KR102048442B1 - Method and apparatus for providing supervised and extended restart in random walks for ranking and link prediction in networks - Google Patents

Abstract

The present invention relates to a method and apparatus for providing an extended extended random walk. According to a first aspect of the present invention, an apparatus for providing an extended random walk includes a normalization unit for normalizing an adjacent matrix representing a connection relationship of at least one node constituting a graph and the at least one node based on a restart probability set for each of the at least one node. It may include a score calculator for calculating the score of each node.

Description

METHOD AND APPARATUS FOR PROVIDING SUPERVISED AND EXTENDED RESTART IN RANDOM WALKS FOR RANKING AND LINK PREDICTION IN NETWORKS}

The present invention relates to a method and apparatus for providing a mapped extended random walk for ranking and connection prediction in a network. More specifically, the RWR (Random Walk with Restart) is extended by changing restart probability of each node in a large graph. The present invention relates to a method and an apparatus for providing a mapped extended random walk that can increase computation speed while using less memory by using a random walk extend with restart (RWER) technique.

Data mining means extracting useful information from large amounts of data. Application of such data mining to a graph is called graph mining, and in particular, a technique for determining the priority of nodes included in the graph is called graph ranking.

Recently, as the usage rate of SNS increases and the amount of web documents stored on the Internet increases, the importance of graph ranking technology for grasping the importance of nodes in the graphs showing the connection relations between SNS users or the web documents is increasing. have.

As a document that proposes a method for performing graph rankings, there is Korean Patent Publication No. 2011-0131094. This document collects one or more nodes and edges from an information network, stores sequences obtained by performing random walks on the collected nodes in a database, and mines the database to identify patterns present in the information network. This has been disclosed.

On the other hand, the background art described above is technical information that the inventors possess for the derivation of the present invention or acquired in the derivation process of the present invention, and is not necessarily a publicly known technique disclosed to the general public before the application of the present invention. .

One embodiment of the present invention is to provide a method and apparatus for providing an extended extended random walk.

One embodiment of the present invention is to provide a method and apparatus for providing an extended extended random walk for determining an optimized restart probability of each node using an efficient learning algorithm.

As a technical means for achieving the above technical problem, according to the first aspect of the present invention, the apparatus for providing an extended random walk includes: a normalization unit for normalizing an adjacent matrix representing a connection relationship of at least one node constituting the graph; It may include a score calculator for calculating the score of each of the at least one node based on the restart probability set for each node.

According to a second aspect of the present invention, in a method for providing an extended random walk by an apparatus for providing an extended random walk, normalizing an adjacent matrix representing a connection relationship between at least one node constituting a graph and the at least one node Computing the score of each of the at least one node based on the restart probability set for each.

According to a third aspect of the present invention, there is provided a computer program for performing an extended random walk providing method, comprising: normalizing an adjacent matrix representing a connection relationship of at least one node constituting a graph and restarting configured for each of the at least one node; Calculating a score of each of the at least one node based on a probability.

According to a fourth aspect of the present invention, there is provided a computer-readable recording medium on which a program for performing an extended random walk providing method is recorded, comprising: normalizing an adjacent matrix representing a connection relationship of at least one node constituting a graph; The method may include calculating a score of each of the at least one node based on a restart probability set for each node.

According to any one of the problem solving means of the present invention described above, an embodiment of the present invention can propose a method and apparatus for providing a mapped extended random walk.

In addition, according to any one of the problem solving means of the present invention, it is possible to provide a method and apparatus for providing an extended extended random walk that can automatically determine the optimized restart probability of each node.

In addition, according to any one of the problem solving means of the present invention can provide a method and apparatus for providing a map extended random walk that can significantly increase the accuracy in calculating the node score using the optimized restart probability.

The effects obtainable in the present invention are not limited to the above-mentioned effects, and other effects not mentioned above may be clearly understood by those skilled in the art from the following description. will be.

1 is an exemplary diagram illustrating a graph for explaining RWR.
2 is an exemplary diagram illustrating a graph for explaining the RWER.
3 is a diagram illustrating an extended random walk providing apparatus according to an embodiment of the present invention.
4 to 5 are flowcharts for explaining an extended random walk providing method according to an embodiment of the present invention.

DETAILED DESCRIPTION Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art may easily implement the present invention. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. In the drawings, parts irrelevant to the description are omitted in order to clearly describe the present invention, and like reference numerals designate like parts throughout the specification.

Throughout the specification, when a part is "connected" to another part, this includes not only "directly connected" but also "electrically connected" with another element in between. . In addition, when a part is said to "include" a certain component, which means that it may further include other components, except to exclude other components unless otherwise stated.

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

Before describing embodiments of the present invention in detail, a graph mining, graph ranking technique, and a random walk with restart (RRW) technique, which is an example of the graph ranking technique, will be described.

Graph mining is about finding useful information in graphs. In addition, the graph ranking technique is one of techniques for performing graph mining, and is a technique for obtaining importance of nodes or proximity between nodes in a graph composed of nodes and edges. As a graph ranking technique, an RWR technique based on a random walk is frequently used. An existing RWR technique will be described in detail with reference to FIG. 1.

1 is a diagram illustrating an example of calculating an RWR score by applying an RWR technique to a graph. 1 shows a graph composed of twelve nodes and edges connecting the nodes. Each node is assigned a node number from 1 to 12. The RWR technique refers to a random surfer (1), a virtual person who moves from a start node to a node among a plurality of nodes included in the graph as a start node (or seed node). This is a technique for calculating the probability of reaching other nodes as a score.

In FIG. 1, node 4 is selected as a start node. The random surfer 1 starts from node 4, which is the starting node, and performs either the random walk or the restart. For example, the random surfer 1 may perform an action (random walk) of moving to one of nodes 1, 3, or 5, or perform an action (restart) of returning to node 4. . In addition, if the random surfer 1 reaches node 9 through several movements, it performs the action of moving to either node 8 or node 10 (random walk) as the next operation, or to node 4. You can perform a rolling action (restart).

That is, the random surfer 1 immediately moves to a neighboring node (random walk) or moves to a start node (restart) every time it moves. In this case, if the probability that the random surfer 1 performs restart is c, the probability of performing the random walk becomes (1-c).

The probability that the random surfer 1 reaches each of the nodes according to one embodiment described herein is called an RWR score, and a column vector r consisting of the RWR scores for each of the nodes is called an RWR score vector. do. In addition, if the adjacency matrix representing the graph is A, the RWR score vector r can be expressed by the following equation.

[Equation 1]

는 각 행의 원소의 합이 1이 되도록 정규화된 인접 행렬이다. 수학식 1로부터 다음의 수학식 2를 얻을 수 있다.In this case, q is a column vector in which the value of the element corresponding to the start node is 1 and the remaining elements are all zero. In addition,

Is an adjacent matrix normalized such that the sum of the elements in each row is one. From Equation 1, the following Equation 2 can be obtained.

[Equation 2]

를 H라고 한다면, RWR 점수 벡터 r은 다음의 수학식 3과 같은 선형 시스템의 해로 구할 수 있다.therefore,

If H is H, the RWR score vector r can be obtained as a solution of a linear system as shown in Equation 3 below.

[Equation 3]

There are two methods of obtaining the RWR score vector r: an iterative approach and a preprocessing approach.

The iterative technique is expressed by Equation 4 in such a manner that the value of r converges within a predetermined range by repeatedly applying Equation 1 to any initial value of r.

[Equation 4]

로부터 시작하여, 다음의 수학식 5를 만족할 때까지 수학식 4를 반복 적용할 수 있다. 물론, 수학식 5는 수렴 조건의 한 예로서, 수렴 조건을 다르게 설정하는 것도 가능하다. 이때,

는 허용 오차 (error tolerance)이다.In this case, i means the number of times the calculation is repeated. The initial value

From Equation 4, Equation 4 may be repeatedly applied until the following Equation 5 is satisfied. Of course, Equation 5 is an example of the convergence condition, and it is also possible to set the convergence condition differently. At this time,

Is the error tolerance.

[Equation 5]

As described above, in the case of the existing RWR, since the preference of each node is not reflected, the random surfer 1 restarts regardless of the position of the random surfer 1 according to the fixed restart probability c. Therefore, the random surfer 1 does not consider the preference of the current node. On the other hand, the random walk (Random Walk with Extended Restart, RWER) according to an embodiment described herein reflects the preference based on the relative score of each node included in the graph randomly by setting the restart probability for each node Can increase the performance.

2 is an exemplary diagram illustrating a graph in which restart probabilities are determined for each node. Referring to FIG. 2, the equation for calculating the probability of moving from the nodes i, j, and k to the U node at time t + 1 at time t in RWER is as follows.

[Equation 6]

: i 노드에서 간선을 따라 이동할 확률

: probability of moving along edge at i-node

Reflecting the probability that the random surfer restarts according to Equation 6, it is as follows.

[Equation 7]

는 u가 시드 노드 s 이면 1 아니면 0이다. here

Is 1 if u is the seed node s or 0.

Based on this example, the RWER model is defined as a recursive equation as follows.

[Equation 8]

는 i 노드로 들어오는 간선이고,

은 i 노드에서 나가는 간선이다. here

Is the edge coming into the i-node,

Is the edge leaving the i node.

Equation 8 is expressed as a matrix as follows.

[Equation 9]

열을 기준으로 정규화된 인접행렬이고, c 는 i번째 재시작확률인

가 원소인 재시작확률 벡터이다.

는

이고 다른 원소는 0인 행렬이고, q는 s 번째 원소는 1 이고 나머지 원소는 0 인 행렬이다. 여기서 c가 같은 값이면, 수학식 4 와 같은 RWR과 같다. here

Adjacent matrix normalized by column, and c is the i th restart probability

Restart probability vector whose element is.

Is

And the other element is a matrix of 0, q is a matrix whose sth element is 1 and the remaining elements are 0. If c is the same value, it is equal to RWR as in Equation 4.

In the following, RWER uses a small amount of memory so that RWER can automatically determine the restart probability of each node by reflecting not only the preference of each node but also the relationship between nodes. However, RWER can quickly calculate the RWER score calculation and restart probability. do. Details will be described below with reference to the drawings.

3 is a block diagram showing the configuration of an extended random walk providing apparatus 100 according to an embodiment of the present invention. Referring to FIG. 3, the apparatus for providing an extended random walk according to an embodiment of the present invention 100 may include a normalization unit 110, a score calculator 120, and a restart probability calculator 130.

The normalization unit 110 may normalize an adjacent matrix representing a connection relationship of at least one node constituting the graph.

That is, the normalization unit 110 may calculate an order matrix D having, as elements, the number of edges having a direction to other nodes for each node based on the adjacent matrix.

이다. Where D is

to be.

The reordering unit 110 may normalize the neighboring matrix based on the column based on the calculated order matrix D, which is expressed as follows.

[Equation 10]

The score calculator 120 may calculate a score of each of the at least one node based on the restart probability set for each of the at least one node.

To this end, the score calculator 120 may set a start vector q having a length n of which an index of the seed node is 1 and another index is 0.

The score calculator 120 may repeatedly calculate the above-described equation (9) based on the score of the node and the restart probability of the node.

That is, an error value that is a difference between the first score of the node where the random surfer traversing the graph is located and the second score calculated through Equation 9 may be calculated.

[Equation 11]

The score calculator 120 may update the first score to the second score, and then, if the calculated error value is less than or equal to a preset tolerance, may stop the iterative calculation of Equation 9.

Meanwhile, the restart probability calculator 130 may calculate a restart probability, which is a probability that the random surfer traversing the graph restarts the traversal at one node, for each of the at least one node.

To this end, the restart probability calculator 130 may perform learning for optimizing the restart probability, which is a probability that the random surfer traversing the graph restarts the traversal at one node, for each of the at least one node.

That is, the restart probability calculator 130 may initialize the restart probability to a preset reference vector and calculate a restart probability that minimizes the loss function in which the node score and the restart probability are input.

The restart probability calculating unit 130 updates the restart probability based on the value of the loss function, and when the updated restart probability converges to a specific value, ends the learning of the restart probability and returns the restart probability to optimally restart each node. You can set the probability.

This process is expressed as a formula below.

[Equation 12]

,

각각은 노드 x, y 각각의 점수이다. Where o is a predetermined reference vector, P is a node set having a high ranking based on the score of the node, and N is a node set having a lower score than a node belonging to P.

,

Each is a score of each of nodes x and y.

In this case, the reference vector o may prevent the restart probability vector c from becoming too small or excessively overfitting and increase the accuracy.

 However, since it is difficult to calculate the restart probability c that satisfies Equation 12, the constraint can be relaxed as shown in the following equation.

 [Equation 13]

: 정규화 파라미터(regularization parameter), h(·) : 손실함수

: Normalization parameter, h (·): loss function

The loss function can be any loss function. Hereinafter, the WMW (Wilcoxon-Mann-Whitney) loss function is used.

The WMW loss function with width b is

[Equation 14]

Differentiating Equation 13 with respect to restart probability c is as follows.

[Equation 15]

는

이고, WMW 손실함수의 도함수

는

이다. here

Is

Derivative of the WMW loss function

Is

to be.

의 도함수

를 획득하기 위해서는 재시작확률 벡터 C 의 i번째 원소인

에 대해 관련된 점수

의 도함수를 계산해야 한다. Related score for restart probability c

Derivative of

In order to obtain, the i th element of restart probability vector C

Related scores for

We need to calculate the derivative of.

이라 하면,

,

,

이다. Where M

Speaking of

,

,

to be.

의 역(inverse)이기 때문에

는 아래의 수식과 같다.M is

Because it's the inverse of

Is shown in the following formula.

[Equation 16]

:(i, j)번째 원소는 1 이고 나머지는 0 인 단일원소(single-entry) 행렬

: Single-entry matrix with (i, j) th element of 1 and the remainder 0

는 아래의 수식과 같이 표현될 수 있다.Based on Equation 16

May be expressed as in the following equation.

[Equation 17]

: s번째 원소가 1 인 길이가 n 인 단위벡터(unit vector)

: a unit vector of length n with the sth element equal to 1

는

에서 계산되어야 한다. 그러면

는 아래와 같은 수식으로 기재될 수 있다. At this time

Is

Should be calculated from then

May be described by the following formula.

Equation 18

:하다마드(Hadamard) 곱, 1: 길이가 n 이고 모든 원소가1 인 벡터

Hadamard product, 1: vector of length n with all elements 1

역시 아래와 같이 계산될 수 있다. Similarly

Can also be calculated as

[Equation 19]

는 아래와 같이 표현될 수 있다. Using Equations 18 and 19, Equation 15

Can be expressed as follows.

[Equation 20]

의 복잡도는

로 전체 수식의 복잡도를 결정한다. In Equation 20

The complexity of

To determine the complexity of the entire equation.

와

를 포지티브 노드와 네거티브 노드의 개수로 나타내면,

는 P의 초기화 시간을 포함하여 복잡도를

까지 낮출 수 있다. At this time,

Wow

If is expressed as the number of positive and negative nodes,

Complexity including the initialization time of P

Can be lowered.

의 역(inverse)이기 때문에 수학식 19 , 20 각각에서의 M(:,s)를 직접 계산하여 M을 획득하는 것이 아닌 점수계산부(120)에서 노드의 점수를 계산하는 반복적인 방법을 이용하여 M(:,s)를 계산할 수 있다. And M in equations 19 and 20

Since it is an inverse of, instead of directly calculating M (:, s) in each of Equations 19 and 20, M is obtained by using an iterative method of calculating the score of the node in the score calculator 120. M (:, s) can be calculated.

In addition, the equations 19 and 20 should also perform calculations on the rows of M, that is, M (x, :), but the iterative method of calculating the score of the node in the score calculator 120 may be based on The problem is that the calculation is performed only on the columns.

The x-th column of M can be calculated by the iterative method as follows.

을

라 하면,

는 수렴

할 때까지 아래의 업데이트 규칙에 따라 반복하여 계산할 수 있다.

of

Say,

Converge

Can be calculated repeatedly according to the update rule below.

[Equation 21]

벡터P: The xth element is 1 and the remaining elements are 0

vector

The restart probability calculator 130 may update the restart probability according to Equation 15 below using the iterative method described above with Equation 15 including a loss function.

[Equation 22]

:학습률

Learning rate

In this case, the restart probability calculator 130 may update the restart probability c according to a gradient-based method until the calculated restart probability converges.

Meanwhile, FIGS. 4 to 5 are flowcharts illustrating a method of providing the extended random walk apparatus 100 to provide the extended random walk.

The extended random walk providing method according to the embodiment shown in FIGS. 4 to 5 includes the steps processed in time series in the extended random walk providing apparatus 100 shown in FIG. 3. Therefore, even if omitted below, the above description of the extended random walk providing apparatus 100 shown in FIG. 3 may also be used in the goods transaction management method according to the embodiments shown in FIGS. 4 to 5. have.

4 is a flowchart illustrating a process of the extended random walk providing apparatus 100 calculating a score of each node based on a restart probability set for each at least one node constituting the graph.

Referring to FIG. 4, the extended random walk providing apparatus 100 may normalize an adjacent matrix indicating a connection relationship between at least one node constituting the graph (S4001).

That is, the extended random walk providing apparatus 100 may calculate the order matrix D indicating the edge order of the adjacent matrix A of the graph to be randomized by the surfer.

를 계산할 수 있다. And the extended random walk providing apparatus 100 is a matrix normalized by multiplying the inverse of the order matrix D and the adjacent matrix A

Can be calculated.

Thereafter, the extended random walk providing apparatus 100 may calculate a score of each of the at least one node based on the restart probability set for each of the at least one node (S4002).

First, the extended random walk providing apparatus 100 may set a start vector q from the seed node s.

The extended random walk providing apparatus 100 may calculate the score of the node according to Equation 9, and may update the score of the node with the calculated score.

The extended random walk providing apparatus 100 may calculate the score of the second node based on the score of the first node connected to the trunk line entering the second node that calculates the score and the restart probability of the first node. The score of the second node may be updated with the score.

To this end, the extended random walk providing apparatus 100 may calculate the restart probability of the first node necessary for calculating the score of the second node.

A method of calculating the restart probability of the first node will be described with reference to FIG. 5.

FIG. 5 is a flowchart illustrating a method in which the extended random walk providing apparatus 100 calculates an optimal restart probability by learning restart probabilities for each node constituting a graph.

Referring to FIG. 5, the extended random walk providing apparatus 100 may initialize the restart probability of the node to the reference vector o (S5001).

The extended random walk providing apparatus 100 may perform learning for optimizing a restart probability, which is a probability that a random surfer traversing the graph restarts the traversal at one node for at least one node.

To this end, the extended random walk providing apparatus 100 may calculate a restart probability for minimizing the value of the loss function in which the score of the node and the restart probability are input (S5002).

를 계산할 수 있다. That is, the extended random walk providing apparatus 10 is expressed by Equation 15 using an iterative method through Equations 16 to 21.

Can be calculated.

값을 이용하여 수학식 15 인

를 계산할 수 있다. And the extended random walk providing device 10 is calculated

Using the value in equation (15)

Can be calculated.

Thereafter, the extended random walk providing apparatus 10 may update the restart probability according to Equation 22 (S5003), and determine whether the restart probability converges (S5004).

When the restart probability converges, the extended random walk providing apparatus 10 may stop updating the restart probability and return a restart probability for the node (S5005).

4, when the score of the second node is updated as described above, the extended random walk providing apparatus 100 may calculate an error that is a difference between the updated score of the second node and the score before the update (S4003). In operation S4004, the updated error value may determine whether the updated error value is less than or equal to the preset tolerance.

If the updated error value is less than or equal to the preset tolerance, the extended random walk providing apparatus 10 may return the updated score as the score of the second node (S4005).

The term '~ part' used in the present embodiment refers to software or a hardware component such as a field programmable gate array (FPGA) or an ASIC, and the '~ part' performs certain roles. However, '~' is not meant to be limited to software or hardware. '~ Portion' may be configured to be in an addressable storage medium or may be configured to play one or more processors. Thus, as an example, '~' means components such as software components, object-oriented software components, class components, and task components, and processes, functions, properties, procedures, and the like. Subroutines, segments of program patent code, drivers, firmware, microcode, circuits, data, databases, data structures, tables, arrays, and variables.

The functionality provided within the components and 'parts' may be combined into a smaller number of components and 'parts' or separated from additional components and 'parts'.

In addition, the components and '~' may be implemented to play one or more CPUs in the device or secure multimedia card.

In addition, the extended random walk providing method according to an embodiment of the present invention may be implemented as a computer program (or computer program product) containing instructions executable by a computer. The computer program includes programmable machine instructions processed by the processor and may be implemented in a high-level programming language, an object-oriented programming language, an assembly language, or a machine language. . The computer program may also be recorded on tangible computer readable media (eg, memory, hard disks, magnetic / optical media or solid-state drives, etc.).

Therefore, the extended random walk providing method according to an embodiment of the present invention can be implemented by executing the computer program as described above by the computing device. The computing device may include at least some of a processor, a memory, a storage device, a high speed interface connected to the memory and a high speed expansion port, and a low speed interface connected to the low speed bus and the storage device. Each of these components are connected to each other using a variety of buses and may be mounted on a common motherboard or otherwise mounted in a suitable manner.

Here, the processor may process instructions within the computing device, such as to display graphical information for providing a graphical user interface (GUI) on an external input, output device, such as a display connected to a high speed interface. Instructions stored in memory or storage. In other embodiments, multiple processors and / or multiple buses may be used with appropriately multiple memories and memory types. The processor may also be implemented as a chipset consisting of chips comprising a plurality of independent analog and / or digital processors.

The memory also stores information within the computing device. In one example, the memory may consist of a volatile memory unit or a collection thereof. As another example, the memory may consist of a nonvolatile memory unit or a collection thereof. The memory may also be other forms of computer readable media, such as, for example, magnetic or optical disks.

In addition, the storage device can provide a large amount of storage space to the computing device. The storage device may be a computer readable medium or a configuration including such a medium, and may include, for example, devices in a storage area network (SAN) or other configuration, and may include a floppy disk device, hard disk device, optical disk device, Or a tape device, flash memory, or similar other semiconductor memory device or device array.

The foregoing description of the present invention is intended for illustration, and it will be understood by those skilled in the art that the present invention may be easily modified in other specific forms without changing the technical spirit or essential features of the present invention. will be. Therefore, it should be understood that the embodiments described above are exemplary in all respects and not restrictive. For example, each component described as a single type may be implemented in a distributed manner, and similarly, components described as distributed may be implemented in a combined form.

The scope of the present invention is shown by the following claims rather than the above description, and all changes or modifications derived from the meaning and scope of the claims and their equivalents should be construed as being included in the scope of the present invention. do.

100: extended random walk providing device
110: normalization unit 120: score calculation unit
130: restart probability calculator

Claims (16)

In the extended random walk providing device,
A normalization unit for normalizing adjacent matrices representing connection relationships of at least one node constituting the graph;
A score calculator configured to calculate a score of each of the at least one node based on a restart probability set for each of the at least one node; And
The restart probability is initialized with a preset reference vector, and based on a loss function using the scores of the nodes constituting the graph, the restart probability is a probability that a random surfer traversing the graph restarts at one node. Extended random walk providing apparatus comprising a restart probability calculation unit for each node. The method of claim 1,
The normalization unit,
An extended random walk is provided which calculates an order matrix having elements as the number of edges having directionality of other nodes for each node based on the adjacent matrix, and normalizes the adjacent matrix based on columns based on the calculated order matrix. Device. The method of claim 1,
The score calculation unit,
And calculating a score of the second node based on the score of the first node connected to the trunk line entering the second node and the restart probability of the first node. The method of claim 3, wherein
The score calculation unit,
Update the first score of the second node with the calculated second score, calculate an error value that is a difference between the second score and the first score, and score the second node if the error value is less than or equal to a preset tolerance; Extended random walk providing device to terminate the update. delete delete The method of claim 1,
The restart probability calculation unit,
And updating the restart probability by reflecting the value of the loss function to the restart probability, and returning the restart probability when the updated restart probability converges to a specific value. In the extended random walk providing apparatus provides an extended random walk,
Normalizing an adjacent matrix representing a connection relationship between at least one node constituting the graph; And
Calculating a score of each of the at least one node based on a restart probability set for each of the at least one node,
The extended random walk method,
Setting a restart probability for each of the at least one node by a random surfer traversing the graph, the probability of restarting the traversal at one node;
The setting of the restart probability for each of the at least one node may include:
Initializing a restart probability with a preset reference vector; And
And calculating the restart probability based on a loss function using the scores of the nodes constituting the graph. The method of claim 8,
Normalizing the adjacent matrix,
Calculating an order matrix having, as elements, the number of edges having directionality of other nodes for each node based on the adjacent matrix; And
And normalizing the adjacent matrix based on the column based on the calculated order matrix. The method of claim 8,
Computing the score of each of the at least one node,
And calculating a score of the second node based on the score of the first node connected to the edge entering the second node and the restart probability of the first node. The method of claim 10,
Computing the score of the second node,
Updating the first score of the second node with the calculated second score and calculating an error value that is a difference between the second score and the first score; And
If the error value is less than or equal to a preset tolerance, ending updating of the score of the second node. delete delete The method of claim 8,
The extended random walk method,
Updating the restart probability by applying the value of the loss function to the restart probability; And
And returning the restart probability if the updated restart probability converges to a specific value. A computer program executed by an extended random walk providing apparatus and stored in a medium for performing the method of claim 8. A computer-readable recording medium having recorded thereon a program for performing the method of claim 8.

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