JP2018195215A - People flow rate prediction device, people flow rate prediction method and people flow rate prediction program - Google Patents

Abstract

To accurately predict people flow rate at each observation point at each point of time.SOLUTION: On the basis of set data including people inflow rate at each point of time at each of a plurality of observation points, set data including people outflow rate at each point of time at each of the plurality of observation points, data on the number of observed people showing the number of people moving at each point of time outflowing from one direction to another direction for each of pairs of observation points, and observation time data showing movement time for each of pairs at the observation points, obtained by observing specific plural people, in order to optimize an object function, a parameter of transition probability, a parameter of movement time and a latent variable are estimated, inputs of a target observation point to be a prediction object and a predicted point of time are accepted and thereby a predicted inflow rate at the target observation point at the predicted point of time is calculated.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a human flow prediction device, a human flow prediction method, and a human flow prediction program for predicting a future human flow at an observation point.

  Human position information obtained from sensors, GPS (Global Positioning System), etc. may be provided as aggregated data so that individuals cannot be tracked from the viewpoint of privacy. Collective data refers to data obtained by collecting samples with a certain granularity with respect to time and space.

  Specifically, the number of people who flowed out from a certain observation point i (flowing amount) and the number of people who flowed into a certain observation point i (flowing amount) at a certain observation time t are given. As a conventional technology, the connection between observation points where humans move is expressed in a graph, and the flow of people on the graph is expressed by a probability model, so that the number of people moving between observation points is estimated based on aggregate data, A method (Collective Flow Diffusion Model) for predicting future human flow has been proposed (see, for example, Non-Patent Document 1).

  Further, in such a conventional technique, “the total number of people who flowed out from an arbitrary observation point at a certain observation time t is equal to the total number of people who flow into an arbitrary observation point at the next observation time (t + 1)”. An algorithm that can learn a probability model while estimating the number of people moving between observation points has been proposed by solving an optimization problem that takes into account the constraint of “preserving the number of people moving” (for example, Non-Patent Document 2). reference).

  By using the learned probabilistic model, it is possible to predict the amount of inflow to each observation point at a future time t ′ when the outflow amount from each observation point at the observation time (t′−1) is given. is there.

A. Kumar, D. Sheldon, and B. Srivastava, “Collective Diffusion over Networks: Models and Inference”, In Proceedings of International Conference on Uncertainty in Artificial Intelligence (UAI), pp. 351-360, 2013. D. Sheldon, T. Sun, A. Kumar, and T. G. Dietterich, “Approximate Inference in Collective Graphical Models”, In Proceedings of International Conference on Machine Learning (ICML), pp. 1004-1012, 2013.

  As described above, in the prior art, “the total number of people who flowed out from an arbitrary observation point at a certain observation time t is equal to the total number of people who flow into an arbitrary observation point at the next observation time (t + 1)”. It is possible to learn a probability model while estimating the number of people moving between observation points based on the aggregated data by solving the optimization problem that takes into account the constraint of “preserving the number of people moving”.

  Imposing the restriction indicating “preservation of the number of people moving” as described above is natural when data from a dense observation point that covers all the space in which the user moves is obtained. This is because dense observation points mean that each person is always observed at some observation point at each time.

  However, considering application to real problems, it is not always possible to assume spatially dense observation points. For example, in a large exhibition event venue, it is conceivable that the inflow and outflow of people can be observed by sensors only at each exhibition booth. As in this example, in a situation where the observation points are spatially sparse, a time delay occurs between the outflow time and the inflow time of the person between the observation points. In other words, it is necessary to consider the travel time between observation points. In such a case, there has been a problem that the prior art is difficult to apply.

  Further, in practical situations, detailed tracking is possible for a small number of users, but only aggregate data may be obtained for most other users. For example, it is possible to track using a Wi-Fi identifier for a small number of users, but for a large number of users, only collective data can be acquired by a camera placed at an observation point. Combining these data (collected data and traceable user movement history) can be expected to improve human flow estimation accuracy. However, the conventional technique has a problem that it is difficult to apply to such data.

  The present invention has been made in view of the above circumstances, and a human flow prediction device, a human flow prediction method, and a human flow prediction program capable of accurately predicting the human flow at each observation point at each time point. The purpose is to provide.

  In order to achieve the above object, the human flow prediction device of the present invention is configured to collect data consisting of inflow amounts of people at each time at each of a plurality of observation points, and outflow of people at each time at each of the plurality of observation points. Collected data consisting of quantity, observed for a specific number of people, observed number data representing the number of people moving at each time flowing from one to the other for each pair of observation points, and observed for a specific number of people , Based on observation time data representing the travel time for each of the observation point pairs, the inflow amount set data, the outflow amount set data, the observation number data, the observation time data, and the observation point pair A latent variable indicating the number of people moving at each time flowing out from one to the other for each of the above, the transition probability that the person moves from one to the other for each of the observation point pairs. And a parameter estimator for estimating the transition probability parameter, the travel time parameter, and the latent variable so as to optimize the objective function expressed using the travel time for each of the observation point pairs. A search unit that accepts input of a target observation point to be predicted and a prediction time, and a parameter of transition probability estimated by the parameter estimation unit to move from an observation point other than the target observation point to the target observation point , Travel time parameters for a pair of the observation point other than the target observation point and the target observation point, and the observation point other than the target observation point from the observation point other than the target observation point toward the target observation point. Based on the number of people who have flowed out and the amount of outflow from observation points other than the target observation point for a time prior to the prediction time. Comprising the predicted human flow rate calculation unit for calculating a predicted flow rate of the target observation point in time, the.

  The parameter estimator uses an EM algorithm to fix the transition probability parameter and the travel time parameter to calculate the latent variable, and to fix the latent variable. The transition probability parameter, the travel time parameter, and the latent variable that optimize the objective function may be estimated by repeating the M step of calculating the travel time parameter.

  The predictor flow rate calculation unit calculates a predicted outflow amount of the target observation point at the prediction time based on a predicted inflow amount of the target observation point at the prediction time, and The transition of the population at the target observation point may be calculated based on the inflow amount of people, the outflow amount of people at each time, the predicted inflow amount, and the predicted outflow amount.

  In order to achieve the above object, the human flow rate prediction method of the present invention is a human flow rate prediction method in a human flow rate prediction apparatus comprising a parameter estimation unit, a search unit, and a predicted human flow rate calculation unit, wherein the parameter estimation unit Is a set of data consisting of the inflow of people at each time at each of a plurality of observation points, a set of data consisting of the outflow of people at each time at each of the plurality of observation points, and observed for a specific plurality of people, Observation number data indicating the number of moving persons at each time for each observation point pair flowing out from one side to the other, and observation indicating the movement time for each of the observation point pairs observed for a plurality of specific persons Based on the time data, one set for each of the inflow volume data, the outflow volume data, the observation number data, the observation time data, and the observation point pair. A latent variable representing the number of people traveling at each time flowing out from one to the other, the transition probability that a person moves from one to the other for each of the observation point pairs, and the movement time for each of the observation point pairs Estimating the transition probability parameter, the travel time parameter, and the latent variable so as to optimize the objective function expressed by using the target observation point to be predicted by the search unit, and A step of receiving an input of a prediction time; a parameter of a transition probability that the predictor flow rate calculation unit moves from an observation point other than the target observation point to the target observation point, which is estimated by the parameter estimation unit; Parameters of travel time for pairs of observation points other than the point and the target observation point, and other than the target observation point for a time before the predicted time The target at the predicted time based on the number of people that have flowed out from the observation point toward the target observation point and the amount of outflow from observation points other than the target observation point for a time before the predicted time And a step of calculating a predicted inflow amount at the observation point.

  In order to achieve the above object, the program of the present invention is a program for causing a computer to function as each part of the human flow rate prediction apparatus.

  According to the present invention, it is possible to accurately predict the human flow rate at each observation point at each time.

It is a block diagram which shows the functional structure of the human flow prediction apparatus which concerns on embodiment of this invention. It is a schematic diagram which shows an example of the information stored in the inflow amount storage part of the human flow prediction apparatus which concerns on embodiment of this invention. It is a schematic diagram which shows an example of the information stored in the outflow amount storage part of the human flow prediction apparatus which concerns on embodiment of this invention. It is a schematic diagram which shows an example of the information stored in the movement history storage part of the human flow prediction apparatus which concerns on embodiment of this invention. It is a graph which shows the shape of Rayleigh distribution at the time of changing parameter (sigma) _ji used with the human flow prediction apparatus which _concerns on embodiment of this invention. It is a graph which shows the cumulative distribution function in [t-1, t] of the Rayleigh distribution used with the human flow prediction apparatus which concerns on embodiment of this invention. It is a flowchart which shows the flow of the parameter estimation process performed in the human flow prediction apparatus which concerns on embodiment of this invention. It is a flowchart which shows the flow of the prediction human flow calculation process performed in the human flow prediction apparatus which concerns on embodiment of this invention. It is a schematic diagram which shows an example of the output content from an output part when the search part of the human flow prediction apparatus which concerns on embodiment of this invention searches.

  Hereinafter, an embodiment of a human flow prediction device according to the present invention will be described with reference to the drawings.

  The human flow rate prediction apparatus according to the present embodiment expresses a connection between observation points where a person moves by a graph, incorporates a movement time between observation points, and expresses a flow of people on the graph by a probability model. In addition, the human flow prediction device according to the present embodiment has a function of learning a probability model while estimating the number of moving people between observation points based on the set data of position information, and uses a learned probability model. Predicts the human flow rate at an arbitrary time.

  In the present embodiment, a collection of various pieces of position information is targeted, and can be applied flexibly according to the collection data obtained by observation.

  Note that the position information referred to here is position information acquired by an indoor or outdoor sensor (BLE (Bluetooth (registered trademark) Low Energy) or the like), a camera, Wi-Fi, or the like. Further, the collective data here refers to data obtained by collecting samples with a predetermined granularity with respect to time and space. Further, it is assumed that the aggregate data targeted here cannot be traced as to where the individual went from where.

  On the other hand, when there are a small number of users that can be tracked by using Wi-Fi identifiers, the data is used as additional information. In the following, as an example, learning of a probability model is performed while estimating the number of people moving between observation points under conditions given general location information set data and movement history for a small number of users. A case where the human flow rate is predicted at the time will be described. Here, model estimation is possible even if there is no movement history for a small number of users as additional information.

  Hereinafter, as an embodiment, learning of a probabilistic model is performed while estimating the number of people moving between observation points under a condition where general set of position information is given, and human flow rate is predicted at a future time The case will be described.

  FIG. 1 is a block diagram showing a functional configuration of a human flow prediction device 100 according to the present embodiment. As shown in FIG. 1, the human flow prediction device 100 includes an inflow amount storage unit 1, an outflow amount storage unit 2, a movement history storage unit 12, an operation unit 3, a search unit 4, a human flow model learning unit 5, and a parameter estimation unit. 6, a transition probability parameter storage unit 7, a moving person storage unit 8, a travel time parameter storage unit 9, a predicted person flow rate calculation unit 10, and an output unit 11.

  Among these, the operation unit 3 and the parameter estimation unit 6 are connected to the inflow amount storage unit 1, the outflow amount storage unit 2, and the movement history storage unit 12. Further, the predictor flow rate calculation unit 10 is connected to the outflow amount storage unit 2.

  The inflow amount storage unit 1 is set data that can be analyzed by the human flow prediction device 100, and stores collective data that includes inflow amounts of people at each time at a plurality of observation points. The inflow amount storage unit 1 reads the requested set data in accordance with a request from the human flow model learning unit 5, and transmits the read set data to the human flow model learning unit 5.

For example, when the observation point is i and the observation time is t, the inflow of a person at the observation point i is represented as N _ti ^IN . The data format stored in the inflow amount storage unit 1 is represented as (i, t, N _ti ^IN ). This data format means that N _ti ^IN people flowed in from the observation point i at time t. The inflow amount storage unit 1 may be configured by a database server or the like that includes a Web server and a database.

  As an example, as shown in FIG. 2, the inflow amount storage unit 1 stores an observation point ID for identifying an observation point, an inflow amount (number of people), and an observation time in association with each time step. Yes.

  The outflow amount storage unit 2 is set data that can be analyzed by the human flow prediction device 100, and stores collective data that includes the amount of outflow of a person at each time at a plurality of observation points. The outflow amount storage unit 2 reads the requested set data in accordance with a request from the human flow model learning unit 5 and transmits the read set data to the human flow model learning unit 5.

For example, when the observation point is i and the observation time is t, the amount of human outflow at the observation point i is represented as N _ti ^OUT . The data format stored in the outflow amount storage unit 2 is represented as (i, t, N _ti ^OUT ). This data format means that N _ti ^OUT persons flowed out from the observation point i at time t. The outflow amount storage unit 2 may be configured by a database server or the like that includes a Web server and a database.

  As an example, as shown in FIG. 3, the outflow amount storage unit 2 stores an observation point ID for identifying an observation point, an outflow amount (number of people), and an observation time in association with each time step. Yes.

  The movement history storage unit 12 stores movement history set data for a small number of users that can be analyzed by the human flow prediction device 100. The movement history storage unit 12 reads the requested set data in accordance with a request from the human flow prediction device 100 and transmits the read set data to the device.

The data format stored in the movement history storage unit 12 is represented as (u, i, t ^out , j, t ⁱⁿ ). This data format means that user u leaves observation point i at time t ^out and arrives at observation point j at time t ⁱⁿ . The movement history storage unit 12 may be configured by a database server or the like that includes a Web server and a database.

  For example, as shown in FIG. 4, the movement history storage unit 12 identifies a user ID, a departure observation point ID for identifying a departure observation point, a departure time, and an arrival observation point for each movement of the user. The arrival observation point ID and the arrival time are stored in association with each other.

  The operation unit 3 receives various operations from the user with respect to the collective data stored in the inflow amount storage unit 1, the outflow amount storage unit 2, and the movement history storage unit 12. The various operations here include an operation for registering stored data, an operation for correcting, and an operation for deleting. The operation unit 3 includes a keyboard, a mouse, a touch panel, and the like as input means, and is realized by a device driver of these input means, control software for a menu screen, and the like.

  The search unit 4 receives an input of a target observation point i for which a human flow rate is to be predicted and a predicted time t ′. Based on the target observation point i and the predicted time t ′ received by the search unit 4, the predicted human flow rate at the predicted time t ′ at the target observation point i calculated by performing the process described later by the predicted human flow rate calculation unit 10. Is output.

  The search unit 4 includes a keyboard, a mouse, a touch panel, and the like as input means, and is realized by a device driver of these input means, control software for a menu screen, and the like.

  The human flow rate model learning unit 5 includes a parameter estimation unit 6, a transition probability parameter storage unit 7, a moving number storage unit 8, and a travel time parameter storage unit 9.

  The parameter estimation unit 6 includes the inflow amount set data stored in the inflow amount storage unit 1, the outflow amount set data stored in the outflow amount storage unit 2, and the movement stored in the movement history storage unit 12. Get historical data. In addition, the parameter estimation unit 6 observes a specific plurality of persons based on the movement history set data, and indicates the number of persons moving at each time point that flows out from one to the other of each pair of observation points. Data and observation time data representing the travel time for each observation point pair observed for a plurality of specific persons are obtained. In addition, the parameter estimation unit 6 determines the number of moving people at each time that flows out from one to the other for each of the inflow volume data, the outflow volume data, the observation number data, the observation time data, and the observation point pair. Transition to optimize the objective function expressed using the latent variable to represent, the transition probability that a person moves from one to the other for each observation point pair, and the movement time for each observation point pair Estimate probability parameters, travel time parameters, and latent variables.

  The parameter estimation unit 6 causes the transition probability parameter storage unit 7 to store the estimated transition probability parameter. The parameter estimation unit 6 stores the number of moving people estimated as a latent variable in the moving number of people storage unit 8. Furthermore, the parameter estimation unit 6 stores the estimated travel time parameter in the travel time parameter storage unit 9.

  The predictor flow rate calculation unit 10 is a parameter of a transition probability of moving from an observation point other than the observation point (target observation point to be predicted) received by the search unit 4 to the target observation point, an observation point other than the target observation point, and The parameter of the travel time for the pair with the target observation point, and the number of people that flowed from the observation point other than the target observation point toward the target observation point for the time before the predicted time received by the search unit 4 The predicted inflow amount at the target observation point at the prediction time is calculated based on the outflow amount from the observation point other than the target observation point for the time before the prediction time.

  In the present embodiment, when creating the human flow model, the transition probability parameter, the travel time parameter, and the latent variable representing the number of people are incorporated into the human flow model, and the connection between observation points is graphed. Express the flow of people on the graph using a probability model.

  Hereinafter, a probability model expressing the flow of people will be described with reference to the drawings.

  <Observation data>

  Here, consider a situation in which a person moves on a complete graph G = (V, E), which is a graph having a branch between any two vertices. V represents a node set, and E represents an edge set.

Node i corresponds to an observation point, and edge E corresponds to a path connecting the observation points. The number of people flowing out from the node iεV at time t is N _ti ^OUT, and the number of people flowing into the node iεV at time (t + 1) is N _{t + 1, i} ^IN . When the number of observation time steps is T,

The inflow of people at the observation point is

It is expressed.

<Observation data (additional information)>
In addition, the number of persons who move from observation point i to observation point j at time t, which can be calculated using the set data (u, i, t ^out , j, t ⁱⁿ ) stored in movement history storage unit 12 is L _{Let tij} be the number of people moving from observation point i to another observation point j

It expresses. Also,

And

<Observation time data (additional information)>
In addition, the n-th sample of the travel time taken when moving from the observation point i to the observation point j is Δ _ijn, and all samples included in the observation data are put together, and Δ _ij = {Δ _ijn | n = 1 ,..., N _ij }. Here, N _ij is the total number of samples moved from observation point i to observation point j included in the observation data.

  <Model parameters>

Transition probability that a person moves from node i to node j

And Here, the node set V _\ i represents a set obtained by removing the node i from the node set V. Further, θ _ij ≧ 0 and Σ _{j∈V \ i} θ _ij = 1 are satisfied. Collective set of transition probabilities between all nodes

It expresses.

Further, a parameter for controlling the degree of time required for the movement from the node i to the node j is assumed to be σ _ij > 0. Collective set of parameters for all nodes

It expresses.

<Latent variable>

The number of people moving from node i to node j at time t is M _tij, and the number of people moving from node i to another node j is collectively

It expresses. These values are not observable,

Is a latent variable.

<Model>

Using a stochastic model, the generation process of the collective data N ^IN of the inflow of people at the observation point and the collective data N ^OUT of the outflow of humans at the observation point under the condition that the model parameters Θ and Σ are given using a probability model. Model. First, it is assumed that the moving number _Mti is generated from a multinomial distribution of the following equation (1).

... (1)

  Next, under the condition where M is obtained, two values shown in the following formulas (2) and (3) are defined.

... (2)

... (3)

Here, the equation (2) represents the number of people flowing out from the node i at the time t, and the equation (3) represents the number of people flowing into the node i at the time (t + 1). Q _τji (t) is a factor for considering the travel time between nodes, and represents the probability of leaving node j at time τ and arriving at node i at time t. N _ti ^OUT and N _{t + 1, i} ^IN are assumed to be generated from Poisson distributions shown in the following formulas (4) and (5), where A _ti and B _{t + 1, i} are averages.

... (4)

... (5)

Here, M _{··· , i} = {M _τji | τ = 1,..., T, j∈V _{\ i} }, σ _{·, i} = {σ _{j, i} | j∈V _{\ i} }.

Next, Q _τji (t) is modeled using the cumulative distribution function of the Rayleigh distribution. At this time, another probability distribution such as a Weibull distribution may be used. The Rayleigh distribution is expressed by the following formula (6) and satisfies the following formula (7).

... (6)

... (7)

FIG. 5 shows an example of the shape of the Rayleigh distribution. By changing the parameter σ _{ji of the} Rayleigh distribution, it is possible to represent different travel times (time delays from departure to arrival) between observation points. In Figure 5, sigma _ji = 0.5 graph 20, sigma _ji = 1.0 in the graph 21, the order of the graph 22 of sigma _ji = 2.0, indicates that the time it takes to move between the observation points is long Yes.

  Next, when the cumulative distribution function of the Rayleigh distribution at [t−1, t] is calculated, the following equation (8) is obtained.

... (8)

FIG. 6 shows an example of the cumulative distribution function Q _τji (t) of the Rayleigh distribution in a certain time interval [t−1, t]. Q _τji (t) is equal to the area of the region 23 indicated by shading in FIG. Q _τji (t) thus determined is incorporated into the above equation (3).

Next, the generation process of the true number of people _Lti for a small number of users under the condition that the model parameter Θ is given is modeled by a probability model. It is assumed that L _ti is generated from a multinomial distribution as shown in the following equation (9). Here, L _ti ^OUT = _{Σj∈V \ i} L _tij .

... (9)

Further, the generation process of the travel time Δ _ijn for a small number of users under the condition that the model parameter Σ is given is modeled by a probability model. It is assumed that the movement time Δ _ijn is generated from the Rayleigh distribution as shown in the following equation (10).

(10)

  The parameter estimation unit 6 assumes that the observation data is generated according to the above-described probability model using the collective data stored in the inflow amount storage unit 1, the outflow amount storage unit 2, and the movement history storage unit 12 as learning data. Above, the unknown variable of the parameter showing the parameter of the transition probability between observation points, the number of people moving between observation points, and the movement time between observation points is estimated. These unknown variables can be estimated by various estimation methods such as an EM algorithm (Expectation-maximization algorithm) and Markov chain Monte Carlo sampling. Here, a method for estimating parameters based on the EM algorithm will be described.

<Parameter estimation method based on EM algorithm>

By marginalizing the likelihood function P (N ^OUT , N ^IN , M | Θ, Σ) of the complete data {N ^OUT , N ^IN , M} with respect to the latent variable M, the observation data {N ^OUT , N ^IN } The likelihood function is expressed as shown in the following equation (11).

... (11)

The log likelihood function logP (N ^OUT , N ^IN | Θ, Σ) is used as an objective function, and a parameter that maximizes the objective function is desired. However, it is difficult to obtain a solution in the closed form for the above equation (9). Therefore, an EM algorithm (see Non-Patent Document 3 below) is used.

[Non-Patent Document 3] B.M. Bishop, Pattern Recognition and Machine Learning, Springer, pp. 450-455, 2006.

  The Q function is a function represented by the following equation (12).

(12)

Here, the parameter set before update is φ = {Θ, Σ}, and the parameter set after update is

It was. Equation (12) above is the posterior distribution

Is used to calculate the weighted average (expected value) of logP (N ^OUT , N ^IN , M | Θ, Σ).

  However, since it is difficult to take the sum for all possible moving persons M, approximation is performed using the MAP (Maximum a posteriori) estimated value of the moving persons M.

  Based on posterior probability maximization, the following equation (13) is obtained.

... (13)

Is used to approximate the Q function as shown in the following equation (14).

... (14)

  In the said nonpatent literature 2, it is experimentally shown that said (14) Formula becomes a good approximation with respect to said (12) Formula. Further, the maximum likelihood estimated value can be obtained by maximizing the equation (14) with respect to the parameters Θ and Σ.

  The parameters Θ and Σ can be estimated by repeating the following E-step and M-step according to the procedure of the EM algorithm.

  << E-step >>

MAP estimation,

Is obtained.

  << M-step >>

Estimate parameters Θ and Σ that maximize.

  Next, a specific method for deriving E-step and M-step will be described.

<Derivation method of E-step>

  The posterior probability of the moving number M is expressed by the following equation (15) from Bayes' theorem.

... (15)

  However, the right side first factor of the above formula (15) is the following formula (16), the right side second factor is the following formula (17), and the right side third factor is the following formula (18).

... (16)

... (17)

... (18)

  Taking the logarithm on both sides of the above equation (15) and taking out only the term relating to the number M of moving people, the following equation (19) is obtained. Here, Stalin approximation logM! ~ MlogM-M is used.

... (19)

  The optimization problem to be solved is the following equation (20).

... (20)

This optimization problem can be solved by the L-BFGS-B method (see Non-Patent Document 4 below) that can consider the domain of the variable M _tij as a constraint.

[Non-Patent Document 4] RH Byrd, P. Lu, J. Nocedal, and C. Zhu, “A Limited Memory Algorithm for Bound Constrained Optimization”, SIAM Journal on Scientific Computing, vol. 16, pp. 1190-1208, 1995 .

<Method for deriving M-step>

  The Q function can be expressed as the following equation (21). Parameters Θ and Σ are obtained by maximum likelihood estimation according to the following equation (21).

... (21)

A method for estimating the parameter Θ will be described. The method of estimating Θ differs depending on whether or not the true number of people L for a small number of users as additional information is available. First, a case where additional information is not available will be described. _Taking only the term relating to the parameter Θ from the above equation (21) and considering that Σ _{jεV \ i} θ _ij = 1, the objective function is expressed as the following equation (22). Note that η is a Lagrange multiplier. Also,

It was.

... (22)

When the above equation (22) is differentiated with respect to θ _ij and set to 0, the following equation (23) is obtained.

... (23)

  When the above equation (23) is modified and the sum of j on both sides is taken, the following equation (24) is obtained.

... (24)

Then, the following equation (25) is obtained.

... (25)

By substituting the above equation (25) into the above equation (23), the following equation (26) which is the maximum likelihood estimated value is obtained.

... (26)

Next, a method for estimating the model parameter Θ when the observation number data L as additional information is available will be described. The first term of the above expression (22) is taken out and is defined as the following expression (27).

... (27)

Next, since it is assumed that the generation model of the observation number data L is given by the above equation (9), the log likelihood function of the model parameter Θ when the observation number data L is given is L _ij = _Assuming Σ _t L _tij , the following equation (28) is used.

... (28)

_Taking into account the above equations (27) and (28) and considering that Σ _{jεV \ i} θ _ij = 1, the new objective function is described as the following equation (29). Here, ξ is a hyper parameter for controlling the degree of contribution to the estimation of the additional information, and can be determined using a cross-validation method or the like.

... (29)

The maximum likelihood estimated value can be obtained in a closed format, and the following equation (30) is obtained.

... (30)

Next, a method for estimating the model parameter Σ will be described. The method of estimating Σ differs depending on whether the travel time Δ _ijn for a small number of users, which is additional information, is available or not. First, a case where observation time data as additional information is not available will be described. If only the term relating to the model parameter Σ is extracted from the above equation (20), the objective function is expressed as the following equation (31).

... (31)

  The optimization problem to be solved is the following equation (32).

... (32)

This optimization problem can be solved by the L-BFGS-B method (see Non-Patent Document 4 above) that can consider the domain of the variable σ _ji as a constraint. Next, an estimation method in the case where travel time _Δijn for a small number of users as additional information can be obtained will be described. Since generation model delta _ijn is assumed that given by equation (10), when formed into a delta _ijn is given, the log-likelihood function of Σ is described as follows (33) The

... (33)

The new objective function is represented by the following equation (34). Here, ω is a hyperparameter for controlling the degree of contribution to the estimation of the additional information, and can be determined using a cross-validation method or the like. The optimization problem to be solved is the following equation (35).

... (34)

... (35)

The transition probability parameter storage unit 7 is a parameter obtained by the parameter estimation unit 6.

The data indicating is stored. The transition probability parameter storage unit 7 may be any storage device that can store and restore the data. For example, the transition probability parameter storage unit 7 itself may be a database, and the transition probability parameter storage unit 7 is a specific area of a general-purpose storage device (memory, hard disk device, etc.) provided in advance in the human flow prediction device 100. There may be.

The moving number storage unit 8 is a latent variable obtained by the parameter estimation unit 6.

The data indicating is stored. The moving number storage unit 8 may be any storage device that can store and restore the data. For example, the moving number storage unit 8 itself may be a database, and the moving number storage unit 8 is a specific area of a general-purpose storage device (memory, hard disk device, etc.) provided in advance in the human flow rate prediction device 100. Also good.

The travel time parameter storage unit 9 is a parameter obtained by the parameter estimation unit 6.

The data indicating is stored. The travel time parameter storage unit 9 may be any storage device that can store and restore the data. For example, the travel time parameter storage unit 9 itself may be a database, and the travel time parameter storage unit 9 is a specific area of a general-purpose storage device (memory, hard disk device, etc.) provided in advance in the human flow rate prediction device 100. There may be.

The predictor flow rate calculation unit 10 is a parameter stored in the transition probability parameter storage unit 7.

And a latent variable stored in the moving number storage unit 8

And parameters stored in the travel time parameter storage unit 9

And the outflow amount N _{t′−1, j} ^OUT from observation points other than the observation point i at time (t′−1 (one time step before the predicted time t ′)) stored in the outflow amount storage unit 2 Based on the above, the predicted flow rate of the observation point i at the prediction time t ′ (inflow amount to the observation point i) is calculated, and the predicted flow rate of the observation point i at the prediction time t ′ (flow rate to the observation point i). ) Will be described later.

  Here, the flow of the parameter estimation process executed by the parameter estimation unit 6 will be described with reference to FIG. FIG. 7 is a flowchart showing the flow of parameter estimation processing.

  In the present embodiment, the parameter estimation processing program is started at a predetermined operation timing using the operation unit 3.

In step S101, the parameter estimation unit 6 performs the latent variable

, Parameters

And parameters

Is initialized.

In step S103, the parameter estimation unit 6 initializes the collective data N ^IN of the inflow amount of people at the observation point and the collective data N ^OUT of the outflow amount of people at the observation point, or the step S105 described later or step S105. Based on the parameters Θ and Σ calculated in S107, the latent variable

Is calculated.

In step S105, the parameter estimation unit 6 sets the parameter according to the above equation (30) based on the moving number M calculated in step S103 and the observed number data L obtained from the movement history set data.

Is calculated.

In step S107, the parameter estimation unit 6 is based on the collective data N ^IN of the inflow amount of people at the observation point, the number of people M calculated in step S103, and the observation time data obtained from the collective data of the movement history. According to the above equation (35), parameters

Is calculated.

  In step S109, the parameter estimation unit 6 determines whether or not a predetermined convergence determination condition is satisfied. In the present embodiment, as a predetermined convergence determination condition, a predetermined convergence determination condition is set when the processes in steps S103 to S107 are repeated a predetermined number of times (for example, 1000 times). When it is determined in step S109 that the predetermined convergence determination condition is satisfied, the process proceeds to step S111. If it is determined in step S109 that the predetermined convergence determination condition is not satisfied, the process proceeds to step S103, and the processes in steps S103 to S107 are performed again using the calculated parameters.

In step S111, the parameter estimation unit 6 is calculated in step S103.

Is stored in the moving number storage unit 8, and the parameter calculated in step S105.

Is stored in the transition probability parameter storage unit 7, and the parameter calculated in step S107

Is stored in the travel time parameter storage unit 9, and the execution of the program for this parameter estimation process is terminated.

  Further, the flow of the human flow rate calculation process executed by the predicted human flow rate calculation unit 10 will be described with reference to FIG. FIG. 8 is a flowchart showing the flow of the human flow rate calculation process.

  In the present embodiment, the program for calculating the human flow rate is started at a timing at which a predetermined operation is performed using the operation unit 3.

  In step S <b> 201, the predicted human flow rate calculation unit 10 acquires the observation point i received by the search unit 4 and the predicted time t ′.

  In step S203, the predicted human flow rate calculation unit 10 initializes the temporary variable j to zero.

In step S205, the predictor flow rate calculation unit 10 determines whether or not the observation point j belongs to the node set V _\ i. If it is determined in step S205 that the observation point j belongs to the node set V _\ i (S205, Y), the process proceeds to step S207. If it is determined in step S205 that the observation point j does not belong to the node set V _\ i (S205, N), the execution of the personal flow rate prediction process program is terminated.

In step S207, the predictor flow rate calculation unit 10 starts the time (t′−1 (one time step before the prediction time t ′) from the observation point j∈V _\ i other than the observation point i specified by the search unit 4. Of people moving to observation point i

Is calculated according to the following equation (36).

... (36)

At this time, the parameters stored in the transition probability parameter storage unit 7

And the amount of human outflow N _{t′−1, j} ^OUT from observation point j∈V _\ i other than observation point i observed at time (t′−1).

  In step S209, the predicted human flow rate calculation unit 10 initializes the temporary variable τ to 1.

  In step S211, the predicted human flow rate calculation unit 10 determines whether or not the temporary variable τ is smaller than the predicted time t ′. If it is determined in step S211 that the temporary variable τ is smaller than the predicted time t ′ (S211, Y), the process proceeds to step S213. If it is determined in step S211 that the temporary variable τ is greater than or equal to the predicted time t ′ (S211, N), the process proceeds to step S217.

In step S213, the predicted human flow rate calculation unit 10 flows out of the observation point j∈V _\ i other than the observation point i at the time τ before the prediction time t ′, and the observation point i at the time t ′ with a time delay. The total sum C _t′ji of the inflow amount flowing into is calculated according to the following equation (37).

... (37)

At this time, the latent variable stored in the moving number storage unit 8

And parameters stored in the travel time parameter storage unit 9

And the sum C _{t′ji of the} inflow amount calculated in the previous step S213 is used.

  In step S215, the predicted human flow rate calculation unit 10 adds 1 to the temporary variable τ, and proceeds to step S111.

  In step S217, the predicted human flow rate calculation unit 10 adds 1 to the temporary variable j, and proceeds to step S105.

The output unit 11 outputs the predicted inflow amount for the observation point i designated by the search unit 4 based on the total inflow amount C _t′ji calculated by the predictor flow calculation unit 10 as described above. . At the same time, the output unit 11 outputs a predicted value of the population at the observation point i at a future time t ′ by using the predicted inflow amount. At this time, in order to calculate the population, a predicted outflow amount is required in addition to a predicted inflow amount at a future time t ′. As a method of calculating the predicted outflow, the ratio of the outflow to the population at the observation point i is obtained based on the outflow from the observation point i at the past time, and the predicted outflow at the future time t ′ according to this ratio. Use a method to calculate quantity. Thus, based on the predicted inflow amount at the observation point i at the future time t ′, the predicted outflow amount at the observation point i at the future time t ′ is calculated, and the inflow amount of the person at each time at the observation point i, Based on the outflow amount of the person at each time, the predicted inflow amount at the future time t ′, and the predicted outflow amount at the future time t ′, the transition of the population at the observation point i is calculated. Further, the output unit 11 includes parameters stored in the transition probability parameter storage unit 7.

The parameter stored in the travel time parameter storage unit 9 is a human flow graph representing the ease of human flow between observation points using

The result of visualizing the distribution representing the travel time for the movement between observation points is output using.

  Here, output is a concept including display on a display, printing on a printer, sound output, transmission to an external device, and the like. Further, the output unit 11 may or may not include an output device such as a display or a speaker. The output unit 11 is implemented by output device driver software, or output device driver software and output devices.

  Hereinafter, a specific example of the output screen 30 output by the output unit 11 will be described with reference to FIG.

  As an example, as illustrated in FIG. 9, the output screen 30 includes a search content display unit 31 for displaying search content. In the search content display unit 31, for example, data indicating the observation point ID and data indicating the predicted time t 'are displayed. Thereby, the user can know the predicted value of the population of the observation point indicated by the observation point ID at the future time t ′.

Further, the output screen 30 has a transition display section 32 for displaying the transition of the population at the observation point i ₁ . The transition display unit 32 displays, for example, the transition of the population at the observation point i ₁ according to the observation point ID received by the search unit 4 and the predicted time t ′. Thus, the user can analyze whether population in specified observation point i ₁ is any transition.

The output screen 30 also has a human flow graph display unit 33 for displaying a human flow graph between observation points. The pedestrian flow graph display unit 33, for example, two-dimensional map in which the flow is shown in humans to observation point i ₁ from each observation point is displayed. Thereby, the user can know the inflow amount from each observation point to the observation point i ₁ at the designated predicted time t ′.

The output screen 30 has an inflow amount display unit 34 for displaying the inflow amount from each observation point. The inflow amount display unit 34 is, for example, inflow from each observation point at specified prediction time t 'to the observation point i ₁ is shown in number table is displayed. Thus, the user can analyze whether people flowing from each observation point to the observation point i ₁ is flowing into the observation point i ₁ through the moving time how much from each observation point.

The output screen 30 has a travel time display unit 35 for displaying travel time from each observation point. The travel time display unit 35 displays, for example, a time-series graph showing the travel time from each observation point to the observation point i ₁ at the designated predicted time t ′. Thus, the user can analyze whether people flowing from each observation point to the observation point i ₁ is flowing into the observation point i ₁ through the moving time how much from each observation point.

  In the present embodiment, the case where the search unit 4 receives an input of a future time t ′ has been described, but the present invention is not limited to this. For example, the past time may be analyzed by receiving a past time in the search unit 4 and an analysis result regarding the past person flow may be output.

  Moreover, the human flow prediction apparatus 100 according to the present embodiment is configured by a computer apparatus including, for example, a CPU (Central Processing Unit), a RAM (Random Access Memory), and a ROM (Read Only Memory) that stores various programs. . Moreover, the computer which comprises the human flow prediction apparatus 100 may be provided with memory | storage parts, such as a hard disk drive and a non-volatile memory. In the present embodiment, the CPU reads and executes a program stored in a storage unit such as a ROM or a hard disk, whereby the hardware resources and the program cooperate to realize the above-described function.

  Further, in the present embodiment, the operation of the components of the function shown in FIG. 1 is constructed as a program and installed in a computer used as the human flow prediction device 100, but is not limited to this. It may be distributed.

  Further, the constructed program may be stored in a portable storage medium such as a hard disk, a flexible disk, or a CD-ROM, and installed in a computer or distributed.

DESCRIPTION OF SYMBOLS 1 Inflow amount storage part 2 Outflow amount storage part 3 Operation part 4 Search part 5 Human flow model learning part 6 Parameter estimation part 7 Transition probability parameter storage part 8 Traveling person number storage part 9 Travel time parameter storage part 10 Predictor flow rate calculation part 11 Output unit 100 Human flow prediction device

Claims (5)

Collective data consisting of the inflow of people at each time at a plurality of observation points, collective data consisting of the outflow of people at each time at each of the plurality of observation points, the observation points observed for a plurality of specific people Observation number data representing the number of persons moving at each time flowing out from one to the other for each of the pairs, and observation time data representing the movement time for each of the pair of observation points observed for a specific plurality of persons Based on the inflow amount data, the outflow amount data, the observation number data, the observation time data, and the number of moving persons at each time point that flowed from one to the other for each of the observation point pairs , A transition probability that a person moves from one to the other for each of the observation point pairs, and a movement time for each of the observation point pairs. A parameter estimating unit so as to optimize the objective function, the parameters of the transition probability parameters of the travel time, and for estimating the latent variables represented Te,
A search unit that accepts input of a target observation point to be predicted and a predicted time;
Parameters of transition probability estimated by the parameter estimation unit to move from an observation point other than the target observation point to the target observation point, travel time for a pair of the observation point other than the target observation point and the target observation point And the target observations for the time before the predicted time, and the number of people that flowed from the observation points other than the target observation point toward the target observation point, and the time before the predicted time. A predictor flow rate calculation unit that calculates a predicted inflow amount of the target observation point at the prediction time based on an outflow amount from an observation point other than a point;
Human flow prediction device with The parameter estimation unit includes an E step of calculating the latent variable by fixing the transition probability parameter and the movement time parameter by an EM algorithm, and fixing the latent variable to the transition probability parameter and the movement. The human flow prediction device according to claim 1, wherein the objective function is optimized by repeating M step for calculating a time parameter, and the transition probability parameter, the travel time parameter, and the latent variable are estimated. . The predicted human flow rate calculation unit calculates a predicted outflow amount of the target observation point at the predicted time based on a predicted inflow amount of the target observation point at the predicted time, and calculates a human flow at each time of the target observation point. The human flow prediction device according to claim 1 or 2, wherein a transition of a population at the target observation point is calculated based on an inflow amount, a human outflow amount at each time, the predicted inflow amount, and the predicted outflow amount. A human flow prediction method in a human flow prediction device including a parameter estimation unit, a search unit, and a predicted human flow calculation unit,
The parameter estimator is a set of data consisting of inflows of people at each time at each of a plurality of observation points, a set of data consisting of outflows of people at each time at each of the plurality of observation points, for a specific plurality of people Observed observation data representing the number of people moving at each time that flowed from one to the other for each of the observation point pairs, and the movement for each of the observation point pairs observed for a plurality of specific people Based on observation time data representing time, outflow from one to the other of each of the inflow volume data, the outflow volume data, the observation number data, the observation time data, and the observation point pair A latent variable representing the number of people moved at each time, a transition probability that a person moves from one to the other for each of the observation point pairs, and each of the observation point pairs A method to optimize the objective function, the parameters of the transition probability parameters of the travel time, and for estimating the latent variables represented using travel time for,
The search unit accepting input of a target observation point to be predicted and a predicted time;
The predictor flow rate calculation unit is a parameter of transition probability estimated by the parameter estimation unit to move from an observation point other than the target observation point to the target observation point, an observation point other than the target observation point, and the target observation. A parameter of travel time for a pair with a point, and the number of people that have flowed out from an observation point other than the target observation point toward the target observation point for a time before the prediction time, and before the prediction time Calculating a predicted inflow amount of the target observation point at the prediction time based on an outflow amount from an observation point other than the target observation point for the time of
A person flow prediction method.   The program for functioning a computer as each part of the human flow prediction apparatus of any one of Claims 1-3.