JP6283331B2 - Flow estimation device, prediction device, and program - Google Patents

Description

  The present invention relates to a flow estimation device, a prediction device, and a program, and more particularly, to a flow estimation device, a prediction device, and a program for estimating a flow.

  If there is movement trajectory data for each individual, it is easy to estimate the flow of the person. However, movement trajectory data for each individual may not be available due to privacy protection or difficulty in collection. On the other hand, data on human density is easy to collect because privacy is protected and tracking for each individual is not required. A technique for estimating a flow from density data has been proposed so far (for example, Non-Patent Document 1).

Akshat Kumar, Daniel Sheldon, Biplav Srivastava, “Collective Diffusion Over Networks”, Models and Inference. UAI 2013

  However, the technique described in Non-Patent Document 1 has a problem in that the difference in flow for each time cannot be considered.

  The present invention has been made to solve the above problems, and an object of the present invention is to provide a flow estimation device, a prediction device, and a program capable of accurately estimating the flow of an object.

In order to achieve the above object, the flow estimation device according to the first invention represents the number or density of people moving from the point i to the point j near the point i at each time t and each point i. Based on the flow data, in the cluster k to which each time t belongs, a parameter representing the distribution of the movement probability representing the probability that the person moves from the point i to each of the points j in the vicinity of the point i and each time in the day A parameter estimation unit for estimating parameters of a flow model for estimating the flow of a person at each time t and each point i, including the probability that each belongs to each cluster, and the number or density of people at each time t and each point i and population data representing, based on the parameters of the flow model that has been estimated by the parameter estimating unit, at each time t and each location i, the point i from the point i Repeated the flow estimation unit that estimates a flow data representing the number or density of the person moving to a point j in the vicinity, until the end condition is satisfied a predetermined, respective processing by the parameter estimation unit and said flow estimator An end determination unit, and the parameter estimation unit estimates a parameter of the flow model based on the flow data estimated by the flow estimation unit.

Further, the flow estimation device according to the second invention is based on flow data representing the number or density of people moving from the point i to the point j near the point i at each time t and each point i. A parameter representing a probability distribution of the person representing the probability that the person moves from the point i to each of the points j near the point i in the cluster k to which each point i belongs, and a probability that each point belongs to each cluster. A parameter estimator for estimating parameters of a flow model for estimating a human flow at each time t and each point i, population data representing the number or density of people at each time t and each point i, and the parameter estimation based on the parameters of the flow model that has been estimated by the Department, at each time t and each point i, of the person moving from the point i to point j in the vicinity of the point i Or a flow estimation unit that estimates flow data representing density, and an end determination unit that repeatedly performs each process by the parameter estimation unit and the flow estimation unit until a predetermined end condition is satisfied, and the parameter estimation The unit estimates a parameter of the flow model based on the flow data estimated by the flow estimation unit.

In addition, the parameter estimation unit includes the flow data estimated by the flow estimation unit, the probability q _sk that each time s in a day belongs to each cluster k, and the prior distribution of the movement probability of moving to the point j. Based on the parameter α _j to be represented, for each combination of the cluster k and the point i, the parameter ^ α _ki representing the distribution of the movement probability is estimated, and from the estimated parameter ^ α _ki , the cluster k The cluster k for each of the clusters k based on the probability q _sk of each time s belonging to each cluster k and the movement probability estimator for estimating the distribution of the person 's movement probability ^ θ _ki at the point i estimating a parameter beta _k representing the distribution of the cluster distribution φ of from estimated the parameters beta _k, to estimate the distribution of the cluster distribution φ of the cluster k Based and cluster distribution estimation unit, and a probability q _sk each time s belongs to each cluster k, and time accuracy eta _k of each cluster k, for each of the cluster k, parameter d representing the distribution of the time average tau _k estimates the _k and f _k, from the estimated parameters d _k and f _k, and average estimation unit that estimates a distribution of time mean tau _k, the probability q _sk each time s belongs to each cluster k, each cluster based with the parameters f _k of k, for each of the cluster k, the time to estimate the parameters a _k and b _k represents the distribution of accuracy eta _k, from the estimated parameters a _k and b _k, a time An accuracy estimator for estimating the distribution of accuracy η _k, the flow data estimated by the flow estimator, and the parameters ^ α _ki , β _k , a _k , b _k , d _k , f _{k of} each cluster _k And On the basis of each of the combinations of the cluster k and the time s, a cluster estimation unit that estimates the probability q _sk that the time s belongs to the cluster k, and the point j based on the parameter ^ α _ki of each cluster k. Each may include a movement probability parameter estimation unit that estimates a parameter α _j representing a prior distribution of movement probabilities of moving to the point j.

Further, the flow estimation unit is configured and population data, estimated by the parameter estimating unit, and the probability q _sk said parameter ^ alpha _ki and each time s belongs to each cluster k of each cluster k, and the flow data The flow data may be estimated such that a gradient of an objective function for estimating the flow data is calculated based on and the objective function is maximized based on the calculated gradient.

Further, the prediction device according to a third aspect of the invention is based on the parameters of the flow model estimated by the flow estimation device, and the person moves from the point i to a point j near the point i at time t. From the movement probability calculation unit that estimates the movement probability that represents the probability of performing, the movement probability estimated by the movement probability calculation unit, and population data that represents the number or density of people at time t and each point i, at time t + 1 A prediction unit that predicts the number or density of people at each point i.

  A program according to the fourth invention is a program for causing a computer to function as each part of the flow estimation device or the prediction device.

  According to the flow estimation apparatus and the program of the present invention, each time t and each point i including a parameter representing a distribution of the movement probability representing the probability that the object moves from the point i to each of the points j in the vicinity of the point i. Parameters of the flow model for estimating the flow of the person at each time t, and based on the input data representing the number or density of objects at each time t and each point i and the estimated flow model parameters, By estimating the flow data representing the number or density of objects moving from point i to point j in the vicinity of point i at each point i, an effect is obtained that the flow of the object can be accurately estimated. .

It is a block diagram which shows the structure of the flow estimation apparatus which concerns on embodiment of this invention. It is a figure which shows the detailed structural example of the parameter estimation part of the flow estimation apparatus which concerns on embodiment of this invention. It is a figure which shows the detailed structural example of the flow estimation part of the flow estimation apparatus which concerns on embodiment of this invention. It is a figure which shows the detailed structural example of the prediction part of the flow estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the estimation process routine in the flow estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the parameter estimation processing routine in the flow estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the flow estimation process routine in the flow estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the prediction process routine in the flow estimation apparatus which concerns on embodiment of this invention. It is an experimental result of the method which concerns on embodiment of this invention. It is an experimental result of the method which concerns on embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Outline according to Embodiment of the Present Invention>

  First, an outline of the embodiment of the present invention will be described. In the embodiment of the present invention, it is an object to estimate the flow of an object from data representing the number or density of objects at a plurality of times. In order to solve the above problems, a flow estimation apparatus according to an embodiment of the present invention includes a parameter estimation unit that estimates a parameter of a flow model, a flow estimation unit that estimates a flow at each point at each time, and a future It was set as the structure provided with the estimation part which estimates a number or a density.

  The embodiment of the present invention targets data representing the number or density of objects at a plurality of times. For example, the number of people within 5 km square per hour is the data. When such data is given, the flow at each point at each time is estimated.

  In the embodiment of the present invention described below, it is assumed that the input data is population data. Further, in the embodiment of the present invention, a case where the present invention is applied to a flow estimation device that estimates population flow based on input population data and predicts population flow will be described as an example.

<First Embodiment>

  Next, the configuration of the flow estimation apparatus according to the first embodiment of the present invention will be described. As shown in FIG. 1, the flow estimation apparatus 100 according to the first embodiment includes a CPU, a RAM, and a ROM that stores a program and various data for executing a flow estimation processing routine described later. Can be configured with a computer. Functionally, the flow estimation apparatus 100 includes an input unit 10, a calculation unit 20, and an output unit 40 as shown in FIG.

The input unit 10 receives input data representing the number of objects at each time t and each point i. In the present embodiment, the population data representing each time t up to time T and the population N _ti at each point i as input data.

Accept. When a vector or a set of vectors is represented, the symbol is preceded by “^”. In the present embodiment, it is assumed that the vicinity information of each point is also given. _{^ J i ⊆ {1, ···} , I} be the set of points in the vicinity of the point i a, ^ _{J i} always to include the point i of itself (i∈ _{^ J} i). In this embodiment, for the sake of simplicity, it is assumed that each point has a square lattice shape, and the neighborhood is obtained by adding itself to the surrounding eight points (| ^ J _i | = J = 9). It can be applied at any shape point and any neighborhood.

  The calculation unit 20 includes an initialization unit 22, a population database 24, a parameter database 26, a flow database 28, a parameter estimation unit 30, a flow estimation unit 32, an end determination unit 34, and a prediction unit 36. It consists of

  The initialization unit 22 reads the population data ^ N received by the input unit 10 and stores the read population data ^ N in the population database 24. The initialization unit 22 initializes flow data ^ M, which will be described later, and a flow model parameter Λ, which will be described later, and stores them in the flow database 28 and the parameter database 26.

  In the population database 24, population data ^ N read by the initialization unit 22 is stored.

  The parameter database 26 stores a flow model parameter Λ described later.

  The flow database 28 stores flow data ^ M representing the number of persons moving from the point i to the point j near the point i at each time t and each point i.

  In the embodiment of the present invention, a flow model shown in the following equation (1) is considered. In the first embodiment, each time is assigned to a cluster, but it is also possible to assign each point to a cluster, and to assign a time and a point to a cluster at the same time.

In the present embodiment, M _tij is the number of people who have moved from the point i at time t to the j th neighborhood. Assuming that the moving data ^ M _ti = (M _tij ) ^J _{j = 1,} which is the flow data, follows a multinomial distribution,

It becomes. Here, θ _kij is the probability of moving from the point i to the jth neighborhood in the cluster k.

  Between the population and the number of people traveling, the sum of the flow from a point matches the population at that point, and the sum of the flow to a point matches the population at the next time,

There is a relationship.

Further, it is assumed that the movement probability ^ θ _ki is generated from the following Dirichlet distribution.

here

Is the Dirichlet parameter,

It is.
The time of cluster k is a normal distribution with mean τ _k and accuracy η _k

Assuming that Here, g represents the time of the day, for example, data representing the hour and minute of the day.

It is assumed that the probability π _gk that time g is assigned to cluster k follows Dirichlet distribution, the average of cluster time follows normal distribution, and accuracy follows gamma distribution. In order to make the calculation efficient, such a conjugate prior distribution is assumed, but other distributions may be used.

  In the following description, the flow and flow model parameters are estimated based on the variational Bayesian method. However, the maximum likelihood estimation method, the maximum posterior probability method, the Markov chain Monte Carlo method, and the like can also be used. When the variational Bayes method is used, the objective function is the lower limit of the marginal likelihood.

  Based on the flow data ^ M stored in the flow database 28 and the flow model parameter {circumflex over (Λ)} stored in the parameter database 26, the parameter estimator 30 determines from the point i to the point i in the cluster k to which each time t belongs. Estimate the flow of people at each time t and each point i, including a parameter representing the distribution of the movement probability representing the probability that the person will move to each of the nearby points j and the probability that each time in the day belongs to each cluster. Estimate the parameters ^ Λ of the flow model for

  Specifically, the parameter estimation unit 30 sets the flow model parameter {circumflex over (Λ)} so that the objective function representing the likelihood of the relationship between the flow data ^ M estimated last time by the flow estimation unit 32 described later and the flow model becomes high. Is estimated. If the accuracy of predicting the flow from the flow model is high, the objective function is high.

  FIG. 2 is a block diagram illustrating a configuration example of the parameter estimation unit 30 according to the embodiment of the present invention. As shown in FIG. 2, the parameter estimation unit 30 includes a reading unit 300, a movement probability estimation unit 302, a cluster distribution estimation unit 304, an average estimation unit 306, an accuracy estimation unit 308, a cluster estimation unit 310, A movement probability parameter estimation unit 312 and a writing unit 314 are provided.

  The reading unit 300 stores the flow data stored in the flow database 28.

Then, the flow model parameters ^ Λ = {^ α, ^ α ^* , ^ β, ^ d, ^ f, ^ a, ^ b, ^ Q} stored in the parameter database 26 are read. here

It is. K represents the number of clusters, S represents the number of times of the day, and the symbol s represents the sth time of the day.

The movement probability estimation unit 302 reads the flow data ^ M read by the reading unit 300 and the flow model parameter ^ Λ, the probability q _sk that each time s in one day belongs to each cluster k, and the point j. Based on the parameter α _j representing the prior distribution of the moving probability to move, the parameter ^ α _ki representing the distribution of the movement probability is estimated for each combination of the cluster k and the point i, and the estimated parameter ^ α _ki From the above, the distribution of the human movement probability ^ θ _ki at the point i of the cluster k is estimated. The distribution that maximizes the objective function is

It becomes. here

And

It is. Here, s (t) is a function that converts time t into time of the day.
In the present embodiment, the movement probability estimation unit 302 estimates the parameter ^ α _ki representing the distribution of movement probability according to the above equation (7) for each combination of the cluster k and the point i, and the estimated parameter ^ from α _ki, in accordance with the above equation (6), to estimate the distribution of the movement probability ^ θ _ki of people at the point i of the cluster k.

The cluster distribution estimation unit 304 determines the cluster k of the cluster k for each cluster k based on the probability q _sk of each time s belonging to each cluster k out of the parameters Λ of the flow model read by the reading unit 300. The parameter β _k representing the distribution φ is estimated, and the distribution of the cluster distribution φ of the cluster _k is estimated from the estimated parameter β _k . The distribution that maximizes the objective function is

It becomes. here

It is.
In the present embodiment, the cluster distribution estimation unit 304 estimates, for each cluster k, a parameter β _k representing the distribution of the cluster distribution φ of the cluster k according to the above equation (9), and from the estimated parameter β _k. Then, the distribution of the cluster distribution φ of the cluster k is estimated according to the above equation (8).

Based on the probability q _{sk of} each time s belonging to each cluster k among the parameters Λ of the flow model read by the reading unit 300 and the time accuracy η _k of each cluster k, the average estimation unit 306 each k to estimate the parameters d _k and f _k representing the distribution of the time average tau _k, from the estimated parameters d _k and f _k, to estimate the distribution of time mean tau _k. The distribution that maximizes the objective function is

It becomes. here

It is.
In the present embodiment, average estimator 306 estimates parameters d _k and f _k representing the distribution of time average τ _k for each cluster k according to the above equations (11) and (12). From the parameters d _k and f _k thus _obtained , the distribution of the time average τ _k is estimated according to the above equation (10).

Based on the probability q _{sk of} each time s belonging to each cluster k among the parameters Λ of the flow model read by the reading unit 300 and the parameter f _k of each cluster k, the accuracy estimation unit 308 determines the cluster k. each hand, to estimate the parameters a _k and b _k represents the distribution of time accuracy eta _k, from the estimated parameters a _k and b _k, estimating the distribution of time accuracy eta _k. The distribution that maximizes the objective function is

It becomes. here

It is.
In the present embodiment, the accuracy estimation unit 308 estimates the parameters a _k and b _k representing the distribution of the time accuracy η _k for each cluster k according to the above equations (14) and (15). The distribution of time accuracy η _k is estimated from the parameters a _k and b _{k according} to the above equation (13).

Cluster estimation unit 310 includes a flow data ^ M read by the reading unit 300, the flow model parameters ^ of lambda, of each cluster k parameter _{^ α ki, β k, a} k, b k, d k, Based on f _k , for each combination of cluster k and time s, the probability q (z _s = k) ≡q _sk that time s of the day belongs to cluster k is estimated. The probability of maximizing the objective function is

It becomes. Where Ψ (•) represents the digamma function,

It is.
In the present embodiment, cluster estimation section 310 estimates the probability q _sk of time s belonging to cluster k according to the above equation (16) for each combination of cluster k and time s. When estimating the probability q _sk of time s belonging to cluster k, the probability q _sk is normalized so that the sum for all clusters k becomes 1 at each time s.

The movement probability parameter estimation unit 312 determines the movement probability of moving to the point j for each point j based on the parameters k α _ki of each cluster k out of the parameters ^ Λ of the flow model read by the reading unit 300. A parameter α _j representing the prior distribution is estimated. Specifically, the movement probability parameter estimation unit 312 estimates ^ α ^* = (α _j ) _{j = 1} ^J , which is a parameter of a prior distribution of movement probabilities. Parameter

The objective function can be maximized by updating with.

  The writing unit 314 uses the parameter ^ Λ estimated by the movement probability estimation unit 302, the cluster distribution estimation unit 304, the average estimation unit 306, the accuracy estimation unit 308, the cluster estimation unit 310, and the movement probability parameter estimation unit 312 as a parameter. Write to database 26.

  Based on the population data ^ N stored in the population database 24 and the flow model parameter ^ Λ stored in the parameter database 26, the flow estimation unit 32 determines the point from point i to point at each time t and each point i. Estimate flow data ^ M representing the number of people moving to a point j near i. Specifically, the flow estimation unit 32 estimates the flow data ^ M so that the objective function representing the likelihood of the relationship between the flow model, the flow data ^ M, and the population data ^ N becomes high. If the accuracy of predicting flow data ^ M from the flow model is high, if the sum of the flow from a point is similar to the population at that point, the sum of the flow to that point is the population at the next time after that point. If it is similar to, the objective function is high.

  FIG. 3 is a block diagram illustrating a detailed configuration example of the flow estimation unit according to the embodiment of this invention. The flow estimation unit 32 includes a reading unit 320, a gradient calculation unit 322, an optimization unit 324, a convergence determination unit 326, and a writing unit 328. In the following, a method of optimization using a gradient will be described, but any optimization method may be used as long as the objective function can be maximized.

  The reading unit 320 reads the population data ^ N stored in the population database 24, the flow data ^ M stored in the flow database 28, and the flow model parameter ^ Λ stored in the parameter database 26. The objective function for estimating the flow is

It becomes. Here, the approximation is performed using the Stirling formula, but the approximation may not be used. Moreover, although the penalty term was introduced in order to achieve the above equations (2) and (3), which are constraints, the constraints may be achieved by constrained optimization. Also,

Is a parameter for adjusting penalties.

The gradient calculation unit 322 is configured such that, among the population data ^ N read by the reading unit 320 and the flow model parameters ^ Λ read by the reading unit 320, the parameter ^ α _ki and each time s of each cluster k are each cluster. Based on the probability q _sk belonging to k and the flow data ^ M read by the reading unit 320, the gradient of the objective function for estimating the flow data ^ M is calculated. The value of the objective function (18) and its gradient by the gradient calculator

Calculate

  The optimization unit 324 estimates the flow data ^ M so as to maximize the objective function based on the gradient calculated by the gradient calculation unit 322. The optimization unit 324 uses the calculated objective function value and the gradient, and obtains a flow (number of movements) that maximizes the objective function, with the optimization unit placing a constraint that the number of movements is positive.

  The convergence determination unit 326 estimates the flow that maximizes the objective function by repeating the gradient calculation unit 322 and the optimization unit 324 until a predetermined convergence condition is satisfied.

  The writing unit 328 writes the flow data ^ M estimated by the flow estimation unit 32 in the flow database 28.

  The end determination unit 34 repeatedly performs each process by the parameter estimation unit 30 and the flow estimation unit 32 until a predetermined end condition is satisfied. As the end condition, the magnitude of change of the objective function, the magnitude of change of the parameter, the number of repetitions, and the like can be used.

  Based on the population data {circumflex over (N)} stored in the population database 24 and the flow model parameter {circumflex over (Λ)} stored in the parameter database 26, the prediction unit 36 calculates the time t + 1 from the population data at each point i. Predict the population at each point i. The prediction unit 36 predicts a future population using population data at a certain time. FIG. 4 is a block diagram illustrating a detailed configuration example of the prediction unit 36 according to the embodiment of this invention. The prediction unit 36 includes a reading unit 360, a movement probability calculation unit 362, and a population prediction unit 364.

The reading unit 360 reads the flow model parameters {circumflex over (Λ)} stored in the parameter database 26 and the population data ^ N _t at the time t stored in the population database 24.

  Based on the flow model parameter ^ Λ read by the reading unit 360, the movement probability calculation unit 362 estimates a movement probability that represents the probability that a person will move from the point i to the point j near the point i at the time t. . Specifically, the movement probability calculation unit 362 is based on the flow model parameter Λ.

The movement probability is calculated by Also

Is an estimated cluster at time t.

The population prediction unit 364 calculates the movement probability estimated by the movement probability calculation unit 362, the time t read by the reading unit 360, and the population data ^ N _t representing the population at each point i, at each point i at time t + 1. Predict the population. Specifically, the population prediction unit 364 calculates the population at time t + 1 based on the movement probability estimated by the movement probability calculation unit 362 and the population data ^ N _t.

Predict with.

  The output unit 40 outputs the population at each point i at time t + 1 predicted by the prediction unit 36 as a result.

<Operation of Flow Estimation Device According to Embodiment of the Present Invention>

  Next, the operation of the flow estimation apparatus 100 according to the embodiment of the present invention will be described. When population data ^ N is received at the input unit 10, the flow estimation apparatus 100 executes an estimation processing routine shown in FIG.

  First, in step S <b> 100, the initialization unit 22 reads the population data ^ N received by the input unit 10, and stores the read population data ^ N in the population database 24. The initialization unit 22 initializes flow data ^ M and a flow model parameter ^ Λ, which will be described later, and stores them in the flow database 28 and the parameter database 26.

  Next, in step S102, the parameter estimation unit 30 calculates the flow model parameter ^ Λ based on the flow data ^ M stored in the flow database 28 and the flow model parameter ^ Λ stored in the parameter database 26. presume. Step S102 is realized by a parameter estimation processing routine shown in FIG.

<Parameter estimation processing routine>
In step S200, the reading unit 300 reads the flow data ^ M stored in the flow database 28 and the flow model parameter ^ Λ stored in the parameter database 26.

In step S202, the movement probability estimation unit 302 performs the above (7) for each combination of cluster k and point i based on the flow data ^ M read in step S200 and the flow model parameter ^ Λ. The parameter ^ α _ki representing the movement probability distribution is estimated according to the equation, and the distribution of the human movement probability ^ θ _ki at the point i of the cluster k is estimated from the estimated parameter ^ α _{ki according} to the above equation (6). To do.

In step S204, the cluster distribution estimation unit 304 calculates the distribution of the cluster distribution φ of the cluster k according to the above equation (9) for each of the clusters k based on the flow model parameter ^ Λ read in step S200. The parameter β _k to be represented is estimated, and the distribution of the cluster distribution φ of the cluster _k is estimated from the estimated parameter β _{k according} to the above equation (8).

In step S206, the average estimation unit 306 determines the time average τ _k for each cluster k according to the above equations (11) and (12) based on the flow model parameter ΛΛ read in step S200. The parameters d _k and f _k representing the distribution of are estimated, and the distribution of the time average τ _k is estimated from the estimated parameters d _k and f _{k according} to the above equation (10).

In step S208, the accuracy estimation unit 308 determines the time accuracy η _k for each cluster k according to the equations (14) and (15) based on the flow model parameter ΛΛ read in step S200. The parameters a _k and b _k representing the distribution of the time are estimated, and the distribution of the time accuracy η _k is estimated from the estimated parameters a _k and b _{k according} to the above equation (13).

In step S210, the cluster estimation unit 310, for each combination of the cluster k and the time s, based on the flow data ^ M read in step S200 and the flow model parameter ^ Λ, according to the above equation (16). , A probability q _sk of time s belonging to cluster k is estimated.

In step S212, the movement probability parameter estimation unit 312 determines the movement probability of moving to the point j for each point j according to the above equation (17) based on the flow model parameter ^ Λ read in step S200. A parameter α _j representing the prior distribution is estimated.

  In step S214, the writing unit 314 writes the parameter ^ Λ estimated in steps S202 to S212 in the parameter database 26, and ends the parameter estimation processing routine.

  Next, returning to the estimation processing routine, in step S104, the flow estimation unit 32, based on the population data ^ N stored in the population database 24 and the parameter ^ Λ of the flow model stored in the parameter database 26, At each time t and each point i, flow data ^ M representing the number of people moving from point i to point j near point i is estimated. Step S104 is realized by the flow estimation processing routine shown in FIG.

<Flow estimation processing routine>
In step S300, the reading unit 320 reads the population data ^ N stored in the population database 24, the flow data ^ M stored in the flow database 28, and the flow model parameter ^ Λ stored in the parameter database 26. .

  In step S302, the gradient calculation unit 322 calculates the flow data ^ M according to the above equation (19) based on the population data ^ N, the flow model parameter ^ Λ, and the flow data ^ M read in step S300. Calculate the gradient of the objective function to estimate.

  In step S304, the optimization unit 324 estimates the flow data ^ M so as to maximize the objective function of the equation (18) based on the gradient calculated in step S302.

  In step S306, the convergence determination unit 326 determines whether a predetermined convergence condition is satisfied. If the convergence condition is satisfied, the process proceeds to step S308. On the other hand, if the convergence condition is not satisfied, the process returns to step S302.

  In step S308, the writing unit 328 writes the flow data ^ M estimated in step S304 to the flow database 28, and ends the parameter estimation processing routine.

  Next, returning to the estimation processing routine, in step S106, the end determination unit 34 determines whether or not a predetermined end condition is satisfied. If the end condition is satisfied, the process proceeds to step S108. On the other hand, if the end condition is not satisfied, the process returns to step S102.

  In step S108, the prediction unit 36 calculates the time t and the population data at each point i based on the population data ^ N stored in the population database 24 and the flow model parameter ^ Λ stored in the parameter database 26. The population at each point i at time t + 1 is predicted. Step S108 is realized by the prediction processing routine shown in FIG.

<Prediction processing routine>
In step S <b> 400, the reading unit 360 reads the flow model parameter {circumflex over (Λ)} stored in the parameter database 26 and the population data ^ N _t at time t stored in the population database 24.

  In step S <b> 402, the movement probability calculation unit 362 performs the operation from the point i to the point i at the time t according to the equation (20) to the equation (21) based on the flow model parameter ΛΛ read by the reading unit 360. A movement probability representing the probability that a person moves to a nearby point j is estimated.

In step S404, the population prediction unit 364 determines the population at each point i at time t + 1 from the movement probability estimated in step S204 and the population data ^ N _t read in step S400 according to the above equation (22). Predict.

  In step S406, the prediction unit 36 outputs the population at each point i at time t + 1 predicted in step S404 as a result, and ends the prediction processing routine.

  Next, returning to the estimation processing routine, in step S110, the output unit 40 outputs the population at each point i at time t + 1 predicted by the prediction unit 36 as a result, and ends the process.

<Example>

  An experiment was conducted to evaluate the method according to the embodiment of the present invention. In the experiment, actual data from Tokyo and Rome were used. In the experiment, the embodiment of the present invention (VCGMM), the embodiment of the present invention (VCGM) in which the number of clusters is 1, and the conventional method (see CGM, Non-patent Reference 1), one hour before. The method of predicting by value (STAY) and the method of predicting by past average (AVE) were compared. In the embodiment (VCGMM) of the present invention, the number of clusters is K = 10. FIG. 9 shows the average absolute error of each method. The first column in FIG. 9 represents the date of the test data. As shown in FIG. 9, in all data, the error about the embodiment of the present invention is the smallest, and it can be said that the flow can be estimated with higher accuracy by the embodiment of the present invention.

  FIG. 10 shows the flow of people estimated using the Tokyo data according to the embodiment of the present invention. Five clusters were extracted from this data. As shown in FIG. 10, it is estimated that there is no flow from 0:00 to 6:30 because many people are sleeping. From 7:00 to 9:30, the flow from the suburbs to the city center is estimated. In addition, after 18:00, the flow from the city center to the suburbs has been estimated. This result suggests that the flow can be estimated appropriately according to the embodiment of the present invention.

  As described above, according to the flow estimation apparatus according to the first embodiment, the movement representing the probability that a person moves from the point i to each of the points j in the vicinity of the point i in the cluster k to which each time t belongs. Estimate the parameters of the flow model for estimating the human flow at each time t and each point i, including the parameters representing the probability distribution and the probability that each time in the day belongs to each cluster. Based on input data representing the number of people at point i and estimated flow model parameters, represent the number of people moving from point i to point j in the vicinity of point i at each time t and at each point i. By estimating the flow data, it is possible to accurately estimate the human flow.

  Further, based on the parameters of the estimated flow model, a movement probability representing a probability that a person moves from the point i to the point j near the point i at the time t is estimated, and the estimated movement probability, the time t, By predicting the number of people at each point i at time t + 1 from input data representing the number of people at each point i, the population can be predicted with high accuracy.

  In addition, if the flow can be estimated from data representing the number or density of objects according to the embodiment of the present invention, it can be utilized for public health, city planning, marketing, disaster countermeasures, and the like.

<Second Embodiment>
Next, a second embodiment will be described. In addition, since the structure of the flow estimation apparatus which concerns on 2nd Embodiment becomes a structure similar to 1st Embodiment, it attaches | subjects the same code | symbol and abbreviate | omits description.

  The second embodiment is different from the first embodiment in that each point is assigned to a cluster.

  The parameter estimator 30 of the flow estimation apparatus according to the second embodiment is based on the flow data ^ M stored in the flow database 28 and the flow model parameter ^ Λ stored in the parameter database 26. Each time t and each location including a parameter indicating a probability distribution of a person representing a probability that a person moves from point i to each of points j near point i in cluster k to which i belongs and a probability that each point belongs to each cluster Estimate a flow model parameter {circumflex over (Λ)} for estimating human flow at point i.

The movement probability estimator 302 includes the flow data ^ M read by the reader 300 and the flow model parameter ^ Λ and the probability that each point belongs to each cluster k and the advance probability of movement to the point j. Based on the parameter α _j representing the distribution, a parameter ^ α _ki representing the distribution of the movement probability is estimated for each combination of the cluster k and the point i, and the point of the cluster k is estimated from the estimated parameter ^ α _ki. Estimate the distribution of the human movement probability ^ θ _ki at i.

The cluster distribution estimation unit 304 determines, for each cluster k, the cluster distribution φ of the cluster k based on the probability that each point belongs to each cluster k among the parameters ^ Λ of the flow model read by the reading unit 300. A parameter β _k representing the distribution is estimated, and the distribution of the cluster distribution φ of the cluster _k is estimated from the estimated parameter β _k .

The average estimation unit 306, based on the probability of the parameters ^ lambda flow model read by reading unit 300, each point belonging to each cluster k, the point accuracy eta _k of each cluster k, each cluster k to estimate the parameters d _k and f _k representing the distribution point average tau _k, from the estimated parameters d _k and f _k, to estimate the distribution point average tau _k.

Based on the probability that each point belongs to each cluster k out of the parameters ^ Λ of the flow model read by the reading unit 300 and the parameter f _k of each cluster k, the accuracy estimation unit 308 assigns each of the clusters k. contrast, estimates the parameters a _k and b _k represents the distribution of point accuracy eta _k, from the estimated parameters a _k and b _k, estimating the distribution of point accuracy eta _k.
Cluster estimation unit 310 includes a flow data ^ M read by the reading unit 300, the flow model parameters ^ of lambda, of each cluster k parameter _{^ α ki, β k, a} k, b k, d k, Based on f _k , for each combination of cluster k and point, the probability that the point belongs to cluster k is estimated.
The movement probability parameter estimation unit 312 determines the movement probability of moving to the point j for each point j based on the parameters k α _ki of each cluster k out of the parameters ^ Λ of the flow model read by the reading unit 300. A parameter α _j representing the prior distribution is estimated.

  The flow estimator 32 of the flow estimator according to the second embodiment uses each of the population data ^ N stored in the population database 24 and the flow model parameter ΛΛ stored in the parameter database 26. The flow data ^ M representing the number of people moving from the point i to the point j near the point i at the time t and each point i is estimated.

The gradient calculation unit 322 is configured such that, among the population data ^ N read by the reading unit 320 and the flow model parameters ^ Λ read by the reading unit 320, the parameter ^ α _ki and each time s of each cluster k are each cluster. Based on the probability q _sk belonging to k and the flow data ^ M read by the reading unit 320, the gradient of the objective function for estimating the flow data ^ M is calculated.

  The optimization unit 324 estimates the flow data ^ M so as to maximize the objective function based on the gradient calculated by the gradient calculation unit 322.

  The prediction unit 36 of the flow estimation apparatus according to the second embodiment performs the time t based on the population data ^ N stored in the population database 24 and the flow model parameter ^ Λ stored in the parameter database 26. The population at each point i at time t + 1 is predicted from the population data at each point i. The prediction unit 36 predicts a future population using population data at a certain time.

  The end determination unit 34 repeatedly performs each process by the parameter estimation unit 30 and the flow estimation unit 32 until a predetermined end condition is satisfied.

  As described above, according to the flow estimation apparatus according to the second embodiment, the movement representing the probability that a person moves from the point i to each of the points j near the point i in the cluster k to which each point i belongs. Estimate the parameters of the flow model for estimating the human flow at each time t and each point i, including the parameters representing the probability distribution and the probability that each point belongs to each cluster, and at each time t and each point i Based on the input data representing the number of people and the parameters of the estimated flow model, the flow data representing the number of people moving from the point i to the point j near the point i at each time t and each point i. By estimating, it is possible to accurately estimate the flow of people.

  The present invention is not limited to the above-described embodiment, and various modifications and applications can be made without departing from the gist of the present invention.

  For example, in the above embodiment, the case where the input data is population data has been described as an example. However, the present invention is not limited to this, and may be data representing the number or density of animals, objects, diseases, and the like.

  Moreover, although the case where the input data representing the number of people at each time t and each point i is used as an example in the above embodiment, the data representing the density of people at each time t and each point i is input data. It may be used as When data representing the density of a person is used as input data, the flow data is flow data representing the density of a person who moves from a point i to a point j near the point i.

  In the above embodiment, the case where each time is assigned to a cluster in the first embodiment has been described as an example, and the case where each point is assigned to a cluster in the second embodiment has been described as an example. However, the present invention is not limited to this, and each time and each point may be assigned to a cluster.

When assigning each time and each point to the cluster, the parameter estimation unit 30 uses the flow data representing the number or density of objects moving from the point i to the point j near the point i at each time t and each point i. Based on the parameters representing the distribution of the movement probability representing the probability that the object will move from the point i to each of the points j in the vicinity of the point i in the cluster k to which each time t and each point i belong, and each time and each point The parameters of the flow model for estimating the flow of the object at each time t and each point i, including the probability that each belongs to each cluster, are estimated.
Then, the flow estimation unit 32 determines each time t and each point i based on the input data representing the number or density of objects at each time t and each point i and the parameters of the flow model estimated by the parameter estimation unit 30. The flow data representing the number or density of objects moving from the point i to the point j in the vicinity of the point i is estimated.

  Moreover, although the case where the parameter estimation part 30, the flow estimation part 32, and the prediction part 36 were comprised as one apparatus was demonstrated to the said embodiment as an example, the flow containing the parameter estimation part 30 and the flow estimation part 32 is demonstrated. The device and the prediction device including the prediction unit 36 may be configured as separate devices.

  Further, the case where the above-described flow estimation device includes each database has been described. For example, each database is provided in an external device of the flow estimation device, and the flow estimation device communicates with the external device using a communication unit. Thus, each database may be referred to.

  Moreover, although the above-mentioned flow estimation apparatus has a computer system inside, if the computer system is using the WWW system, it shall also include a homepage provision environment (or display environment).

  In the present specification, the embodiment has been described in which the program is installed in advance. However, the program can be provided by being stored in a computer-readable recording medium.

DESCRIPTION OF SYMBOLS 10 Input part 20 Operation part 22 Initialization part 24 Population database 26 Parameter database 28 Database 30 Parameter estimation part 32 Flow estimation part 34 Termination determination part 36 Prediction part 40 Output part 100 Estimation apparatus 300 Reading part 302 Movement probability estimation part 304 Cluster distribution Estimating unit 306 Average estimating unit 308 Accuracy estimating unit 310 Cluster estimating unit 312 Movement probability parameter estimating unit 314 Writing unit 320 Reading unit 322 Gradient calculating unit 324 Optimization unit 326 Convergence determining unit 328 Writing unit 360 Reading unit 362 Moving probability calculation Department 364 Population Forecasting Department

Claims (6)

Based on the flow data representing the number or density of people moving from the point i to the point j in the vicinity of the point i at each time t and each point i, from the point i to the cluster k to which each time t belongs. each time in the parameters and one day the person to each point j in the vicinity of the point i represents the distribution of the movement probability representing the probability of moving includes the probability of belonging to each cluster, the human at each time t and each location i A parameter estimator for estimating the parameters of the flow model for estimating the flow;
Based on the population data representing the number or density of people at each time t and each point i and the parameters of the flow model estimated by the parameter estimation unit, from the point i at each time t and each point i A flow estimator for estimating flow data representing the number or density of the person moving to the point j in the vicinity of the point i;
An end determination unit that repeatedly performs each process by the parameter estimation unit and the flow estimation unit until a predetermined end condition is satisfied;
Including
The parameter estimation unit estimates a parameter of the flow model based on the flow data estimated by the flow estimation unit. Based on the flow data representing the number or density of people moving from the point i to the point j in the vicinity of the point i at each time t and each point i, from the point i to the cluster k to which each point i belongs. Estimate the flow of a person at each time t and each point i, including a parameter representing the probability distribution of the person moving to each point j near the point i and the probability that each point belongs to each cluster. A parameter estimator for estimating the parameters of the flow model for
Based on the population data representing the number or density of people at each time t and each point i and the parameters of the flow model estimated by the parameter estimation unit, from the point i at each time t and each point i A flow estimator for estimating flow data representing the number or density of the person moving to the point j in the vicinity of the point i;
An end determination unit that repeatedly performs each process by the parameter estimation unit and the flow estimation unit until a predetermined end condition is satisfied;
Including
The parameter estimation unit estimates a parameter of the flow model based on the flow data estimated by the flow estimation unit. The parameter estimation unit includes:
Based on the flow data estimated by the flow estimation unit, the probability q _sk that each time s in a day belongs to each cluster k, and the parameter α _j representing the prior distribution of the movement probability of moving to the point j. , For each combination of the cluster k and the point i, a parameter ^ α _ki representing the distribution of the movement probability is estimated, and from the estimated parameter ^ α _ki , the person at the point i of the cluster k is estimated . A movement probability estimator for estimating the distribution of the movement probability ^ θ _ki ;
Based on the probability q _sk of each time s belonging to each cluster k, a parameter β _k representing the distribution of the cluster distribution φ of the cluster _k is estimated for each of the clusters k, and from the estimated parameter β _k , A cluster distribution estimation unit for estimating a distribution of the cluster distribution φ of the cluster k;
Probability q _sk each time s belongs to each cluster k, based the time accuracy eta _k of each cluster k, for each of the cluster k, estimates parameters d _k and f _k representing the distribution of the time average tau _k An average estimator for estimating the distribution of time average τ _k from the estimated parameters d _k and f _k ;
Probability q _sk each time s belongs to each cluster k, based with the parameters f _k of each cluster k, for each of the clusters k, the parameters a _k and b _k representing the distribution of the time accuracy eta _k An accuracy estimation unit that estimates and estimates the distribution of time accuracy η _k from the estimated parameters a _k and b _k ;
Based on the flow data estimated by the flow estimation unit and the parameters ^ α _ki , β _k , a _k , b _k , d _k , f _k of each cluster k, the cluster k and the time s For each combination, a cluster estimator for estimating the probability q _sk of time s belonging to cluster k;
A movement probability parameter estimator for estimating a parameter α _j representing a prior distribution of movement probabilities of moving to the point j for each point j based on the parameters ^ α _ki of each cluster k;
The flow estimation apparatus according to claim 1, comprising: The flow estimation unit is based on the population data, the parameter ^ α _ki of each cluster k and the probability q _sk that each time s belongs to each cluster k estimated by the parameter estimation unit, and the flow data. 4. The flow estimation according to claim 3, wherein a gradient of an objective function for estimating the flow data is calculated, and the flow data is estimated to maximize the objective function based on the calculated gradient. apparatus. Based on the parameters of the flow model estimated by the flow estimation device according to any one of claims 1 to 4, the person moves from the point i to a point j near the point i at time t. A movement probability calculation unit for estimating a movement probability representing a movement probability;
A prediction unit that predicts the number or density of people at each point i at time t + 1 from the movement probability estimated by the movement probability calculation unit and population data representing the number or density of people at the time t and each point i; ,
A prediction device including:   The program for functioning a computer as each part of the flow estimation apparatus of any one of Claims 1-4, or the prediction apparatus of Claim 5.