JP6088962B2 - Position coordinate estimation apparatus, method and program - Google Patents

Description

  The present invention relates to a position coordinate estimation apparatus, method, and program, and more particularly, to explain a process in which events (information transmission, buzzwords, illnesses, etc.) are spread and propagated through human beings. The present invention relates to a position coordinate estimation apparatus, method, and program for estimating the proximity of a position as a positional relationship.

  Information propagation analysis is a social network analysis method that connects people with events. This method assumes that a user's involvement in an event has occurred based on the influence of others around that user, and based on information on which event each user was involved in which event. The propagation rate between users (αji, where j is a propagation source user and i is a propagation destination user) indicating the ease of propagation between users is estimated (for example, see Non-Patent Document 1).

  In addition, a model in which this method is developed in the time series direction can cope with a change in propagation rate between users (for example, see Non-Patent Document 2).

  These prior art outputs use a directed graph in which the user is a node and the propagation rate between users is the edge weight between the nodes.

Manuel Gomez-Rodriguez, David Balduzzi, Bernhard Scholkopf: Uncovering the Temporal Dynamics of Diffusion Networks. ICML 2011: 561-568. Manuel Gomez-Rodriguez, Jure Leskovec, Bernhard Scholkopf: Structure and dynamics of information pathways in online media.WSDM 2013: 23-32.

  In the above prior art, if the total number of users to be analyzed is N, each user is characterized based on the relationship with other N-1 users. In other words, it is a technique for expressing each user with an N-dimensional feature amount including the relationship with the user.

  For example, suppose that it is desired to apply the output of the prior art to the apparatus and to understand the relationship between N people in a schematic manner. In that case, if the total number of users N becomes as large as 100, 10,000, 1,000,000, not only the number of users that must be compared increases but also in order to understand the relationship between each user. Since the amount of features that must be increased, it is difficult to process manually even if an easy-to-understand diagram is obtained.

  The number of dimensions of features that are easy for humans to handle and intuitively understand is 2 or 3. For example, the position information of the object in the real space may be expressed in two dimensions such as latitude and longitude, and may be expressed more three-dimensionally including the concept of height.

  In a method in which a user is arranged in a two-dimensional or three-dimensional space while repeating trial and error manually, a method that accurately reflects the propagation rate that should be expressed cannot always be obtained.

  The prior art does not have a method of compressing the N-dimensional feature quantity characterizing each user into a dimension that is easy for humans to handle.

  In the methods of Non-Patent Documents 1 and 2, N × (N−1) propagation rates had to be estimated mechanically. Since the number of parameters that the machine has to estimate on the order of the square of N increases, there is a problem that when N is a large value, the amount of calculation becomes enormous or the accuracy of estimation decreases.

  The present invention has been made in view of the above points. Characterizing each user in a D-dimensional (<< N-dimensional) latent space, the proximity of persons who are likely to generate propagation is represented by the D dimension ( An object of the present invention is to provide a position coordinate estimation apparatus, method, and program that can be described by the distance between feature quantities expressed in a << N-dimensional) latent space.

According to one aspect, assuming that event propagation from user to user is triggered in response to a distance relationship between users located in a latent space having at least one or more dimensions, A position coordinate estimation apparatus for estimating a position coordinate of a user,
Based on propagation history information, which is time information indicating that multiple users were involved in an observed event, the users who have a strong tendency to be related to the same or close time to the observed event are placed close together Repeating the process for all observed events while updating and converging each user's position coordinates to reasonably explain (ie, optimize) the latent events There is provided a position coordinate estimation apparatus having coordinate estimation means for uniquely determining the position coordinates of each user in the space and storing them in a coordinate storage means.

  According to one aspect, the model is assumed to be easy to propagate between users depending on the user's position coordinates expressed in the D-dimensional space, and the model is described in a reasonable manner to explain all observed events. By optimizing, the position coordinates of each user in the D-dimensional (<< N-dimensional) latent space are obtained. Thereby, the ease of propagation between users can be expressed by a distance relationship in a D-dimensional latent space smaller than the total number N of users.

  Also, for example, when D = 2 or D = 3, it can be developed as a two-dimensional or three-dimensional drawing, and the ease of propagation between users in a form that is easy for the user of the apparatus to understand. It is possible to present a distance relationship that reflects.

It is a structural example of the position coordinate estimation apparatus in one embodiment of the present invention. It is a flowchart of the coordinate estimation part in one embodiment of this invention. It is an example of the information stored in the propagation history memory | storage device in one embodiment of this invention. It is an example of the coordinate information stored in the coordinate memory | storage part in one embodiment of this invention. It is an example of a structure of the search part in one embodiment of this invention. It is an output example (coordinate estimation) of the output part in one embodiment of the present invention. It is an output example (propagation simulation) of the output part in one embodiment of this invention.

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

  FIG. 1 shows a configuration example of a position coordinate estimation apparatus according to an embodiment of the present invention.

  A position coordinate estimation apparatus 10 shown in the figure includes an operation unit 11, a search unit 12, a coordinate estimation unit 13, a coordinate storage unit 14, a propagation probability calculation unit 15, and an output unit 16. The operation unit 11 and the coordinate estimation unit 13 Are connected to an external propagation history storage device 20. In addition to the above configuration, a memory (not shown) that temporarily stores information input from the operation unit 11 and the search unit 12, a calculation result, and the like is also included.

  The propagation history storage device 20 stores propagation history information analyzed by the position coordinate estimation device 10, reads the propagation history information according to a request from the position coordinate estimation device 10, and transmits the information to the position coordinate estimation device 10. To do. In addition to the propagation history information, event information may be stored. As shown in FIG. 3A, typical propagation history information stored in the propagation history storage device 20 includes a user ID for uniquely identifying a user, and an event for which the user is involved. It consists of an event ID and time information related to the event. For example, when a buzzword information propagation analysis is handled in social media such as a blog, an event ID is assigned to each buzzword. Then, time information when each user transmits a buzzword is stored as propagation history information together with the user ID and event ID. Note that the propagation history information handled in the present invention may be anything as long as propagation occurs through a person, such as a disease infection history or a product purchase history. When dealing with a disease infection history, an event ID is assigned to each disease name, and when dealing with a product purchase history, an event ID is assigned to each product. Further, the time information may be time information when the user is involved in the event, or may be an elapsed time from the starting time when each event occurs after the time when the event first occurred. A time index such as the first and second observations may be used. The propagation history storage device 20 is a Web server that holds Web pages, a database server that includes a database, or the like.

  The operation unit 11 receives various operations from the operator for the propagation history storage device 20. The various operations are operations for registering, modifying, and deleting information stored in the propagation history storage device 20. The operation unit 11 can also present the propagation history information stored in the propagation history storage device 20 to the operator of the position coordinate estimation device 10. The input means of the operation unit 11 may be anything such as a keyboard, a mouse, a menu screen, or a touch panel. The operation unit 11 can be realized by a device driver of input means such as a mouse or control software for a menu screen.

  The search unit 12 specifies a condition for the output of the position coordinate estimation apparatus 10. An operator of the position coordinate estimation apparatus 10 receives various parameters (such as the number of dimensions of the latent space) of the coordinate estimation unit 13 as input, and outputs the coordinates of each user in the latent space estimated by the position coordinate estimation apparatus 10. Can be requested. It is also possible for the operator to generate a virtual event and request the position coordinate estimation apparatus 10 for the result of the propagation simulation. In this case, the operator inputs the user who generates the virtual event and the elapsed time since the virtual event occurs. The conditions relating to the propagation simulation are transferred to the propagation probability calculation unit 15. The input unit of the search unit 12 may be anything such as a keyboard, mouse, menu screen, or touch panel. The search unit 12 can be realized by a device driver of an input means such as a mouse or a menu screen control software.

  For simplification of explanation, the propagation model proposed in the present invention will be described before the explanation of the coordinate estimation unit 13 and the propagation probability calculation unit 15.

  The present invention is based on the concept of survival time analysis. Let T be the time when an event occurred. f (t) is the propagation probability density function of T,

は、その累積分布関数である。時間ｔまでにイベントが起きていない確率を示す生存関数S(t)は、以下の通りである。

Is the cumulative distribution function. The survival function S (t) indicating the probability that no event has occurred by time t is as follows.

伝搬確率密度関数f(t)と生存関数S(t)が与えられると、時間tまでにイベントが起きていない条件の下で、その直後にイベントが起き易い瞬間率として以下のハザード関数h(t)が定義できる。

Given the propagation probability density function f (t) and survival function S (t), under the condition that no event has occurred by time t, the following hazard function h ( t) can be defined.

これらの生存時間分析の基本的事項に基づき、位置座標推定装置１０では、あるユーザｊが時間t_jにあるイベントに関与した条件の下での、あるユーザiが時間t_iにそのイベントに関する可能性を示す関数を伝搬確率密度関数

Based on these basic items of survival analysis, the position coordinate estimation apparatus 10 allows a user i to relate to an event at time t _i under a condition in which a user j is involved in an event at time t _j. Probability density function

で表す。

Represented by

For example, when an exponential function is selected as the probability distribution of each function, the propagation probability density function f _ji (Δ _ji ), the hazard function h _ji (Δ _ji ), and the survival function S _ji (Δ _ji ) are as follows.

ここで、Δ_jiは時刻t_jから時刻t_iまでに経過した時間間隔、α_jiはユーザjからユーザiへの伝搬しやすさを示す変数である。位置座標推定装置１０においては、伝搬率α_jiは、D次元の潜在空間における各ユーザの座標の近さで決まると仮定する。

Here, Δ _ji is a time interval elapsed from time t _j to time t _i , and α _ji is a variable indicating ease of propagation from user j to user i. In the position coordinate estimation apparatus 10, it is assumed that the propagation rate α _ji is determined by the proximity of each user's coordinates in the D-dimensional latent space.

x_jはユーザjのD次元潜在空間上におけるD次元座標、またx_iはユーザiのD次元潜在空間上におけるD次元座標であり、どちらも次元数Dのベクトル値である。

x _j is a D-dimensional coordinate in the D-dimensional latent space of the user j, and x _i is a D-dimensional coordinate in the D-dimensional latent space of the user i, both of which are vector values of the dimension number D.

はD次元潜在空間上におけるユーザjの座標とユーザiの座標との間の距離を示す。βは座標間の距離の影響範囲を決定付けるパラメータであり、β＞0である。ユーザiとユーザjの潜在空間上における距離が近いほど、α_jiの値は高くなる。つまり、伝搬が起こりやすくなる。例えば、ブログなどのソーシャルメディアにおいて、流行語の情報伝搬分析を扱う場合には、ユーザ（ブログ）jと、ユーザ（ブログ）jにハイパーリンクを張っているユーザ（ブログ）iとの間には情報伝搬が起こりやすい。ハイパーリンクが存在しなくても、ユーザ（ブログ）iは、Webページのブックマーク機能や、検索エンジンなどの別の方法でユーザ（ブログ）jの発言に目を通しており、伝搬が起きるケースもある。位置座標推定装置１０はユーザ（ブログ）jがある流行語を発言すると、その直後にユーザ（ブログ）iも同じ流行語を発言するといった伝搬履歴情報が存在することを元に、２ユーザの距離

Indicates the distance between the coordinates of user j and the coordinates of user i in the D-dimensional latent space. β is a parameter that determines the influence range of the distance between coordinates, and β> 0. The closer the distance between user i and user j in the latent space is, the higher the value of α _ji is. That is, propagation is likely to occur. For example, in social media such as blogs, when handling buzzword information propagation analysis, between user (blog) j and user (blog) i that has a hyperlink to user (blog) j Information propagation is likely to occur. Even if the hyperlink does not exist, the user (blog) i may be observing the remarks of the user (blog) j by another method such as a bookmark function of a Web page or a search engine, and propagation may occur. When the position coordinate estimation apparatus 10 speaks a buzzword with a user (blog) j, immediately after that, the user (blog) i also speaks the same buzzword, and there is propagation history information.

を小さく、つまり、２ユーザの座標を近くに配置する（伝搬のしやすさを示すパラメータα_jiが大きくなる）よう座標を推定することができる。推定した座標は、「情報空間におけるユーザ間の近さ」を説明するものであり、流行語の伝搬が起き易いユーザ間の関係を説明するものである。

The coordinates can be estimated so that the coordinates of the two users are placed close to each other (the parameter α _ji indicating the ease of propagation is increased). The estimated coordinates explain “closeness between users in the information space”, and explain the relationship between users where buzzwords are likely to propagate.

  In addition, when dealing with a disease infection event, it is easy for a user i to have a disease infection from a user i who is close to the user j and living area (communication route, work place, residence) and human relations (relatives, friends, etc.). Conceivable. The position coordinate estimation apparatus 10 determines the distance between two users based on propagation history information that if a user j is infected with a certain disease, the user i is also infected with the disease immediately after that.

を小さく、つまり、２ユーザの座標を近くに配置する（伝搬のしやすさを示すパラメータα_jiが大きくなる）よう座標を推定することもできる。推定した座標の近さは、ユーザ間の生活圏の近さや、人間関係の近さなどを反映するものである。

It is also possible to estimate the coordinates so that the coordinates of the two users are arranged close to each other (that is, the parameter α _ji indicating the ease of propagation increases). The closeness of the estimated coordinates reflects the closeness of the living area between the users and the closeness of the human relationship.

  The coordinate estimation unit 13 will be described based on the above.

  The coordinate estimation unit 13 reads the propagation history information from the propagation history storage device 20 and estimates the coordinates of each user (node) in the D-dimensional latent space based on the propagation history information. The position coordinate estimation device 10 automatically estimates by maximizing the log-likelihood function for all the observation data (propagation history set) stored in the propagation history storage device 20 (minimizing the negative log-likelihood function). Is done. The negative log-likelihood function L of all observed data is as follows.

なお、イベントをc、

The event is c,

はユーザjにおいてイベントcが起きた時刻、

Is the time when event c occurred for user j,

はユーザiにおいてイベントcが起きた時刻をそれぞれ表し、

Represents the time at which event c occurred for user i,

である。実際は、式(7)に式(3)〜式(6)を代入した負の対数尤度関数を考える。

It is. Actually, consider a negative log-likelihood function obtained by substituting Equations (3) to (6) into Equation (7).

Then minimize negative log likelihood function (maximizing the log-likelihood function) for estimating the coordinates x _k of each user k. In the explanation so far, for the sake of explanation, j is the propagation source user and i is the propagation destination user, but here, each user regardless of whether it is the propagation source user or the propagation destination user. K is newly introduced as a variable to represent.

As a method for obtaining an optimal solution by a sequential search mathematical method, there is a solution method using a quasi-Newton method. In the quasi-Newton method, the current estimation parameter x _k is moved in the direction in which the value of the function L decreases based on the change of the gradient, while the function L is differentiable. It is a technique. In the quasi-Newton method, in order to calculate the change in the gradient of the function when the estimation parameter x _k is changed, an equation in which the function L is partially differentiated by each estimation parameter x _k is required. Street.

ユーザkに関するx_kの偏微分を考える場合、式(7)において、ユーザkが伝搬元の場合（k=jの場合）と、伝搬先の場合（k=iの場合）のケースに場合分けて偏微分し、それを最終的にまとめることで式(8)が求まる。式(8)においては、ユーザkに対する他のユーザを表す変数として新たにｌを導入している。具体的には、ユーザkが伝搬元の場合（k＝jの場合）における伝搬先iを、また、ユーザkが伝搬先の場合（k=iの場合）における伝搬元jを、変数ｌは表していることになる。ｌ'およびk'は累計演算するためのユーザを表す変数である。

When considering partial differentiation of x _k with respect to user k, in Equation (7), the case is divided into the case where user k is the propagation source (when k = j) and the case where propagation is the destination (when k = i). Equation (8) is obtained by partial differentiation and finally summing them up. In equation (8), l is newly introduced as a variable representing another user for user k. Specifically, the variable i is the propagation destination i when the user k is the propagation source (when k = j), and the propagation source j when the user k is the propagation destination (when k = i). It will represent. l ′ and k ′ are variables representing a user for cumulative calculation.

  FIG. 2 is a flowchart of the coordinate estimation unit in one embodiment of the present invention.

  What the position coordinate estimation device 10 wants to estimate is the coordinates for all users.

である。

It is.

When the number of dimensions D, the end condition Min Diff, and the maximum number of repetitions Max m are input, the coordinate estimation unit 13 stores these values in a memory (not shown) (step 101). The coordinates x _k of each user k is initialized to a random (step 102). Also, the temporary variable m is initialized to m = 0 (step 103).

The value L _m of the negative log likelihood function in the current estimated value is obtained by (7) (step 104), and Diff is obtained last time in the iterative processing from step 104 to step 111, ie, | L _m −L _m−1 | The absolute value of the difference from the log likelihood function value L _m−1 is set (step 105). If Diff ≦ Min Diff (step 106, Yes), the process ends. If Diff> Min Diff, a value _obtained by partial differentiation with respect to the coordinate x _k of the user k is calculated as kεK (K is the total number of users) by the equation (8) (step 108).

  The coordinates of all users are optimized using the quasi-Newton method (step 109). If m <Max m (step 110, Yes), m = m + 1 is set (step 111), and the processing from step 104 is repeated. . If M ≧ Max m (step 110, No), the process is terminated.

  The coordinate estimation unit 13 stores the coordinates related to all users obtained above in the coordinate storage unit 14.

  The coordinate storage unit 14 stores the D-dimensional coordinates of each user estimated by the coordinate estimation unit 13.

The propagation probability calculation unit 15 receives, as input, the user j specified by the search unit 12 that has generated the virtual event and the elapsed time Δt since the generation of the virtual event. The probability F _ji (Δt) that the user i is involved in the virtual event is calculated.

The probability value is a value obtained by integrating the propagation probability density function f _ji (Δt) of Expression (3) in the time interval from the event occurrence time to the time when Δt has elapsed. At that time, the calculation is performed using the D-dimensional coordinates of each user stored in the coordinate storage unit 14. The probability value calculated for each user is transferred to the output unit 16.

  In response to requests from the search unit 12 and the propagation probability calculation unit 15, the output unit 16 receives information on coordinates stored in the coordinate storage unit 14, and results of simulation of events virtually generated by the operator, that is, The probability that each user is involved in the virtual event is presented to the operator of the position coordinate estimation apparatus 10. Specifically, when presenting the coordinate information stored in the coordinate storage unit 14, the output unit 16 receives a command from the search unit 12, and receives coordinate information from the coordinate storage unit 14 based on the command. Obtain and output. When presenting the result of the simulation, the output unit 16 acquires an instruction from the search unit 12, activates the propagation probability calculation unit 15, and acquires and outputs the calculation result of the propagation probability calculation unit 15.

  Here, output is a concept including display on a display, printing on a printer, sound output, transmission to an external device, and the like. The output unit 16 may or may not include an output device such as a display or a speaker. The output unit 16 can be realized by driver software of an output device, or driver software of an output device and an output device.

  Hereinafter, the position coordinate estimation apparatus 10 will be described using a specific example.

  FIG. 3 is an example of information stored in the propagation history storage device according to the embodiment of the present invention.

  As shown in the figure, the propagation history storage device 20 stores a combination of user information for uniquely identifying a user and time information related to each user. Further, only event information may be stored together as shown in FIG. The propagation history information records the time (event occurrence time) when the corresponding event first occurred, and the event information records the time when the corresponding event occurred and the observation end time. If the time when the event actually occurs and the observation end time are given by another information source, they may be used. If each user is not involved in the event at the observation end time, the time information related to the user's event is stored as an infinite value.

  FIG. 4 shows an example of coordinate information stored in the coordinate storage unit according to the embodiment of the present invention.

  (A) in the figure shows the coordinates when the search unit 12 designates “2” as the dimension D of the stay space, and (b) shows the coordinates when “3” is designated as the dimension D of the stay space. 3 is an example of information stored in a storage unit 14. Note that a value of 4 or more and less than the number of users may be set as the number of dimensions.

  FIG. 5 shows a configuration example of the search unit in the embodiment of the present invention.

  When the search unit 12 shown in the figure displays an area for inputting the number of latent dimensions at the time of coordinate estimation, a coordinate estimation execution button, an area for specifying an event generation user when performing a propagation simulation, and an area for setting an elapsed time. The operator of the position coordinate estimation apparatus 10 performs input. In the figure, the buttons for the coordinate estimation execution function and the propagation simulation function are shown as separate buttons, but the processes from the coordinate estimation execution to the propagation simulation may be configured in one stop. Further, in conjunction with the output unit 16, an event occurrence user and an elapsed time may be designated by a selection operation on information presented by the output unit 16.

  In the present invention, when the propagation model between persons is optimized based on the propagation history information, the positional relation of each person in the D-dimensional space is obtained from the distance relation, and the graphical representation can be performed as it is.

  FIG. 6 shows an output example of the output unit in the embodiment of the present invention.

  In this figure, the output is when “2” is selected as the number of latent dimensions and the total number of users is “8”. It is possible to confirm the relationship of propagation by placing users in a relationship where propagation is likely to occur nearby. Further, the coordinate information may be output in a table format as shown in FIG.

  FIG. 7 shows an output example of the propagation simulation. It is “User 8” that the event first occurred. In FIG. 7, a white circle indicates a user for whom no event has occurred, and a black circle indicates a user for whom an event has occurred. It is possible to confirm a prediction result as to which user the event will occur by the specified elapsed time. Here, the display as illustrated in FIG. 7 is for visualizing two-dimensional or three-dimensional information such as spreadsheet software, Excel (registered trademark), gnuplot (http://www.gnuplot.info/). Application software shall be used.

  Actually, the probability that an event will occur at a certain time for each user is calculated based on the propagation probability density function (equation (3)). If this probability value exceeds a certain threshold, it is considered that an event has occurred. In addition, as the expression of the probability value, the color intensity of each node (user) may be used, or the probability value may be displayed at adjacent coordinates of each node (user). In other words, any method may be used as long as it represents how easily an event occurs in each node (user).

  The operation of each component of the position coordinate estimation apparatus 10 shown in FIG. 1 can be constructed as a program, installed in a computer used as the position coordinate estimation apparatus, executed, or distributed via a network. It is.

  The present invention is not limited to the above-described embodiments, and various modifications and applications are possible within the scope of the claims.

DESCRIPTION OF SYMBOLS 10 Position coordinate estimation apparatus 11 Operation part 12 Search part 13 Coordinate estimation part 14 Coordinate memory | storage part 15 Propagation probability calculation part 16 Output part

Claims (5)

Assuming that the propagation of the event from user to user is caused in correspondence with the distance relationship between the users arranged in the latent space having at least one or more dimensions, the position coordinates of the user in the latent space are estimated. A position coordinate estimation device,
Based on propagation history information, which is time information indicating that multiple users were involved in an observed event, the users who have a strong tendency to be related to the same or close time to the observed event are placed close together Repeating the process for all observed events while updating and converging each user's position coordinates to reasonably explain (ie, optimize) the latent events A position coordinate estimation apparatus comprising coordinate estimation means for uniquely determining the position coordinates of each user in space and storing the coordinates in a coordinate storage means. When a propagation source user who first participated in the event and an elapsed time since the occurrence of the event are given, position coordinates are acquired from the coordinate storage means, and based on the acquired position coordinates, the propagation source user The position coordinate estimation apparatus according to claim 1, further comprising propagation probability calculation means for calculating a probability that a user around the event is related to the event. In a computer, it is assumed that the propagation of an event from user to user is caused in correspondence with a distance relationship between users arranged in a latent space having at least one dimension, and the position of the user in the latent space A position coordinate estimation method for estimating coordinates,
Based on propagation history information, which is time information indicating that multiple users were involved in an observed event, the users who have a strong tendency to be related to the same or close time to the observed event are placed close together Repeating the process for all observed events while updating and converging each user's position coordinates to reasonably explain (ie, optimize) the latent events A position coordinate estimation method characterized by performing a coordinate estimation step of uniquely determining the position coordinates of each user in space and storing them in a coordinate storage means. When a propagation source user who first participated in the event and an elapsed time since the occurrence of the event are given, position coordinates are acquired from the coordinate storage means, and based on the acquired position coordinates, the propagation source user The position coordinate estimation method according to claim 3, further comprising a propagation probability calculation step of calculating a probability that users around the event are related to the event.   A position coordinate estimation program for causing a computer to function as each means of the position coordinate estimation apparatus according to claim 1.

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