KR101701373B1 - Apparatus and method for generating community structure perturbation index - Google Patents

Abstract

The apparatus for deriving the cluster structure disturbance according to an embodiment of the present invention includes an original cluster assignment vector for an original cluster structure including at least two or more nodes and a first cluster assignment vector for at least one of the at least two nodes in the original cluster structure A vector generating unit for generating a disturbance cluster allocation vector for a disturbance cluster structure from which the node has been removed; a vector generating unit for generating a disturbance cluster allocation vector for the original disturbance cluster structure, the original conditional entropy for the original cluster structure, A conditional entropy generation unit for generating a disturbance conditional entropy for the disturbance community structure indicating a degree of difference between the original conditional entropy and the original community structure, A cluster structure indicative of the extent of disturbance by removal And an index derivation unit for deriving the index derivation unit.

Description

[0001] APPARATUS AND METHOD FOR GENERATING COMMUNITY STRUCTURE PERTURBATION INDEX [0002]

The present invention relates to an apparatus and a method for deriving a degree of disturbance of a community structure, and more particularly, to a method and apparatus for deriving a degree of disturbance of a community structure when the nodes constituting the community structure are removed, The present invention relates to an apparatus and method for deriving a cluster structure disturbance index indicating a degree of disturbance of a cluster structure in consideration of role uniqueness.

In a social, technical, or natural network, nodes on the network have a strong cluster structure. At this time, the cluster structure can correspond to a functional module such as a protein or a cell network. Fig. 1 is a diagram exemplifying such a community structure. Referring to FIG. 1, there are hub nodes 10, 20 and 30 which are central, and peripheral nodes 10, 20 and 30 connected to the hub nodes 10, There are nodes 11 to 18, 21 to 28, and 31 to 38.

The maintenance of the community structure is very important for the efficient operation of the technical network such as the server network. The maintenance of the community structure is based on quantifying the importance of the role of the nodes constituting the community structure ≪ / RTI > In this case, the role of a node means a role of a node or a group of nodes contributing to maintenance of a community structure.

More specifically, in the context of quantifying the importance of the role of a node, conventionally there are two factors, namely, the within-module degree Z and the participation coefficient P, The significance of the role was quantified.

The subordinate degree Z in the module is an index indicating the degree to which a certain node in this specific cluster is connected to other nodes in the specific cluster when there is a specific cluster, and can be expressed by Equation 1, for example.

Wherein, Z _i is the node i and the slave modules in Fig having a particular cluster S _i, κ _i to node i are a particular cluster S _i (Bar) κ _si is the average of the κ values computed for all nodes in a particular cluster S _i , and σ _{k Si} is the sum of the degrees of linkage to other nodes in a particular cluster S _i This is the standard deviation of k values computed for all nodes.

In addition, the participation coefficient P is an index indicating the variability of connection to nodes belonging to a cluster other than a specific cluster in a specific cluster when there is a specific cluster. For example, Can be expressed by Equation (2).

Where P _i is the participation coefficient of node i, k _i is the degree to which node i _is connected to other nodes in the entire network, and κ _{is the} degree to which node i is associated with a node set belonging to any cluster S. In addition, N _M is the number of all clusters, and S is an index indicating one of the clusters.

However, in the method of quantifying the role of the node based on the above two factors, the uniqueness of the role, that is, the uniqueness of the role is not considered. Therefore, we can not predict the disturbance (or change) that the cluster structure experiences when a node is removed or a node fails.

The hub node 40 is connected to the peripheral nodes 41 to 48 in FIG. 2A, so that the hub node 40 can be used as the hub node 40, Has a higher value than the peripheral nodes (41 to 48). In FIG. 2B, the hub node 50 and another hub node 51 likewise have a high dependency rate in the module as shown in FIG. 2A. In addition, in the case of the participation coefficient, only one cluster is shown in FIGS.

In this case, when the hub node 40 is removed in FIG. 2A, the cluster structure of FIG. 2A is divided into eight individual cluster structures. That is, since the role of the hub node 40 in the cluster structure of FIG. 2A is unique, the removal of the hub node 40 causes a large change in the cluster structure. It can be said that the hub node 40 plays a relatively important role in maintaining the cluster structure.

On the other hand, when the hub node 50 is removed in FIG. 2B, one cluster structure is still maintained by another hub node 51 having the same connection as the removed hub node 50. That is, since the role of the hub node 50 in the cluster structure of FIG. 2B overlaps with that of another hub node 51, the removal of the hub node 50 does not cause a large change in the cluster structure . In other words, it can be said that the hub node 50 does not play a relatively important role in maintaining the cluster structure.

Nevertheless, the results of quantifying the importance of the role of the hub node 40 of FIG. 2A and the hub node 50 of FIG. 2B according to the conventional method are almost the same. This is because the conventional method does not consider the uniqueness of the role for the node.

However, considering the uniqueness of a role for a node and predicting changes occurring in the cluster structure when a node is removed or a node fails based on the uniqueness can be utilized in various fields as follows. For example, it can be predicted in advance that the aggregation structure of each sub-network on a large-scale online network or a network of inter-terrorist organizations will undergo the greatest change when a node is removed. In addition, the connection information between the brain modules obtained through the brain neural network such as MRI or DFI can predict in advance which one of the modules can cause the greatest impact on the brain function network when a failure occurs. In addition, it can be used as a mechanism for price / value determination of individual actors in a telecommunication network, and can help predict the change of the entire network structure in a social infrastructure network disaster situation such as a power network overload situation.

On the basis of this, it can be said that there is a need to consider the uniqueness of the role of the node in quantifying the importance of the role of the node.

Korean Patent Publication No. 10-2008-0070960 (published on Aug. 1, 2008)

A problem to be solved by the present invention is to provide an apparatus and method for quantifying the importance of a role of a node in consideration of role uniqueness of the role of the node.

It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. will be.

The apparatus for deriving the cluster structure disturbance according to an embodiment of the present invention includes an original cluster assignment vector for an original cluster structure including at least two or more nodes and a first cluster assignment vector for at least one of the at least two nodes in the original cluster structure A vector generating unit for generating a disturbance cluster allocation vector for a disturbance cluster structure from which the node has been removed; a vector generating unit for generating a disturbance cluster allocation vector for the original disturbance cluster structure, the original conditional entropy for the original cluster structure, A conditional entropy generation unit for generating a disturbance conditional entropy for the disturbance community structure indicating a degree of difference between the original conditional entropy and the original community structure, A cluster structure indicative of the extent of disturbance by removal And an index derivation unit for deriving the index derivation unit.

The original community structure differs from the disturbance community structure in that the original community structure is a quantity of information indicating a difference in structure with the disturbance community structure based on the disturbance community structure, The disturbance community structure differs from the original community structure in that the disturbance community structure is a quantity of information indicating a difference in structure with the original community structure based on the original community structure.

Also, the index derivation unit may derive a value obtained by dividing the sum of the original conditional entropy and the disturbance conditional entropy by the number of nodes constituting the disturbance cluster structure, as the cluster structure disturbance index.

A method for deriving a degree of disturbance of a community structure according to another embodiment of the present invention includes the steps of: (a) in an original community structure including at least two or more nodes, Generating an original cluster structure, and (b) removing a first node, which is one of the nodes constituting the original cluster structure, from the disturbance cluster structure, wherein the remaining nodes except for the first node belong to the disturbance cluster structure (C) generating an original conditional entropy for the original community structure indicating a degree of difference between the original community structure and the disturbance community structure; (d) ) The disturbance community structure, which indicates the extent to which the disturbance community structure differs from the original community structure, Generating a ropi and (e) may include the step of deriving the community structure disturbance index indicating the degree of disturbance by the removal of the first node based on the original conditional entropy and the conditional entropy disturbance.

In the step (c), the extent to which the original community structure differs from the disturbance community structure may be determined by comparing the original community structure with the disturbance community structure based on the disturbance community structure, Wherein the disturbance community structure differs from the original community structure in the step (d), wherein the disturbance community structure indicates a difference in structure with the original community structure on the basis of the original community structure Information amount.

In the step (e), a value obtained by dividing the sum of the original conditional entropy and the disturbance conditional entropy by the number of nodes constituting the disturbance cluster structure may be derived as the cluster structure disturbance index.

According to another aspect of the present invention, a method for deriving the degree of disturbance of the community structure can be implemented in a recording medium on which a computer program for performing such a method is recorded.

According to an embodiment of the present invention, the importance of the role of the node can be quantified by considering the role uniqueness of the role of the node. Therefore, it can be predicted in advance that the cohesion structure of each sub-network on the social network between large-scale on-line network and terrorist organization will undergo the biggest change when the node is removed. In addition, the connection information between the brain modules obtained through the brain neural network such as MRI or DFI can predict in advance which one of the modules can cause the greatest impact on the brain function network when a failure occurs. In addition, it can be used as one of the price / value settlement mechanisms of individual actors in the telecommunication network, and it can help predict the change of the whole network structure in the social infrastructure network disaster situation such as the power network overload situation.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an exemplary diagram illustrating a cluster structure composed of at least two nodes. FIG.
Figures 2a and 2b are diagrams illustrating exemplary community structures.
3 is a diagram illustrating an example of a configuration of a device for deriving disturbance level of a community structure according to an embodiment of the present invention.
FIG. 4 is a diagram illustrating a procedure of a method of deriving a disturbance degree of a community structure according to an embodiment of the present invention.
FIGS. 5A and 5B are views showing the nodes before and after the nodes are removed from the cluster structure.
Figs. 6A and 6B are diagrams illustrating nodes before and after removal from a cluster structure. Fig.

BRIEF DESCRIPTION OF THE DRAWINGS The advantages and features of the present invention, and the manner of achieving them, will be apparent from and elucidated with reference to the embodiments described hereinafter in conjunction with the accompanying drawings. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. To fully disclose the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims.

In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear. The following terms are defined in consideration of the functions in the embodiments of the present invention, which may vary depending on the intention of the user, the intention or the custom of the operator. Therefore, the definition should be based on the contents throughout this specification.

3 is a diagram illustrating an example of a configuration of a device for deriving disturbance level of a community structure according to an embodiment of the present invention.

First, a disturbance level deriving apparatus (hereinafter referred to as disturbance level deriving apparatus) 100 is a hybrid implementation of at least a part of software and hardware, and includes a processor and a memory for storing instructions executed by the processor May be implemented on a programmable machine that is selectively activated or reconfigured by an electronic device or a computer program containing it.

Also, at least some of the features and / or functionality presented in an embodiment of the present invention may be implemented in an end user computer system, a computer, a network server or server system, a mobile computing device (e.g., a personal digital assistant (PDA) At one or more general purpose network host machines, such as a cellular telephone, a smart phone, a laptop, a tablet computer, or the like), a consumer electronic device, or any other suitable electronic device or any combination thereof.

Referring to FIG. 3, the disturbance level derivation apparatus 100 may include an input unit 120, a vector generation unit 140, a conditional entropy generation unit 160, and an index derivation unit 180. However, since this is according to one embodiment, it may not include at least one configuration or may include other configurations.

The input unit 120 may receive data on a cluster structure, and may be configured to read data stored in a file in a computing device such as a computer. The data on the community structure input through the input unit 120 may be in various formats. Here, the format of the detailed configuration of the input unit 120 or the format of the data on the cluster structure is a virtual one of ordinary skill in the art, so a detailed description thereof will be omitted.

The vector generation unit 140 generates a cluster assignment vector for the community structure, and may be implemented in a computing device such as a computer. The cluster assignment vector is a vector indicating whether a node on the network is included in the cluster structure and is generated by Equation (3).

Here, s is an index designating one of all m clusters, l _s is the number of links (links) belonging to the cluster s, L is the number of links (connections) belonging to the entire network, and d _s is the sum of degrees of all nodes in cluster s. In addition, generating cluster assignment vectors is described in Non-Patent Literature Newman, M. and M. Girvan (2004), "Finding and evaluating community structure in networks." Physical review. E, Statistical, nonlinear, and soft matter physics 69 (2 Pt 2): 026113, so a detailed description thereof will be omitted.

According to one embodiment, the vector generator 140 generates an original cluster assignment vector for the original community structure. The original cluster structure means a cluster structure including at least two nodes.

In addition, the vector generation unit 140 generates a disturbance cluster assignment vector for the disturbance community structure. The disturbance cluster structure means a cluster structure in which the first node, which is one of the nodes included in the original cluster structure, is removed.

Here, the disturbance community structure may mean a community structure in which at least two or more nodes other than one of the nodes included in the original community structure are removed. In this case, the vector generation unit 140 generates at least two A disturbance cluster assignment vector for a disturbance community structure with more than one node removed may be generated.

The conditional entropy generator 160 generates a conditional entropy for the original and disturbed community structures, and can be implemented in a computing device such as a computer.

More specifically, the conditional entropy generator 160 generates the original conditional entropy of the original cluster assignment vector based on the original cluster assignment vector and the disturbance cluster assignment vector. Herein, the original conditional entropy may mean the amount of information additionally required to explain the original community structure based on the disturbance community structure, but this is not limitative.

In addition, the conditional entropy generator 160 generates disturbance conditional entropy for the disturbance cluster assignment vector based on the original cluster assignment vector and the disturbance cluster assignment vector. Here, the disturbance conditional entropy may mean the amount of information additionally required to explain the disturbance community structure based on the original community structure, but the present invention is not limited thereto.

In one embodiment, the conditional entropy generator 160 may generate the conditional entropy for the original and disturbed community structures according to Equation (4) below.

Here, the function H (X | Y) derives the conditional entropy, specifically the amount or uncertainty of the information needed to infer X based on Y, and a more detailed formula is described on the right-hand side. Here, the technique itself for generating the conditional entropy by such a function H and the right-side equation is itself a non-patent document Karrer, B., E. Levina, et al. (2008). "Robustness of community structure in networks." Physical Review E 77 (4) and Meila, M. (2007). "Comparing clusterings - an information based distance." Journal of Multivariate Analysis 98 (5): 873-895. Therefore, detailed description thereof will be omitted.

Also, C represents an original community structure, and C 'represents a disturbance community structure. Therefore, H (C | C ') represents the amount of information that is additionally required to describe the original cluster structure based on the disturbance cluster structure, and H (C' | C) represents the disturbance cluster structure based on the original cluster structure Means the amount of information that is additionally required to illustrate.

Based on this, the fact that the conditional entropy value generated by the conditional entropy generator 160 is large means that there is a large structural difference between the original community structure and the disturbance community structure. That is, if the corresponding node is removed or the node fails, it means that a large change in the cluster structure including the node may occur.

On the other hand, the small value of conditional entropy means that there is little structural difference between original and disturbed community structure. That is, even if the corresponding node is removed or the node fails, it means that there is no significant change in the cluster structure including the node because the node has the same or similar role as the corresponding node.

Here, according to an exemplary embodiment, assuming that the original cluster structure includes N nodes, the value of the conditional entropy may have a value of at least 0 at the maximum log N, for example.

The index derivation unit 180 derives a community structure perturbation index (CPI) for a node included in the cluster structure, and may be implemented in a computing device such as a computer. The cluster structure disturbance index is an index that indicates the uniqueness of the role of the node, and therefore can be an indicator of the degree of disturbance due to the removal of the node.

More specifically, the index derivation unit 180 calculates a population structure disturbance index indicating the degree of disturbance due to removal of the first node based on the original conditional entropy and the disturbance conditional entropy generated by the conditional entropy generation unit 160 . In this case, the index derivation unit 180 may divide the sum of the original conditional entropy and the disturbance conditional entropy, and divide the sum by the number of nodes constituting the disturbance cluster structure. The divided value may be deduced by the cluster structure disturbance index , Which can be expressed by the following equation (5).

Here, CPI _i represents the cluster structure disturbance index of the i-th node.

(N, g) denotes the total link set, and C (N, g) denotes the number of nodes included in the original network C _i denotes the original assignment vector element corresponding to node i on the original network. In addition, the backslash '\' is defined as when the operator removes C (N, g) \C _i refers to the removal of the elements C _i in the original vector element assignment.

Since the cluster structure disturbance index compares the original cluster structure before the node i is removed and the disturbance cluster structure after the node i is removed as described above, the first factor of the function V is the original cluster structure before the node i is removed . However, the function V can in order to compare the original community structure and disturb community structure node in, that is, since the dimension of the node must be the same in the above equation, C (N, g) the function arguments removal of the C _i for the calculated after calculating the V as the first argument. In other words, the first factor of function V is expressed as a factor that removes C _i in terms of computation, but it is actually about the original cluster structure before node i is removed.

In addition, g _i is a set of links belonging to the node i, and, C (N / i, g / g _i) the community structure of the network, removal of the i-th node and a link (connection) set gi connected thereto from the source community structure , That is, disturbance assignment vector for disturbed community structure.

Therefore, using the cluster structure disturbance index derived according to Equation (5), the role uniqueness can be derived for a certain node, so that the influence on the cluster structure can be quantified when the corresponding node is removed or a failure occurs in the corresponding node. In addition, as shown in Equation (5), since the cluster structure disturbance index is normalized (by log | N | -1), the size of the index can be more easily recognized.

Hereinafter, functions and effects according to an embodiment of the present invention will be described.

FIG. 4 is a diagram illustrating a procedure of a method of deriving the degree of disturbance of a community structure according to an embodiment of the present invention. The method of deriving the degree of disturbance of the community structure, as shown in FIG. 3, And may be performed by the apparatus 100.

Referring to FIG. 4, in the original cluster structure including at least two nodes, the step of generating the first cluster assignment vector indicating the degree to which the nodes belong to the original cluster structure is performed by the vector generation unit 140 (S110).

Next, a step of generating a disturbance cluster assignment vector for the disturbance community structure is performed, and this step may be performed by the vector generation unit 140 (S120). The disturbance cluster structure may mean a cluster structure in which at least two nodes other than the nodes included in the original cluster structure are removed from any one of the nodes included in the original cluster structure, Is as described above.

Next, a step of generating a conditional entropy for the original cluster structure is performed, and this step may be performed by the conditional entropy generation unit 160 (S130).

More specifically, the conditional entropy generator 160 generates the original conditional entropy of the original cluster assignment vector based on the original cluster assignment vector and the disturbance cluster assignment vector. Herein, the original conditional entropy may mean the amount of information additionally required to explain the original community structure based on the disturbance community structure, but this is not limitative.

Next, a step of generating a conditional entropy for the disturbed community structure is performed, and such a step may be performed by the conditional entropy generation unit 160 (S140).

More specifically, the conditional entropy generator 160 generates disturbance conditional entropy for the disturbance cluster assignment vector based on the original cluster assignment vector and the disturbance cluster assignment vector. Here, the disturbance conditional entropy may mean the amount of information additionally required to explain the disturbance community structure based on the original community structure, but the present invention is not limited thereto.

On the basis of this, the large value of conditional entropy means that there is a large structural difference between original and disturbed community structure. That is, if the corresponding node is removed or the node fails, it means that a large change in the cluster structure including the node may occur.

On the other hand, the small value of conditional entropy means that there is little structural difference between original and disturbed community structure. That is, even if the corresponding node is removed or the node fails, it means that there is no significant change in the cluster structure including the node because the node has the same or similar role as the corresponding node.

Here, according to an exemplary embodiment, assuming that the original cluster structure includes N nodes, the value of the conditional entropy may have a value of at least 0 at the maximum log N, for example.

Next, a step of deriving the cluster structure disturbance index is performed, which can be performed by the index derivation unit 180. [

The cluster structure disturbance index is an index that indicates the uniqueness of the role of the node, and therefore can be an indicator of the degree of disturbance due to the removal of the node.

More specifically, the index derivation unit 180 calculates a population structure disturbance index indicating the degree of disturbance due to removal of the first node based on the original conditional entropy and the disturbance conditional entropy generated by the conditional entropy generation unit 160 . In this case, the index derivation unit 180 may divide the sum of the original conditional entropy and the disturbance conditional entropy, and divide the sum by the number of nodes constituting the disturbance cluster structure. The divided value may be deduced by the cluster structure disturbance index have.

Therefore, by using the cluster structure disturbance index, the role uniqueness can be derived for a certain node, so that the influence on the cluster structure can be quantified when the corresponding node is removed or when the corresponding node fails. In addition, since the cluster structure disturbance index is normalized (by log | N | -1), the size of such an index can be recognized more easily.

As described above, according to the embodiment of the present invention, since the role uniqueness can be derived for a node, it is possible to quantify the influence on the cluster structure when the corresponding node is removed or a failure occurs in the corresponding node. In addition, since the cluster structure disturbance index is normalized (by log | N | -1), the size of such an index can be recognized more easily.

Figs. 5A and 5B and Figs. 6A and 6B illustrate the node before and after the node is removed from the cluster structure.

When the hub node 40 shown in FIG. 5A is removed, the cluster structure 49 of FIG. 5A is divided into eight cluster structures (one cluster structure for each peripheral node) as shown in FIG. 5B. That is, since the role of the hub node 40 in the cluster structure of FIG. 5A is unique, the removal of the hub node 40 causes a large change in the cluster structure. That is, the cluster structure disturbance index of the hub node 40 has a relatively high value. Referring to Equation 5, N is 9, log 8 is 3, g (40) is (40,41), (40,42), ..., (40,47), )}to be. Therefore, since the value of H (C | C ') is 1.5 and the value of H (C' | C) is 1.5, finally, the value of the cluster structure disturbance index of the hub node 40 is 1. That is, additional information required for explaining the disturbance cluster structure of FIG. 5B in the original cluster structure of FIG. 5A is defined by the probability distribution and the joint probability distribution vector, and the allocation vector components excluding the hub node 40 are denoted by Cx, C ' (x) = (1), P (C'x) = (1/8, 1/8, 1/8, 1/8, 1/8, 1/8, 1, / 8, 1/8), P (Cx, C'x) = (1/8, 1/8, 1/8, 1/8, 1/8, 1/8, to be. Substituting this into Equations (4) and (5), the cluster structure disturbance index has a value of 1.

6A, the hub node 60 and the peripheral nodes 61 to 64 connected thereto form one cluster structure 71, and the hub node 70 and the peripheral nodes 65 to 68 connected to the hub node 70 And another cluster structure 72 is formed. That is, two cluster structures are formed.

In this case, when the hub node 60 is removed, the cluster structure of FIG. 6A is merely merged into one cluster structure in two cluster structures as shown in FIG. 6B, . That is, the role of the hub node 50 in the cluster structure of FIG. 2B is not unique and overlaps with that of another hub node 51, and the removal of the hub node 50 does not cause a large change in the cluster structure . That is, the cluster structure disturbance index of the hub node 60 has a relatively low value. (C '| C) has a value of 0 and H (C' | C ') has a value of 0, and therefore, The value of the cluster structure disturbance index of the hub node 60 and the hub node 70 is zero.

6A is defined by a probability distribution and a joint probability distribution vector, and the allocation vector components except for the hub node 60 are denoted by Cx and C ', respectively. In other words, the additional information necessary for explaining the disturbance cluster structure of FIG. (1), P (C'x) = (1) and P (Cx, C'x) = (1), respectively. Substituting this into Equations (4) and (5), the cluster structure disturbance index has a value of zero.

Based on this, it can be seen that the value of the cluster structure disturbance index is different according to the uniqueness of the role of the node.

Meanwhile, the method of deriving the disturbance index of the community structure according to an embodiment of the present invention can be implemented in a recording medium on which a computer program is recorded.

Combinations of each step of the flowchart and each block of the block diagrams appended to the present invention may be performed by computer program instructions. These computer program instructions may be loaded into a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus so that the instructions, which may be executed by a processor of a computer or other programmable data processing apparatus, And means for performing the functions described in each step are created. These computer program instructions may also be stored in a computer usable or computer readable memory capable of directing a computer or other programmable data processing apparatus to implement the functionality in a particular manner so that the computer usable or computer readable memory It is also possible for the instructions stored in the block diagram to produce a manufacturing item containing instruction means for performing the functions described in each block or flowchart of the block diagram. Computer program instructions may also be stored on a computer or other programmable data processing equipment so that a series of operating steps may be performed on a computer or other programmable data processing equipment to create a computer- It is also possible that the instructions that perform the processing equipment provide the steps for executing the functions described in each block of the block diagram and at each step of the flowchart.

Also, each block or each step may represent a module, segment, or portion of code that includes one or more executable instructions for executing the specified logical function (s). It should also be noted that in some alternative embodiments, the functions mentioned in the blocks or steps may occur out of order. For example, two blocks or steps shown in succession may in fact be performed substantially concurrently, or the blocks or steps may sometimes be performed in reverse order according to the corresponding function.

The foregoing description is merely illustrative of the technical idea of the present invention and various changes and modifications may be made by those skilled in the art without departing from the essential characteristics of the present invention. Therefore, the embodiments disclosed in the present invention are intended to illustrate rather than limit the scope of the present invention, and the scope of the technical idea of the present invention is not limited by these embodiments. The scope of protection of the present invention should be construed according to the following claims, and all technical ideas within the scope of equivalents should be construed as falling within the scope of the present invention.

100: Device for deriving the disturbance level of the community structure
120: Input unit
140: Vector generating unit
160: conditional entropy generation unit
180: index derivation unit

Claims (7)

An original cluster assignment vector for an original cluster structure including at least two nodes and a disturbance cluster assignment vector for a disturbance cluster structure in which the first node, which is one of the at least two nodes in the original cluster structure, Vector generating part;
The original conditional entropy of the original community structure indicating the extent to which the original community structure differs from the disturbance community structure and the disturbance to the disturbance community structure indicating the extent to which the disturbance community structure differs from the original community structure A conditional entropy generation unit for generating a conditional entropy; And
And an index derivation unit for deriving a cluster structure disturbance index indicating a degree of disturbance due to removal of the first node based on the original conditional entropy and the disturbance conditional entropy
Apparatus for deriving disturbance degree of community structure.
The method according to claim 1,
Wherein the original community structure differs from the disturbance community structure in that the original community structure is a quantity of information indicating a difference in structure with the disturbance community structure based on the disturbance community structure,
Wherein the disturbance community structure differs from the original community structure in that the disturbance community structure is an amount of information indicating a difference in structure with the original community structure based on the original community structure,
Apparatus for deriving disturbance degree of community structure.
The method according to claim 1,
Wherein the index derivation unit comprises:
A value obtained by dividing the sum of the original conditional entropy and the disturbance conditional entropy by the number of nodes constituting the disturbance cluster structure is derived as the cluster structure disturbance index
Apparatus for deriving disturbance degree of community structure.
A method of deriving the disturbance degree of the community structure by the apparatus for deriving the disturbance degree of the community structure,
(a) generating an original cluster structure including at least two nodes, the first cluster assignment vector indicating the degree to which the node belongs to the original cluster structure;
(b) a disturbance community structure that is a community structure in which a first node, which is one of the nodes constituting the original community structure, is removed; and a second community that represents the degree to which the remaining nodes except for the first node belong to the disturbance community structure Generating an assignment vector;
(c) generating an original conditional entropy for the original community structure, the original conditional entropy representing the degree to which the original community structure differs from the disturbance community structure;
(d) generating disturbance conditional entropy for the disturbance community structure, the degree of disturbance community structure being different from the original community structure; And
(e) deriving a cluster structure disturbance index indicating a degree of disturbance due to removal of the first node based on the original conditional entropy and the disturbance conditional entropy
A method for deriving disturbance degree of community structure.
5. The method of claim 4,
The degree to which the original community structure differs from the disturbance community structure in the step (c) is that the original community structure is a quantity of information indicating a difference in structure with the disturbance community structure on the basis of the disturbance community structure And,
The degree to which the disturbance community structure differs from the original community structure in the step (d) is that the disturbance community structure is a quantity of information indicating a difference in structure with the original community structure on the basis of the original community structure To
A method for deriving disturbance degree of community structure.
5. The method of claim 4,
The step (e)
A value obtained by dividing the sum of the original conditional entropy and the disturbance conditional entropy by the number of nodes constituting the disturbance cluster structure is derived as the cluster structure disturbance index
A method for deriving disturbance degree of community structure.
A recording medium on which a computer program for performing a method for deriving a disturbance degree of the community structure according to any one of claims 4 to 6 is recorded.

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