh)=[herr₁(m*Δt,M_gh)herr₂(Δt,M_gh)...herr_p'(m*Δt,M_gh)](14)

perr_p'(m*Δt,M_gh)=w (herrs_p(m*Δt,M_gh))(15)

perr_p'(m*Δt,M_gh)=[MS₁(m*Δt,M_gh)MS₂(m*Δt,M_gh)...MS_p'(m*Δt,M_gh)](16)

Wherein, E_opt(M_gh) represent the optimal threshold trained；herr_j(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the benchmark data in the real time data in j section and benchmark section after (m* Δ t) moment threshold process；M represents mode M_ghUnder, Δ t is to the quantity in j section before (m* Δ t) duration compression with the difference data in benchmark section；herrs_p(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of (m* Δ t) moment p bar section difference data；Perr_p’(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of difference data after the compression of (m* Δ t) moment p bar section；MS_j' (m* Δ t, M_gh) represent mode M_ghUnder, (the m* Δ t) moment, j section difference data compression after quantity；P ' represents the quantity after (m* Δ t) moment LZW coding；Compression ratio is:

5) based on LZW decoding technique, it is achieved road traffic spatial data reconstructs, and its process is as follows:

The difference data in p bar section Yu benchmark section being reconstructed, in conjunction with benchmark data, it is achieved the decompression of p bar section real time data, its general expression is as follows:

dperr_p(m*Δt,M_gh)=w'(perr_p'(m*Δt,M_gh))(17)

dperr_j(m,M_gh)=w'(perr_j(Tn,M_gh))(18)

CSM_j(m,M_gh)=SB (m, M_gh)+dperr_j(m,M_gh)(19)

Wherein, w ' represents the decoding of LZW；dperr_p(m* Δ t, M_gh) represent mode M_ghUnder, the difference data in (m* Δ t) moment decoded p section and benchmark section；CSM_p(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in p bar section of (m* Δ t) moment reconstruct.

6) parameter of the road traffic spatial data compression of Based PC A and LZW coding is determined

In the road traffic spatial data compression process of Based PC A and LZW coding, it is designed into following parameter: SB (m* Δ t), ST_i(m*Δt)、E_i(m* Δ t), per, err_i(m* Δ t), n, wherein, E_i(m* Δ t) can be obtained by SB (m) and per, n and err_i(m* Δ t) can by SB (m* Δ t), ST_i(m*Δt),E_i(m* Δ t) determines, the parameter setting done here is the general impact analysis to the road traffic spatial data compression encoded based on LZW.

Owing to the precision of algorithm is respectively arranged with impact by these parameters, individually analyze each parameter and the impact of arithmetic accuracy is not ensured that the optimum of algorithm, therefore should consider the impact that this highway traffic data is compressed by all parameters when carrying out Algorithm Analysis simultaneously.

Introduce compression alignment parameters the impact of arithmetic accuracy is analyzed:

${\mathrm{CR}}_p(m,M_{gh})=\frac{{\mathrm{CM}}_a(m,M_{gh})}{{\mathrm{CM}}_b(m,M_{gh})}---\left(20\right)$

Wherein, CR_p(m,M_gh) represent at mode M_ghUnder, Δ t is to the compression ratio in (m* Δ t) period p bar section；CM_a(m,M_gh) represent at mode M_ghUnder, Δ t to (m* Δ t) period p bar section compression before data amount check；CM_b(m,M_gh) be expressed as at mode M_ghUnder, Δ t to (m* Δ t) period p bar section compress after data amount check.

Namely for different (SB (m* Δ t, M_gh), ST_j(m* Δ t, M_gh), Per), there is corresponding CR_p(m,M_gh).Therefore there is following equation:

CR_p(m* Δ t, M_gh)=f (SB (m* Δ t, M_gh), ST_j(m* Δ t, M_gh), Per) (21)

I.e. f (SB (m* Δ t, M_gh), ST_j(m* Δ t, M_gh), Per) and CR_p(m* Δ t, M_gh) there is certain distribution relation f, find CR_p(m* Δ t, M_gh) maximum time corresponding (SB (m, M_gh), ST_j(m, M_gh), Per), it is optimized parameter and sets process.Therefore can obtain such as drag:

Minf (SB (m* Δ t, M_gh), ST_j(m* Δ t, M_gh), Per) (22)

$\begin{array}{cc}Where& {\mathrm{CR}}_p(m*\mathrm{\&Delta;}t,M_{gh})=\frac{{\mathrm{CM}}_a(m*\mathrm{\&Delta;}t,M_{gh})}{{\mathrm{CM}}_b(m*\mathrm{\&Delta;}t,M_{gh})}\end{array}$

Finally (SB (m* Δ t, M_gh), ST_j(m* Δ t, M_gh), Per) value can be determined by the training of road traffic benchmark data and training data.

7) experimental result

Based on road traffic space reference data and the training data of same mode, obtain optimized parameter (SB ((m* Δ t), ST_j(m), Per).This experimental result is compressed mainly for the car amount velocity amplitude in section.Extract road traffic space real time data, encode based on LZW, it is achieved the compression of road traffic space real time data.

Choose compression ratio (CR), absolute error (AE), to percentage error (marerr), error to standard deviation (σ) as the index of road traffic flow precision of prediction, CR is in the existing description of formula (20), and all the other computing formula are as follows respectively:

$AE=\frac{1}{p}\underset{p}{\mathrm{\&Sigma;}}|{\mathrm{CSM}}_p(m*\mathrm{\&Delta;}t,M_{gh})-{\mathrm{SM}}_p(m*\mathrm{\&Delta;}t,M_{gh})|---\left(23\right)$

$marerr=\frac{1}{p}\frac{\underset{p}{\mathrm{\&Sigma;}}|{\mathrm{CSM}}_p(m*\mathrm{\&Delta;}t,M_{gh})-{\mathrm{SM}}_p(m*\mathrm{\&Delta;}t,M_{gh})|}{{\mathrm{SM}}_p(m*\mathrm{\&Delta;}t,M_{gh})}---\left(24\right)$

$\mathrm{\&sigma;}=\sqrt{\frac{\underset{p}{\mathrm{\&Sigma;}}\left(y_p\right(m*\mathrm{\&Delta;}t,M_{gh})-\stackrel{\&OverBar;}{e_p}(m*\mathrm{\&Delta;}t,M_{gh}\left)\right)}{p-1}}---\left(25\right)$

Wherein

y_p(m*Δt,M_gh)=CSM_p(m*Δt,M_gh)-SM_p(m*Δt,M_gh)

$\stackrel{-}{e_p}(m*\mathrm{\&Delta;}t,M_{gh})=\frac{1}{p}\underset{p}{\mathrm{\&Sigma;}}{y}_p(m*\mathrm{\&Delta;}t,M_{gh})$

Wherein, y_p(m*Δt,M_gh) represent mode M_ghUnder, the error amount of real time data after (m* Δ t) moment p bar section real time data and reconstruct,For mean error.

Based on above analysis, it is known that the road traffic section with dependency is three sections of HI3009b, HI3008b and HI7058b.The data selecting these three sections are compressed research and the application of algorithm.

HI3009b, HI7058b section compression result statistical analysis such as table 2 below, shown in 3.

Date	18	19	25	26	average
						CR	11.80	10.91	11.08	9.00	10.70
AE	11.24	10.94	12.43	12.05	11.67
						marerr	12.42	12.54	12.78	13.87	12.90
σ	13.93	12.56	14.88	13.64	13.75

Table 2

Date	18	19	25	26	average
						CR	16.74	16.00	15.65	11.80	15.05
AE	6.65	6.93	6.83	7.41	6.96
						marerr	6.87	7.67	7.07	8.51	7.53
σ	8.65	9.33	8.87	9.79	9.16

Table 3.

Claims (2)

1. the road traffic spatial data compression method of a Based PC A and LZW coding, it is characterised in that: said method comprising the steps of:

1) based under same mode, spatially the highway traffic data of different sections of highway set up road traffic features reference sequences；Based PC A method, chooses the road traffic section set with dependency, and its process is as follows:

Extracting the road traffic historical data in s bar section from reason traffic characteristic reference sequences, the collection data in every section are r, and transform it into the matrix of s × r, are designated as: A_sⅹr；

Matrix A_sⅹrThe average of jth row is:

$a_j=\frac{1}{s}\underset{i=1}{\overset{s}{\&Sigma;}}{A}_{i,j}---\left(1\right)$

Based on a_j, it is thus achieved that A_sⅹrNormalization matrix SA_sⅹr:

${\mathrm{SA}}_{i,j}=(A_{i,j}-a_j){\left(\underset{i=1}{\overset{s}{\&Sigma;}}{\left(A_{i,j}-a_j\right)}^2\right)}^{-\frac{1}{2}}---\left(2\right)$

The covariance matrix CSA of normalization matrix SA is:

$CSA=\frac{1}{s-1}({\mathrm{SA}}^T*SA)---\left(3\right)$

Obtain the eigenvalue D and characteristic vector V of covariance matrix CSA, then D=[λ₁,λ₂…λ_r]；λ₁≥λ₂≥…≥λ_r；Characteristic of correspondence vector is: V=[v₁,v₂…v_r]；

Choose λ₁, λ₂The projection matrix VA that characteristic of correspondence vector is constituted_r×2=[v₁,v₂], based on projection matrix and normalized training matrix, ask for A_sⅹrMain constituent matrix A PC_r×2:

APC_s×2=SA_sⅹr×VA_r×2(4)

Based on APC_s×2, two dimensional surface draws the distribution in s bar section, the distribution density of point represents corresponding road section strength of correlation, by correlation analysis, sets threshold value δ, selects the dependency p+1 bar section more than δ, and its process is as follows:

Wherein, i, j represents i-th respectively, j bar section, 0 < i < s, 0 < j < s；Represent relevance function；

2) selection reference section, and using its data as road traffic benchmark data spatially；Extract under same mode, the historical data in spatially other section, as training data, based on road traffic benchmark data under same mode, spatially, it is determined that the optimal threshold of space road traffic difference data, its process is as follows:

S_i(m*Δt,M_gh)=ST_i(m*Δt,M_gh)-SB(m*Δt,M_gh)(6)

e_i(m,M_gh)=[S_i(Δt,M_gh)S_i(2*Δt,M_gh)...S_i(m*Δt,M_gh)](7)

${\mathrm{he}}_i(m,M_{gh})=\left\{\begin{array}{cc}0,& e_i(m,M_{gh})<E_i(m,M_{gh})\\ e_i(m,M_{gh}),& e_i(m,M_{gh})>E_i(m,M_{gh})\end{array}\right.---\left(8\right)$

pe_i(n,M_gh)=w (he_i(m,M_gh))(9)

pe_i(n,M_gh)=[S_i'(1,M_gh)S_i'(2,M_gh)...S_i'(n,M_gh)](10)

Wherein, Δ t is the collection period of road traffic state data；(m* Δ t) is m-th road traffic state data collection cycle, and 0≤m≤N, N represents the quantity of the transport information gathered every day；I (1≤i≤p) represents i-th section；ST_i(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in (m* Δ t) moment i section；SB (m* Δ t, M_gh) represent mode M_ghUnder, the benchmark data in (m* Δ t) moment benchmark section；S_i(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the training data in (m* Δ t) moment i section and the benchmark data in benchmark section；e_i(m, M_gh) represent mode M_ghUnder, Δ t is to the difference data of the benchmark data in training data and the benchmark section in (m* Δ t) period i section；he_i(m, M_gh) represent mode M_ghUnder, Δ t process to (m* Δ t) period threshold after the difference data of benchmark data in training data and benchmark section in i section；E_i(m, M_gh) represent mode M_ghUnder, the threshold value chosen to (m* Δ t) period i section of Δ t；pe_i(n, M_gh) represent mode M_ghUnder, Δ t is to result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；S_i' (n, M_gh) for mode M_ghUnder, Δ t is to nth data in result after LZW encodes of the difference data in (m* Δ t) period i section and benchmark section；M represents at mode M_ghUnder, Δ t is to the quantity in the i section before (m* Δ t) duration compression with the difference data in benchmark section；N represents at mode M_ghUnder, Δ t is to the road traffic quantity after (m* Δ t) duration compression；W represents that LZW encodes；Compression ratio is

3) data in spatially other section are extracted, as real time data；Mode M_ghUnder, based on road traffic benchmark data spatially, obtain road traffic difference data, its general expression is as follows:

MS_j(m*Δt,M_gh)=SM_j(m*Δt,M_gh)-SB(m*Δt,M_gh)(11)

err_j(m,M_gh)=[MS_j(Δt,M_gh)MS_j(2*Δt,M_gh)...MS_j(m*Δt,M_gh)](12)

Wherein, j (1≤i≤p) represents j-th strip section；SM_j(m* Δ t, M_gh) represent mode M_ghUnder, the real time data in (m* Δ t) moment j section；MS_j(m* Δ t, M_gh) for mode M_ghUnder, the difference data of the real time data in (m* Δ t) moment j section and the benchmark data in benchmark section；err_j(m, M_gh) for mode M_ghUnder, Δ t is to the difference data of the benchmark data in real time data and the benchmark section in (m* Δ t) period j section；

4) realize the compression of road traffic spatial data based on LZW coding, its process is as follows:

The optimal threshold that the difference data in i section with benchmark section is trained is incorporated into same mode M_gh, j section and benchmark section difference data in, encode in conjunction with LZW, it is achieved the compression of j section and benchmark section difference data, its general expression is as follows:

${\mathrm{herr}}_j(m*\mathrm{\&Delta;}t,M_{gh})=\left\{\begin{array}{c}0,{\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh})<E_{opt}\left(M_{gh}\right)\\ {\mathrm{err}}_j(m*\mathrm{\&Delta;}t,M_{gh}),{\mathrm{err}}_j(m,M_{gh})>E_{opt}\left(M_{gh}\right)\end{array}\right.---\left(13\right)$

herrs_p(m*Δt,M_gh)=[herr₁(m*Δt,M_gh)herr₂(Δt,M_gh)...herr_p'(m*Δt,M_gh)](14)

perr_p'(m*Δt,M_gh)=w (herrs_p(m*Δt,M_gh))(15)

perr_p'(m*Δt,M_gh)=[MS₁(m*Δt,M_gh)MS₂(m*Δt,M_gh)...MS_p'(m*Δt,M_gh)](16)

Wherein, E_opt(M_gh) represent the optimal threshold trained；herr_j(m* Δ t, M_gh) represent mode M_ghUnder, the difference data of the benchmark data in the real time data in j section and benchmark section after (m* Δ t) moment threshold process；M represents mode M_ghUnder, Δ t is to the quantity in j section before (m* Δ t) duration compression with the difference data in benchmark section；herrs_p(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of (m* Δ t) moment p bar section difference data；Perr_p’(m*Δt,M_gh) represent mode M_ghUnder, the magnitude-set of difference data after the compression of (m* Δ t) moment p bar section；MS_j' (m* Δ t, M_gh) represent mode M_ghUnder, (the m* Δ t) moment, j section difference data compression after quantity；P ' represents the quantity after (m* Δ t) moment LZW coding；Compression ratio is:

2. the road traffic spatial data compression method of Based PC A and LZW coding as claimed in claim 1, it is characterised in that: described compression method also comprises the steps:

5) based on LZW decoding technique, it is achieved road traffic spatial data reconstructs, and its process is as follows:

The difference data in p bar section Yu benchmark section being reconstructed, in conjunction with benchmark data, it is achieved the decompression of p bar section real time data, its general expression is as follows:

dperr_p(m*Δt,M_gh)=w'(perr_p'(m*Δt,M_gh))(17)

dperr_j(m,M_gh)=w'(perr_j(Tn,M_gh))(18)

CSM_j(m,M_gh)=SB (m, M_gh)+dperr_j(m,M_gh)(19)

Wherein, w ' represents the decoding of LZW；dperr_p(m* Δ t, M_gh) represent mode M_ghUnder, the difference data in (m* Δ t) moment decoded p section and benchmark section；CSM_p(m* Δ t, M_gh) represent mode M_ghUnder, the highway traffic data in p bar section of (m* Δ t) moment reconstruct.