CN117273287B - Tensor-matrix coupling-based subway passenger flow prediction method - Google Patents
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Abstract
The invention discloses a subway passenger flow prediction method based on tensor-matrix coupling, which belongs to the field of traffic prediction and comprises the following steps: step 1, obtaining subway passenger flow data, interest point data and weather condition data; step 2, constructing a subway passenger flow prediction model based on tensor-matrix coupling decomposition; and step 3, solving an optimization model by adopting an alternate direction multiplier method to obtain a subway passenger flow prediction value in a certain time interval in the future. According to the method, the subway passenger flow matrix data are expanded into the third-order subway passenger flow tensor by introducing the time dimension, the weather feature matrix and the interest point matrix are used as auxiliary information, the calculation complexity of the prediction model is reduced, and the accuracy of the subway passenger flow prediction result is improved.
Description
Technical Field
The invention belongs to the field of traffic prediction, and particularly relates to a subway passenger flow prediction method based on tensor-matrix coupling.
Background
With rapid construction and development of cities, urban traffic travel is receiving more and more attention. The subway is an important component of urban rail transit and is also a green travel tool. OD pair (origin-destination pairs) data, namely passenger flow between any two stations of the subway, can be extracted from subway IC card data, and a data base is provided for subway bidirectional passenger flow prediction.
Synchronous prediction of passenger flow between any two stations of a subway is a challenging task, and the existing research mainly applies a method combining matrix decomposition and a neural network model to predict based on the passenger flow matrix. The linear relation between the time series data can be mined by adopting a method of high-order weighted dynamic modal decomposition based on matrix decomposition and the like; the space-time correlation between subway passenger flow matrix data can be mined by combining a subway system modeling into a directed graph into a graph rolling gate control loop unit (GCGRU).
However, the existing subway passenger flow volume prediction method has the following problems: space-time characteristics and correlation excavation among subway flow data are insufficient; the information of multi-source influence factors which have obvious influence on subway passenger flow, such as weather characteristics, urban functional area distribution and the like, is underutilized; the combined prediction model based on the neural network has high computational complexity.
Disclosure of Invention
In order to solve the problems of insufficient space-time characteristic mining, insufficient multi-source influence factor information utilization and high model calculation complexity of the existing prediction method between subway traffic data, the invention provides a subway passenger flow prediction method based on tensor-matrix coupling, which expands subway passenger flow matrix data into three-order subway passenger flow tensors by introducing time dimension, takes a weather characteristic matrix and an interest point matrix as auxiliary information, reduces calculation complexity of a prediction model and improves accuracy of subway passenger flow prediction results.
The technical scheme of the invention is as follows:
a subway passenger flow prediction method based on tensor-matrix coupling comprises the following steps:
step 1, obtaining subway passenger flow data, interest point data and weather condition data;
step 2, constructing a subway passenger flow prediction model based on tensor-matrix coupling decomposition;
and step 3, solving an optimization model by adopting an alternate direction multiplier method to obtain a subway passenger flow prediction value in a certain time interval in the future.
Further, in the step 1, passenger flow data between different subway stations is extracted according to the passenger ticket number, the transaction time, the transaction station and the transaction type information contained in the subway card swiping data, and the obtained subway passenger flow data is defined as a subway passenger flow matrix sequenceWherein->Is a time interval->The number of subway stations; />Elements of (a)Indicate->The time interval is from->Subway station to the->Passenger flow volume of individual subway stations; setting a diagonal element of the subway passenger flow matrix to 0;
capturing data of different interest points within a kilometer range of a subway station from a Goldmap APP by using a web crawler technology, and defining the obtained interest point data as an interest point matrixWherein->The number of the types of the interest points; />Element->Indicate->Surrounding of subway station->The number of seed points of interest; the interest points comprise schools, hospitals, malls, office buildings and residential areas;
capturing weather condition data on a weather website by using web crawler technology, and defining the weather condition data as a weather feature matrixWherein->For the time dimension +.>The number of weather condition types; />Is a binary indication matrix, wherein the elements are represented by the following formula:
(1)；
wherein,indicate->First->Weather conditions.
Further, in the step 1, the subway passenger flow volume matrix is sequencedIntroducing a time dimension->And expands to third-order subway passenger flow tensor +.>Wherein->，/>Days.
Further, the specific process of constructing the subway passenger flow volume prediction model based on tensor-matrix coupling decomposition in the step 2 is as follows:
step 2.1, tensor of third-order subway passenger flow volumeDecomposition into three rank-one tensor sums using tensor decomposition algorithm, denoted +.>Wherein->、/>、/>Are allFactor matrix of->Is the rank of tensor decomposition algorithm decomposition, +.>Representing an outer product operation; tensor->The matrix developed along the first mode is +.>The expression decomposed by tensor decomposition algorithm at this time is reduced to +.>Wherein the symbol->Is Khatri-Rao product, < >>Transpose the symbol;
step 2.2, the interest point matrixDecomposing into a matrix of two small dimensions using a matrix decomposition algorithm, denoted +.>Wherein->、/>All are->Is a factor matrix of (2);
step 2.3, weather feature matrixDecomposition into +.>Wherein->、/>All are->Is a factor matrix of (2);
step 2.4, coupling the interest point matrix, the weather feature matrix and the subway passenger flow tensor in the subway station dimension and the time dimension respectively, and sharing the corresponding factor matrix during decomposition, namely、/>The following are all->、/>A representation; thus, the objective function of the subway passenger flow prediction model based on tensor-matrix coupling decomposition is expressed as:
(2)；
wherein,representing a square error between an initial subway passenger flow tensor and a reconstruction tensor obtained by decomposing by a tensor decomposition algorithm; />Representing the square error between the initial interest point matrix and the reconstruction matrix obtained by decomposition of the tensor decomposition algorithm; />Representing the square error between the initial weather feature matrix and the reconstruction matrix obtained by decomposing the tensor decomposition algorithm;
step 2.5, adding regularization term into the objective function, and optimizing a subway passenger flow prediction model based on tensor-matrix coupling decomposition as follows:
(3)；
wherein,representing a set of factor matrices; />、/>、/>Are regularization parameters.
Further, the specific process of the step 3 is as follows: according to the pair of the formulas (4) and (8)、/>、/>、/>、/>The five factor matrixes are updated and iterated until the set maximum iteration times are reached, and the factor matrixes are obtained>、/>、/>Is the optimal solution of (a); finally, by the calculation formula->Obtaining tensor after completing the missing data, namely obtaining a certain time interval +.>A predicted value of subway passenger flow volume in the subway;
(4)；
(5)；
(6)；
(7)；
(8)；
wherein,is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a unit matrix; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration;is a factor matrix->First->A value after the second iteration; />Is tensor->A matrix that expands along a second mode; />Is a factor matrix->First->A value after the second iteration; />Is tensor->A matrix that expands along the third mode.
The beneficial technical effects brought by the invention are as follows: aiming at the problem that the current prediction method is insufficient in mining the space-time characteristics and the relevance thereof between the subway passenger flow data, the method comprises the steps of expanding subway passenger flow matrix data into third-order subway passenger flow tensors by introducing time dimension, and mining the space-time characteristics and the relevance thereof between the data by adopting a tensor decomposition method; aiming at the problem that the current prediction method is insufficient in utilization of influence factor information, a data mining method is adopted to generate a weather feature matrix and an interest point matrix optimized prediction model; aiming at the problem of high calculation complexity of the traditional combined prediction model based on the neural network, the weather feature matrix, the interest point matrix and the subway passenger flow tensor are respectively coupled in the time dimension and the subway station dimension, the same factor matrix is shared in the model decomposition process, the calculation of the factor matrix is reduced, and the calculation complexity of the model is reduced.
Drawings
Fig. 1 is a schematic diagram of a method for predicting subway passenger flow based on tensor-matrix coupling.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and detailed description:
the subway passenger flow data has strong daily similarity and weekly similarity in the time dimension, has strong correlation with the space position of a subway station in the space dimension, and has strong time-space correlation. The tensor method can express potential information of each module after tensor decomposition while preserving the multidimensional property of the data, and excavates space-time characteristics and relevance among the data.
Weather factors, geographical environments around subway stations and urban functional area distribution have close relations with passenger flow modes of subway stations. Based on the point of interest type, the weather feature matrix is generated by adopting weather conditions such as sunny weather, rainy weather, cloudy weather and the like, and the interest point matrix is constructed as auxiliary information based on the urban interest point types such as schools, hospitals, office buildings and residential areas.
On the basis of tensor decomposition and matrix decomposition, the subway passenger flow tensor, the weather feature matrix and the interest point matrix share the same factor matrix in corresponding dimensions to be coupled, so that the calculation of the factor matrix is reduced, and the complexity of model calculation is reduced;
as shown in fig. 1, a subway passenger flow volume prediction method based on tensor-matrix coupling includes the following steps:
and step 1, acquiring subway passenger flow data, interest point data and weather condition data.
Passenger ticket number, transaction time, transaction site, transaction type (inbound and outbound) and other information contained in subway card swiping data are used for extracting passenger flow data (the data of the invention are from Qingdao subway group Limited company) among different subway sites, and the obtained subway passenger flow data are defined as a subway passenger flow matrix sequenceWherein->Is a time interval->The number of subway stations; />Element->Indicate->The time interval is from->Subway station to the->Passenger flow volume of individual subway stations; and setting the diagonal line element of the subway passenger flow matrix to 0.
Introducing subway passenger flow matrix sequences into a time dimensionAnd expands to third-order subway passenger flow tensorWherein->，/>Days. Due to time interval only->The real passenger flow matrix in the time interval can be obtained after all passengers in the subway passenger train arrive at the destination, and the historical average passenger flow matrix is adopted to replace the incomplete subway passenger flow matrix。
Capturing data of different interest points within a kilometer range of a subway station from a Goldmap APP by using a web crawler technology, and defining the obtained interest point data as an interest point matrixWherein->For the number of kinds of interest points, the interest points include schools, hospitals, malls, office buildings, residential areas and the like. />Element->Indicate->Surrounding of subway station->The number of points of interest.
Capturing weather condition data on a weather website (China weather exchange) by using web crawler technology, and defining the weather condition data as a weather feature matrixWherein->The number of weather conditions includes sunny weather conditions, rainy weather conditions, snowy weather conditions, cloudy weather conditions and the like. Matrix->Is a binary indication matrix, wherein the elements are represented by the following formula:
(1)；
wherein,indicate->First->Weather conditions.
And 2, constructing a subway passenger flow prediction model based on tensor-matrix coupling decomposition.
Basic principle of model construction: the main body information tensor and the auxiliary information matrix are coupled in the same dimension, and share the corresponding factor matrix, so that the auxiliary information is fully utilized, the calculation complexity of the model is reduced, and the prediction accuracy of the model is improved. The subway passenger flow data prediction model is used for decomposing the tensor and the matrix into a plurality of factor matrixes and updating the factor matrixes by setting the predicted value as the missing value, and the optimal factor matrix obtained after updating is used for inner product reconstruction tensor to complement missing data in the original tensor, so that subway passenger flow prediction is completed.
Tensor of third-order subway passenger flow volumeDecomposition into three rank-one tensor sums using tensor decomposition algorithm, denoted +.>Wherein->、/>、/>All are->Factor matrix of->Is the rank of tensor decomposition algorithm decomposition, +.>Representing an outer product operation. Tensor->The matrix developed along the first mode is +.>The expression decomposed by tensor decomposition algorithm at this time is reduced to +.>Wherein the symbol->Is the product of Khatri-Rao.
Matrix the interest pointsDecomposition into two smaller dimensional matrices using matrix decomposition algorithms, denoted asWherein->、/>All are->Is a factor matrix of (2);
matrix weather characteristicsDecomposition into +.>Wherein、/>All are->Is a factor matrix of (a) in the matrix.
Coupling the interest point matrix, the weather feature matrix and the subway passenger flow tensor in the subway station dimension and the time dimension respectively, and sharing the corresponding factor matrix during decomposition, namely、/>The following are all->、/>And (3) representing. Thus, the objective function of the subway passenger flow prediction model based on tensor-matrix coupling decomposition can be expressed as:
(2)；
wherein,representing a square error between an initial subway passenger flow tensor and a reconstruction tensor obtained by decomposing by a tensor decomposition algorithm; />Representing the square error between the initial interest point matrix and the reconstruction matrix obtained by decomposition of the tensor decomposition algorithm; />And (5) representing the square error between the initial weather feature matrix and the reconstruction matrix obtained by decomposing the tensor decomposition algorithm.
The smaller the sum of the errors represented by the objective function, the better the complement of the missing data in the original tensor is represented. To prevent overfitting, regularization terms are added to the objective function. Therefore, the subway passenger flow prediction model based on tensor-matrix coupling decomposition can be optimized as follows:
(3)；
wherein,representing a set of factor matrices; />、/>、/>Are regularization parameters.
The model converts the subway passenger flow prediction problem into an optimization problem of an objective function.
And step 3, solving an optimization model by adopting an alternate direction multiplier method to obtain a subway passenger flow prediction value in a certain time interval in the future.
The least squares (ALS) and gradient descent methods are most commonly used in current research to solve the optimization problem, but matrix decomposition and tensor decomposition are non-convex, and these commonly used methods cannot obtain a globally optimal solution for the objective function. Therefore, the invention contemplates the use of the alternate direction multiplier ADMM to solve the optimization model. The method combines the advantages of dual decomposition and Lagrange multiplier method to decompose a large global problem into a plurality of smaller and simpler local sub-problems to be solved respectively, so as to obtain a global optimal solution.
The specific process for solving the optimization model by the alternate direction multiplier method is as follows:
according to the pair of the formulas (4) and (8)、/>、/>、/>、/>The five factor matrixes are updated and iterated until the set maximum iteration times are reached, and the factor matrixes are obtained>、/>、/>Is the optimal solution of (a); finally, through a calculation formulaObtaining tensor after completing the missing data, namely obtaining a certain time interval +.>A predicted value of subway passenger flow volume in the subway;
(4)；
(5)；
(6)；
(7)；
(8)；
wherein,is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is of size +.>Is a matrix of units of (a); />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is tensor->A matrix that expands along a second mode; />Is a factor matrix->First->A value after the second iteration; />Is tensor->A matrix that expands along the third mode.
To demonstrate the feasibility of the invention, a partial data presentation is given:
the subway passenger flow matrix obtained in the step 1 is shown in table 1:
TABLE 1 subway passenger flow matrix
。
The interest point matrix obtained in step 1 is shown in table 2:
TABLE 2 Point of interest matrix
。
The weather feature matrix obtained in step 1 is shown in table 3:
TABLE 3 Point of interest data matrix
。
The subway passenger flow prediction value in a future time interval is obtained through the tensor-matrix coupling decomposition subway passenger flow prediction model constructed in the step 2 and the optimal solving process in the step 3 and is shown in the table 4:
TABLE 4 subway passenger flow volume predictive value matrix
。
By comparing the predicted value in the table 4 with the actual value in the table 1, the prediction method provided by the invention can capture the passenger flow law among all subway stations and has higher accuracy.
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (1)
1. A subway passenger flow volume prediction method based on tensor-matrix coupling is characterized by comprising the following steps:
step 1, obtaining subway passenger flow data, interest point data and weather condition data;
step 2, constructing a subway passenger flow prediction model based on tensor-matrix coupling decomposition;
step 3, solving an optimization model by adopting an alternate direction multiplier method to obtain a subway passenger flow prediction value in a certain time interval in the future;
in the step 1, passenger flow data among different subway stations are extracted according to passenger ticket card numbers, transaction time, transaction stations and transaction type information contained in subway card swiping data, and the obtained subway passenger flow data are defined as a subway passenger flow matrix sequenceWherein->Is a time interval->The number of subway stations; />Element->Indicate->The time interval is from->Subway station to the->Passenger flow volume of individual subway stations; setting a diagonal element of the subway passenger flow matrix to 0;
capturing data of different interest points within a kilometer range of a subway station from a Goldmap APP by using a web crawler technology, and defining the obtained interest point data as an interest point matrixWherein->The number of the types of the interest points; />Element->Indicate->Surrounding of subway station->The number of seed points of interest; the interest points comprise schools, hospitals, malls, office buildings and residential areas;
capturing weather condition data on a weather website by using web crawler technology, and defining the weather condition data as a weather feature matrixWherein->For the time dimension +.>The number of weather condition types; />Is a binaryAn indication matrix, wherein the elements are represented by the formula:
(1)；
wherein,indicate->First->Planting weather conditions;
in the step 1, subway passenger flow matrix sequencesIntroducing a time dimension->And expands to third-order subway passenger flow tensor +.>Wherein->，/>Days;
the specific process of constructing the subway passenger flow prediction model based on tensor-matrix coupling decomposition in the step 2 is as follows:
step 2.1, tensor of third-order subway passenger flow volumeDecomposition into three rank-one tensor sums using tensor decomposition algorithm, denoted +.>Wherein->、/>、/>All are->Factor matrix of->Is the rank of tensor decomposition algorithm decomposition, +.>Representing an outer product operation; tensor->The matrix developed along the first mode isThe expression decomposed by tensor decomposition algorithm at this time is reduced to +.>Wherein the symbol->Is Khatri-Rao product, < >>Transpose the symbol;
step 2.2, the interest point matrixDecomposing into a matrix of two small dimensions using a matrix decomposition algorithm, denoted +.>Wherein->、/>All are->Is a factor matrix of (2);
step 2.3, weather feature matrixDecomposition into +.>Wherein、/>All are->Is a factor matrix of (2);
step 2.4, coupling the interest point matrix, the weather feature matrix and the subway passenger flow tensor in the subway station dimension and the time dimension respectively, and sharing the corresponding factor matrix during decomposition, namely、/>The following are all->、/>A representation; thus, the objective function of the subway passenger flow prediction model based on tensor-matrix coupling decomposition is expressed as:
(2)；
wherein,representing a square error between an initial subway passenger flow tensor and a reconstruction tensor obtained by decomposing by a tensor decomposition algorithm; />Representing the square error between the initial interest point matrix and the reconstruction matrix obtained by decomposition of the tensor decomposition algorithm; />Representing the square error between the initial weather feature matrix and the reconstruction matrix obtained by decomposing the tensor decomposition algorithm;
step 2.5, adding regularization term into the objective function, and optimizing a subway passenger flow prediction model based on tensor-matrix coupling decomposition as follows:
(3)；
wherein,representing a set of factor matrices; />、/>、/>Are regularization parameters;
the specific process of the step 3 is as follows: according to the pair of the formulas (4) and (8)、/>、/>、/>、/>The five factor matrixes are updated and iterated until the set maximum iteration times are reached, and the factor matrixes are obtained>、/>、/>Is the optimal solution of (a); finally, by the calculation formula->Obtaining tensor after completing the missing data, namely obtaining a certain time interval +.>A predicted value of subway passenger flow volume in the subway;
(4)；
(5)；
(6)；
(7)；
(8)；
wherein,is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration;is a unit matrix; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is a factor matrix->First->A value after the second iteration; />Is tensor->A matrix that expands along a second mode; />Is a factor matrix->First->A value after the second iteration; />Is tensor->A matrix that expands along the third mode.
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