JP5198994B2 - Time required prediction system, method and program - Google Patents

Description

  The present invention relates to a system, a method, and a program for predicting a time required for traveling on a route on a traffic route with a vehicle or the like.

  In recent years, traffic prediction has become an important issue in urban planning. The so-called Intelligent Transportation System has been actively researched, especially since the late 1990s.

  In this case, one problem is to systematically estimate the required time along a certain route. This is because it is desirable to be able to predict the approximate required time between arbitrary routes for security, convenience, and other reasons.

  As a conventional technique, the technique described in Japanese Patent Application Laid-Open No. 11-306480 creates a reference file for creating a reference travel time for each unit section of a target section from expressway ticket data, and this created reference It is disclosed that similar reference travel times for the past several days are extracted from travel time, the parameters of a statistical model are estimated, and the travel time of the day is predicted using the estimated parameters.

  On the other hand, as more recent documents, Japanese Patent Application Laid-Open No. 2003-272084, “T. Nakata and J. Takeuchi, Mining traffic data from probe-car system for travel time prediction. In Proc. ACM SIGKDD Intl. Conf. Knowledge Discovery and Data mining, pages 817-822, 2004 "describe a time prediction system based on a time series model based on an autoregressive model.

  However, in order to estimate the autoregressive model accurately, a sufficiently large number of samples are necessary. Therefore, the target of time required for prediction is limited to highways, highways, and avenues where many samples are easily obtained. It was.

  On the other hand, when trying to realize a high-accuracy road traffic system linked to a car navigation system, the conventional technology that requires many samples to obtain a predetermined accuracy would deviate from highways, main roads, and main streets. If a car enters an exit or side street, it is difficult to collect a large number of samples related to such exits and side streets in advance. It was difficult to predict.

Japanese Patent Laid-Open No. 11-306480 JP 2003-272084 A T. Nakata and J. Takeuchi, Mining traffic data from probe-car system for travel time prediction. In Proc. ACM SIGKDD Intl. Conf. Knowledge Discovery and Data mining, pages 817-822, 2004

  An object of the present invention is to provide a technique that enables a required time to be accurately predicted even on a relatively poor street of past travel history based on data of a required time of a route recorded in advance.

  As a result of studying the above as a problem to be solved, the present inventor has come up with the following technique.

  First, as a premise of the present invention, an intersection that may pass and a main point of the road are marked as nodes, and a character string is given as a label to a link connecting the nodes. The character string as a label is preferably unique for each link, but a non-unique label can also be used. For example, labels in which directions such as “north”, “south”, and “north-northwest” are encoded can be used. More generally, an integer represented by 8 bytes is sufficient. By doing so, the learning route recorded in the past is expressed as a sequence of character strings.

  On the other hand, a given route for which the required time is to be predicted is similarly expressed as a sequence of character strings.

  When a path is represented by a sequence of character strings in this way, a similarity measure called a character string kernel method can be used. The character string kernel is a similarity measure developed for the purpose of comparing DNA sequences and the like in the field of bioinformatics (computational biology), and its effectiveness is known for tasks such as classification. A preferred string kernel method is the p-spectrum kernel method.

  According to the present invention, route information recorded in the past is automatically weighted based on the degree of similarity automatically by computer processing using a technique called Gaussian process regression. Then, the time required for the given route is predicted probabilistically using the weighting information.

  As described above, according to the present invention, it is possible to predict the required time stochastically by Gaussian process regression by weighting with a value obtained by applying the string kernel method to the path. Due to the parameter approaching nature of the process regression, it is possible to provide a relatively accurate prediction of the required time even for a nearby route with few samples. The application of Gaussian process regression also provides a natural variance of the required time prediction.

  Embodiments of the present invention will be described below with reference to the drawings. It should be understood that these examples are for the purpose of illustrating preferred embodiments of the invention and are not intended to limit the scope of the invention to what is shown here. Further, throughout the following drawings, the same reference numerals denote the same objects unless otherwise specified.

  Referring to FIG. 1, there is shown a block diagram of computer hardware for realizing a system configuration and processing according to an embodiment of the present invention. In FIG. 1, a CPU 104, a main memory (RAM) 106, a hard disk drive (HDD) 108, a keyboard 110, a mouse 112, and a display 114 are connected to the system bus 102. The CPU 104 is preferably based on a 32-bit or 64-bit architecture, such as Intel Pentium (trademark) 4, Intel Core (trademark) 2 DUO, AMD Athlon (trademark), etc. Can be used. The main memory 104 preferably has a capacity of 512 KB or more, more preferably a capacity of 1 GB or more.

  Although not shown individually, the hard disk drive 108 is pre-measured or prepared, which will be described later in connection with the operating system and the processing program, map information, map display program, and FIGS. The route and its time information are stored. The operating system may be any compatible with the CPU 104, such as Linux (trademark), Microsoft Windows Vista, Windows XP (trademark), Windows (trademark) 2000, Apple Mac OS (trademark).

  The keyboard 110 and the mouse 112 are used to operate graphic objects such as icons, taskbars, and windows displayed on the display 114 in accordance with a graphic user interface provided by the operating system. The keyboard 110 and the mouse 112 are also used to perform a route instruction operation on a map, which will be described later, and an operation to start or end a required time prediction program.

  The display 114 is preferably, but is not limited to, a 32-bit true color LCD monitor with a resolution of 1024 × 768 or higher. The display 114 is used to display a map including a route for predicting the required time.

  The hard disk drive 108 further stores a program for performing calculation processing according to the present invention described later. This program can be written in any existing programming language such as C ++, C #, Java ™. When using Windows Vista, Windows XP (trademark), Windows (trademark) 2000, or the like as an operating system, it can be implemented as an application program including a GUI by using the function of the Win32 API.

  Furthermore, a tablet 118 is connected to the bus 102 through the USB interface 116 for inputting a route on which the required time is to be predicted on the display 114. The tablet 118 is not limited to this, but may be implemented, for example, by a technique described in Japanese Patent Laid-Open No. 2001-273089. In short, it has an interface in which a locus traced with a tablet with an input pen can be taken into the computer body as coordinates.

  Although not shown in the figure, the system of FIG. 1 is connected to a network by a protocol such as TCP / IP, and through this network, map information, a map display program, a previously measured or prepared route and its time information, etc. You may make it acquire.

Figure 2 is a path x of the measurement of the advance time required in a particular region ^{(1), x (2)} , ..., x (i), ..., indicate the x ^(N). For convenience, only x ⁽¹⁾ , x ^(i), and x ^(N) are shown in FIG. These routes are routes in which the driver has traveled by car from the starting point to the destination while maintaining the legal speed as much as possible. At that time, to measure the time required, for example, the time required for the path x ^(i), is recorded as y ^(i).

  It is better to have more information about the driving route and time in advance, and it is better to run without hesitation. There is a limit to keeping it.

  The actual route can be measured systematically using the GPS mounted on the traveling vehicle. That is, when the GPS indicates that the car is approaching the position registered as a node by the map information, the system records the position. When a plurality of positions recorded in this way are connected, a route is determined. A character string is assigned to a link from one position to the next by an appropriate algorithm.

  Alternatively, in addition to actually driving by car, it is also possible to estimate and record the required time along a certain route using distance on the map, legal speed, and other empirical values.

FIG. 3 shows an enlarged part of a certain dimension travel route x ⁽ⁱ⁾ . That is, in order to apply the present invention, a symbol P _j-1 as a node at a key point (intersection, T-junction, or other main point on a road) in a map corresponding to a specific region, P _j , P _{j + 1} , ... are assigned in advance. Such node information on the map is not limited to this, but for example,
It can be obtained by using the electronic map shown at http://www.gsi.go.jp/MAP/CD-ROM/2500/t2500.htm.

  In FIG. 3, the road is indicated by a region with a pattern, and the route actually traveled is indicated by a solid line.

  As shown in FIG. 3, the route is composed of a collection of links as roads connecting the nodes. Thus, according to the present invention, a label or a character string is assigned to each such link.

  The label or character string is preferably a long 8-byte integer. For example, a character string such as 10150600. However, the present invention is not limited to this, and may be a random character string such as A53wKz9s that is a mixture of letters and numbers.

  Since an ID is given to each node, a character string to be assigned to a link can be generated using such an ID.

  Alternatively, a randomly generated unique character string may be sequentially assigned to the link.

In FIG. 3, nodes on the map indicate P _j−1 , P _j , P _{j + 1} , P _{j + 2} , P _{j + 3,} etc.
L _m , L _{m + 1} , L _{m + 2} , L _{m + 3, and the} like are character strings as labels attached to links that connect these nodes. With such a label, the path is a string of strings, such as path x ⁽ⁱ⁾ = (..., L _m , L _{m + 1} , L _{m + 2} , L _{m + 3} , ..) It can be expressed as a line. It is desirable that such a character string be unique throughout the map. For example, the character string can be determined by using the direction of the link connecting the nodes (eg, south-southwest, north-northwest, angle to latitude). The string is not necessarily unique throughout the map, but can still be used in the present invention.

  FIG. 4 is a path x that is input from the tablet 118 shown in FIG. For this input, for example, a map is displayed on the display 114, and the route is indicated by a solid line of a predetermined color on the map displayed on the display 114 as the operator operates the input pen on the tablet 118. It is to be understood that any interface known to those skilled in the art, such as operation with the mouse 112, may be used, but is not limited to such an interface.

The route x input in this way is converted into a sequence of character strings in the same manner as in FIG. 3 according to the sequence of nodes at the passing point. That is, the input path x is previously inputted route x in FIG. ^{2 (1), x (2} ), ..., x (i), ..., partially with one of x ^(N) If they match, the same character string is given to the matching part.

  Next, an algorithm of a required time prediction technique according to the present invention and its implementation will be described. A program for executing the following algorithm is written and compiled in advance in an arbitrary program language such as C ++, C #, Java (trademark), etc., and stored in the hard disk drive 108 as an executable program. . In response to the operation of the keyboard 110 or the mouse 112, the operating system loads the program into the main memory 108 and executes it. The execution result is displayed on the display 114 or stored in the hard disk drive 108.

First, the learning route and the required time data stored in advance are formulated again as follows.
Data D ≡ {(x ⁽ⁿ⁾ , y ⁽ⁿ⁾ | n = 1,2, ..., N}
Here, x ⁽ⁿ⁾ is the nth route stored in advance, and y ⁽ⁿ⁾ is the required time.

  First, the Gaussian process regression model used by the present invention will be described. According to the study by the present inventor, there is a complicated functional relationship between the path and the required time y, which cannot be assumed by linear regression or polynomial regression.

Therefore, the following probability model was assumed.
p (y ⁽ⁿ⁾ | f _n ) = N (y ⁽ⁿ⁾ | f _n , σ ² )

N (y ⁽ⁿ⁾ | f _n , σ ² ) is a Gaussian distribution, and is specifically defined as follows.

That is, N (y ⁽ⁿ⁾ | f _n , σ ² ) represents a normal distribution with y ⁽ⁿ⁾ as a probability distribution, the average is f _n , and the variance is σ ² . σ is preferably determined from the data D, but the value may be designated by the user. Further, f _n is a latent variable of the regression model and needs to be determined from the data D. Since there are the same number of latent variables as observed values, in principle, an arbitrary non-linear relationship can be expressed.

The only assumption here about f _n is that it follows a prior mean zero distribution as
p (f _N ) = N (f _N | 0, K)

Here, f _N = (f ₁ , f ₂ ,..., F _N ) ^T , and K is a covariance matrix called a kernel matrix generated based on x ⁽ⁿ⁾ . A specific method of calculating K used in the present invention will be described in detail later.

FIG. 5 is a schematic diagram of Gaussian process regression. As can be seen from this figure, the parameter f _N is taken into account when calculating y ⁽ⁿ⁾ for each measurement data x ⁽ⁿ⁾ . Each measurement data x ⁽ⁿ⁾ is independent from each other, but f _n is related to different n. That is, there is an assumption that similar x ⁽ⁿ⁾ should be similar to f _n .

This time, we come to the problem of how to define the similarity between x ⁽ⁿ⁾ . According to the present invention, x ⁽ⁿ⁾ is represented as a sequence of character strings, and the similarity is calculated as the sequence of character strings. This will also be described in detail later.

  FIG. 6 is a flowchart of a process for calculating a kernel matrix and other necessary parameters based on the data D according to one embodiment of the present invention. In the present invention, the variance value σ is also given in advance. In this embodiment, σ is manually input to the system by the user.

In step 602 of FIG. 5, a loop of m = 1, 2,..., N is rotated in a loop of n = 1, 2,..., N, and step 604 and step 606 are repeatedly executed. Is done. That is, the loop is executed N ² times.

In step 604, the path x ⁽ⁿ⁾ and the path x ^(m) are converted into a sequence of character strings according to the correspondence shown in FIG. Note that this step can be omitted when the path x ⁽ⁿ⁾ and the path x ^(m) have been converted in advance.

In step 606, (n, m) elements of the kernel matrix K are calculated based on the path x ⁽ⁿ⁾ and the path x ^(m) . At this time, a technique called p-spectrum kernel method is used. It is based on the following formula.

Here, N _u (x ⁽ⁿ⁾ ) is the number of times the partial character string u appears in x ⁽ⁿ⁾ , and Σp represents a set of partial character strings of length p. Here, in the present embodiment, preferably, p is 2 or 3. Since p is a constant determined in advance as described above, it may be omitted in the following description for convenience.

A simple implementation of the calculation of N _u (x ⁽ⁿ⁾ ) is as follows.
(1) The partial sequences of length p of x ⁽ⁿ⁾ are listed in order from the beginning, and all are stored in the hash table A. This A is a hash table in which a partial series is a key and the number of appearances is a value.
(2) Similarly, store all partial sequences of length p of x ^(m) in hash table B.
(3) For each key of A (this is u), the value at A is taken out. That is N _u (x ⁽ⁿ⁾ ).
(4) If u is included as a key for B, the value is extracted. That is N _u (x ^(m) ). If not included, N _u (x ^(m) ) = 0.
For other various implementation methods, refer to http://www.kernel-methods.net/.

In order to absorb the change of the kernel function due to the length of the string,
Assume that k _p (x ⁽ⁿ⁾ , x ^(m) ) is normalized as follows.

In this manner, in step 602, a kernel matrix K having k _p (x ⁽ⁿ⁾ , x ^(m) ) as (n, m) elements is obtained.

In step 608, a matrix C is first calculated by C = K + σ ² I _N.
Here, I _N is an N × N unit matrix.

When C is calculated in this way, the next is calculation of the inverse matrix C ⁻¹ of C. When the order of the matrix becomes several thousand or more, it is difficult to directly calculate the inverse matrix. Therefore, using the method described in Leon Bottou, Olivier Chapelle, Dennis DeCoste and Jason Weston, et. "Large-Scale Kernel Machines", MIT Press, 2007, Chap 9 It becomes possible.

Thus, when C ⁻¹ is calculated in step 608, the result is temporarily stored in the hard disk drive 108. Specifically, each element of C ⁻¹ is stored in the hard disk drive 108 with an index.

In step 610, b ≡ C ⁻¹ y _N is calculated and the result is stored in the hard disk drive 108. Here, y _N = (y ⁽¹⁾ , y ⁽²⁾ ,..., Y ^(N) ) ^T.
This b will be used later in the actual calculation of the required time.

FIG. 7 is a flowchart showing a process for calculating and outputting the required time and its variance for a new route x input by the tablet 118 or the like. In FIG. 7, at step 702, a vector k is calculated for the path x as follows.
k ≡ (k (x, x ⁽¹⁾ ), k (x, x ⁽²⁾ ), ..., k (x, x ^(N) )) ^T
The function k () here is the same as that used in step 606 of FIG.

In step 704, d≡C ⁻¹ k is calculated and the result is stored in the hard disk drive 108.

In step 706, a predicted value m = k ^T b of the required time for the route x is calculated and output. This vector b is calculated in step 610 of the flowchart of FIG. 6 and stored in the hard disk drive 108. This calculated result is preferably automatically displayed on the display 114 using an appropriate GUI.

In step 708, the variance s ^{2 of the} required time indicated by the following equation is calculated and output.
s ² = σ ² + k (x, x)-k ^T d
In this equation, k (x, x) is the same as that used in step 606 of FIG. 6, and d is calculated in step 704 and stored in the hard disk drive 108. This calculated result is preferably automatically displayed on the display 114 using an appropriate GUI.

  FIG. 8 is a flowchart of a process according to another embodiment of the calculation process of FIG. In FIG. 8, steps 802, 804, and 806 may be the same as steps 602, 604, and 606 in the flowchart of FIG.

  Step 808 differs from step 608 in the flowchart of FIG. 6 in that the given variance σ is not given by the user, but is calculated by a technique called evidence approximation of Gaussian process regression. The evidence approximation is a method for determining σ so as to maximize the log marginal likelihood.

ただし、この式で、p(y⁽ⁿ⁾|f_n) = N(y⁽ⁿ⁾|f_n,σ²) Log marginal likelihood is defined by the following formula:

Where p (y ⁽ⁿ⁾ | f _n ) = N (y ⁽ⁿ⁾ | f _n , σ ² )

When integration is performed with a normal distribution formula, for y _N = (y ⁽¹⁾ , y ⁽²⁾ , ..., y ^(N) ) ^T , the following is obtained.

この勾配の式において、ｂ ≡ Ｃ^-1y_Nである。 Here, the matrix C is the same as that described in step 608 and the like. Since it is difficult to analytically find σ that maximizes this equation, the gradient method is used. That is, when the above equation is partially differentiated by σ ² , the following equation is obtained.

In this gradient equation, b≡C ⁻¹ y _N.

をもとめる。
（３）次に、ある小さい値λを用いて、σの値を次のように変更する。

（４）このように変更した値σを数５に代入する。
（５）そこで、数５の前回からの変化量がある閾値よりも小さくなっていると、収束していると看做して、そのときのσの値が、結果の値である。まだ収束していると看做せない場合は、ステップ（２）に戻る。 Using this gradient equation, σ is obtained as follows.
(1) As an initial value of σ, for example, a variance of {y ⁽¹⁾ , y ⁽²⁾ ,..., Y ^(N) } is used.
(2) At the current σ, b = C ⁻¹ y _N and tr (C ⁻¹ ) are calculated, and these values are applied to the above gradient equation to obtain the value of the above gradient.

Seek.
(3) Next, using a small value λ, the value of σ is changed as follows.

(4) The value σ thus changed is substituted into Equation 5.
(5) Therefore, if the amount of change from the previous time of Formula 5 is smaller than a certain threshold value, it is considered that it has converged, and the value of σ at that time is the value of the result. If it cannot be regarded as convergent, the process returns to step (2).

Returning to step 808 in the flowchart of FIG. 8, when the value of σ is determined in this way, C ⁻¹ is calculated in the same manner as in step 608 of FIG. Is remembered.

  Step 810 may be the same as step 610 in FIG.

The kernel function k _p () can be changed as follows.
k (x ⁽ⁿ⁾ , x ^(m) ) = k _p (x ⁽ⁿ⁾ , x ^(m) ) + k ₀ (x ⁽ⁿ⁾ , x ^(m) )

This additional term k ₀ (x ⁽ⁿ⁾ , x ^(m) ) is, for example, the following equation.

Here, the attribute set A indicates the attributes of the expressway and other during construction. w _l is a weight of 1 to 3 for attribute l, and v _l (x ⁽ⁿ⁾ ) is 1 if x ⁽ⁿ⁾ satisfies attribute l, 0 if it does not satisfy attribute It becomes. By adding such additional terms, road conditions can be reflected in the kernel function.

  As mentioned above, although the Example of this invention has been described in relation to the example applied to the time required for the route on the road, the present invention is not limited to this, and the present invention can also be applied to the super flow line analysis. Is possible.

  For example, not only is it applied to the prediction of the required time in the supermarket, but if the route that the customer moved along a route and the data of the resulting product sales amount are stored in association with each other, The sales amount can also be predicted. Then, the present invention can also be applied to a super layout design study that brings about a flow line that further increases the sales amount.

It is a block diagram of the hardware constitutions for carrying out the present invention. It is a figure which shows the some path | route recorded and preserve | saved in advance. It is a figure which shows the node of the path | route of FIG. 2, and the label of a link. It is a figure which shows the input path | route on the map. It is a figure which shows the principle of a Gaussian process regression. It is a figure which shows the flowchart of the process for calculating a required parameter for required time prediction based on a 1st Example. It is a figure which shows the flowchart of the process for outputting the predicted value of a required time, and the value of dispersion | distribution using the calculated parameter. It is a figure which shows the flowchart of the process for calculating a required parameter for required time prediction based on 2nd Example.

Claims (9)

A system for predicting the time required to travel a route by computer processing,
Storage means by which the computer can read and write data;
A plurality of geographical points are set as nodes, a route connecting the nodes is set as a link, a label made up of a number or a character string is given to each link, and information on a route connecting the different nodes with the link, Means for storing in the storage means together with information on the time required for the route using the label;
Means for providing a route represented by the label and for which a time required is predicted;
A kernel matrix whose (n, m) element is a value calculated by the string kernel method from the nth path expressed using a label and the mth path expressed using a label Means for calculating K and storing the value in said storage means;
Matrix C = K + σ ² I _N (where σ is a variance value for predicting the required time, I _N is an N × N unit matrix, and N is the number of routes) Means for storing the value in the storage means;
Means for calculating an inverse matrix of C and storing the value in the storage means;
y _N is a vector in which the required times of N routes are arranged, and means for weighting the route information stored in the storage means by C ⁻¹ y _N ,
Means for predicting the required time of a route for which the required time is to be predicted based on the weighting information;
Time required prediction system.   The system of claim 1, wherein the variance is a user provided value.   The system of claim 1, wherein the string kernel method is a p-spectral kernel method. A method for predicting the time required to travel a route by computer processing,
A plurality of geographical points are set as nodes, a route connecting the nodes is set as a link, a label is given to each link, and information on a route connecting the different nodes with the link is used by using the label. Storing in the storage means of the computer together with information on the time required for the route;
A kernel matrix whose (n, m) element is a value calculated by the string kernel method from the nth path expressed using a label and the mth path expressed using a label Calculating K and storing the value in the storage means;
Matrix C = K + σ ² I _N (where σ is a variance value for predicting the required time, I _N is an N × N unit matrix, and N is the number of routes) Storing the value in the storage means;
Calculating an inverse matrix of C and storing the value in the storage means;
y _N is a vector in which the required times of N routes are arranged, and the information of the route stored in the storage means is weighted by C ⁻¹ y _N , and
Based on the information of the weighting comprises the step of predicting a time required for the route to be predictive of the required time,
Time required prediction method.   The method of claim 4, wherein the variance is a user provided value.   The method of claim 4, wherein the string kernel method is a p-spectrum kernel method. A program that predicts the time required to travel a route by computer processing,
In the computer,
A plurality of geographical points are set as nodes, a route connecting the nodes is set as a link, a label is given to each link, and information on a route connecting the different nodes with the link is used by using the label. Storing in the storage means of the computer together with information on the time required for the route;
A kernel matrix whose (n, m) element is a value calculated by the string kernel method from the nth path expressed using a label and the mth path expressed using a label Calculating K and storing the value in the storage means;
Matrix C = K + σ ² I _N (where σ is a variance value for predicting the required time, I _N is an N × N unit matrix, and N is the number of routes) Storing the value in the storage means;
Calculating an inverse matrix of C and storing the value in the storage means;
y _N is a vector in which the required times of N routes are arranged, and the information of the route stored in the storage means is weighted by C ⁻¹ y _N , and
Based on the weighting information, the step of predicting the required time of the route for which the required time is to be predicted is executed.
Time required prediction program.   The program according to claim 7, wherein the variance is a value provided by a user.   The program according to claim 7, wherein the character string kernel method is a p-spectrum kernel method.

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