Information processor, information processing method, and program

Abstract

To provide a network analysis technology for a multilayer network obtained by synthesizing a plurality of networks.SOLUTION: An information processor includes: an acquisition unit for acquiring a first network and a second network; a superposition unit for superposing the first network with the second network depending on a degree of reflection to generate a third network; and an extraction unit for extracting a community of a seed node in the third network, where the extracted community is extended or contracted depending on variation in the degree of reflection.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present disclosure relates to an information processing apparatus, an information processing method, and a program.

Background Art

[0002] Community extraction is one of the most commonly used approaches for network analysis. It has a wide range of applications such as friend recommendation on social media, product recommendation to users, public opinion analysis, and identification of terrorist group clusters.

Prior Art Documents

Non-Patent Documents

[0003]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] In conventional community extraction, a single network has been targeted. However, a single network is merely fragmented information cut out from a complex network in the real world. Therefore, in community extraction based on such fragmented information, the method may not be sufficient as a means for analyzing the network structure and the behavior of each node.

[0005] In recent years, research has been conducted on multi-layer networks in which a plurality of layers are stacked with one network as one layer. For example, as an example of a multi-layer network in the real world, there is an airline network (transportation network between airports). This is a model in which airports are nodes and non-stop flights between airports are edges, and it can be treated as a multi-layer network by considering the airline networks of different airlines as different layers.

[0006] An object of the present disclosure is to provide a network analysis technique for a multi-layer network synthesized from a plurality of networks.

Means for Solving the Problem

[0007] One aspect of the present disclosure includes an acquisition unit that acquires a first network and a second network, a superimposing unit that superimposes the first network and the second network according to a reflection degree to generate a third network, and an extraction unit that extracts a community of seed nodes in the third network, and the community to be extracted expands or contracts according to a change in the reflection degree, relating to an information processing apparatus.

Effect of the Invention

[0008] According to the present disclosure, it is possible to provide a network analysis technique for a multi-layer network synthesized from a plurality of networks.

Brief Description of the Drawings

[0009]

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DETAILED DESCRIPTION OF THE INVENTION

[0010] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings.

[0011] In the following embodiments, an information processing apparatus that executes network analysis on a multi-layer network generated by synthesizing a plurality of networks is disclosed.

[0012] [SUMMARY OF THE DISCLOSURE] The information processing apparatus 100 according to the following embodiments generates a multi-layer network in which a plurality of networks are superimposed, and extracts, as a community of the seed node, a node group in the generated multi-layer network whose degree of closeness to the seed node is equal to or greater than a predetermined threshold. The information processing apparatus 100 weights the network to be superimposed according to the reflectivity parameter r described in detail below, and generates a multi-layer network from the weighted network. Then, the information processing apparatus 100 extracts the community of the seed node in the generated multi-layer network.

[0013] The reflectivity parameter r described later assigns weights to each network when two networks are superimposed. The closer r is to 0, the closer the community extracted in the multi-layer network is to the community of one of the networks constituting the multi-layer network, and the closer r is to 1, the reflectivity parameter is designed so that the community extracted in the multi-layer network is closer to the community of the other network constituting the multi-layer network.

[0014] Generally, in a multi-layer network, the meanings of the two layers are different for network analysts, and it is important to determine to what extent the community of each layer is reflected in determining the community after superposition. The reflectivity parameter r can be considered to indicate the reflectivity of the community of each layer. For the reflectivity parameter r, for fast search of the optimal reflectivity by binary search or the like, (1) the reflectivity increases monotonically, and (2) the reflectivity takes a wide range of values so that it can cope with any reflectivity that the user considers optimal, whether large or small, is important. When community extraction is performed while increasing the reflectivity parameter r, a method will be disclosed later in which the reflectivity monotonically increases / decreases with a wide variation range.

[0015] Specifically, as the community extraction method, APPR (Approximate Personalized PageRank) is used, and the reflectivity is controlled by utilizing the fact that the closeness index DNPPR (Degree-Normalized PPR) for determining the nodes to be attributed to the community is controllable by weighting the edges. WAPPRS can show that (1) the reflectivity increases monotonically and (2) the reflectivity can vary over a wide range.

[0016] As a plurality of networks to be superimposed, for example, assume that there are a base layer and an additional layer as shown in FIG. 1. As shown in the figure, the base layer is composed of seven black nodes and six edges connecting the nodes as shown. Note that the nodes indicated by the dashed lines in the base layer do not exist in the base layer but only in the additional layer. For the seed node S in the base layer, three nodes surrounded by a dashed line can be extracted as a community.

[0017] On the other hand, the additional layer is composed of six black nodes and seven edges connecting the nodes as shown. The nodes indicated by the dashed lines in the additional layer do not exist in the additional layer but only in the base layer. For the seed node S in the additional layer, four nodes surrounded by a dashed line can be extracted as a community.

[0018] As shown in the figure, the information processing apparatus 100 synthesizes the base layer and the additional layer to form a multi-layer network. That is, the union of the node set of the base layer and the node set of the additional layer is used as the node set of the multi-layer network, and the base layer and the additional layer are superimposed so that the union of the edge set of the base layer and the edge set of the additional layer becomes the edge set of the multi-layer network. The community for the illustrated seed node S in the multi-layer network can be, for example, the node group illustrated by the dashed line.

[0019] The community of the seed node S in the multi-layer network can vary according to the value of the reflectivity parameter r (0 ≤ r ≤ 1). That is, as shown in FIG. 2, the information processing apparatus 100 multiplies each edge of the base layer by (1 - r) and multiplies each edge of the additional layer by r. In other words, for each edge in the multi-layer network, (1 - r) is multiplied when the edge is in the base layer, and r is multiplied when the edge is in the additional layer.

[0020] By changing the value of the reflectivity parameter r, the community of the seed node in the multi-layer network can also vary. For example, as shown in FIG. 3, when the reflectivity parameter r is close to 0, the community of the seed node S in the multi-layer network is the same as or similar to the community of the seed node S in the base layer. On the other hand, when the reflectivity parameter r is close to 1, the community of the seed node S in the multi-layer network is the same as or similar to the community of the seed node S in the additional layer.

[0021] In this way, by changing the value of the reflectivity parameter r, it is possible to expand and contract the community for the seed node of the multi-layer network generated by superimposing the base layer and the additional layer.

[0022] Here, the information processing apparatus 100 may be implemented by a computing device such as a server, a personal computer (PC), a smartphone, or a tablet, and may have, for example, a hardware configuration as shown in FIG. 4. That is, the information processing apparatus 100 includes a drive device 101, a storage device 102, a memory device 103, a processor 104, a user interface (UI) device 105, and a communication device 106 that are interconnected via a bus B.

[0023] Programs or instructions for realizing various functions and processes in the information processing apparatus 100 may be stored in a removable storage medium such as a CD-ROM (Compact Disk-Read Only Memory) or a flash memory. When the storage medium is set in the drive device 101, the program or instruction is installed from the storage medium via the drive device 101 into the storage device 102 or the memory device 103. However, the program or instruction does not necessarily have to be installed from the storage medium and may be downloaded from any external device via a network or the like.

[0024] The storage device 102 is realized by a hard disk drive or the like and stores files, data, etc. used for the execution of the installed program or instruction together with the installed program or instruction.

[0025] The memory device 103 is realized by a random access memory, a static memory, etc. When the program or instruction is activated, the program or instruction, data, etc. are read from the storage device 102 and stored. The storage device 102, the memory device 103, and the removable storage medium may be collectively referred to as a non-transitory storage medium.

[0026] The processor 104 may be realized by one or more CPUs (Central Processing Unit), GPUs (Graphics Processing Unit), processing circuitry, etc. that may be composed of one or more processor cores, and executes various functions and processes of the information processing apparatus 100 according to data such as programs, instructions, and parameters necessary for executing the programs or instructions stored in the memory device 103.

[0027] The user interface (UI) device 105 may be composed of input devices such as a keyboard, a mouse, a camera, and a microphone, output devices such as a display, a speaker, a headset, and a printer, and input / output devices such as a touch panel, and realizes an interface between the user and the information processing device 100. For example, the user may operate the information processing device 100 by operating a keyboard, a mouse, etc. on the GUI (Graphical User Interface) displayed on the display or the touch panel.

[0028] The communication device 106 is realized by various communication circuits that execute wired and / or wireless communication processing with communication networks such as external devices, the Internet, a LAN (Local Area Network), and a cellular network.

[0029] However, the above-described hardware configuration is merely an example, and the information processing device 100 according to the present disclosure may be realized by any other appropriate hardware configuration.

[0030] [Information Processing Device] Next, the information processing device 100 according to an embodiment of the present disclosure will be described. FIG. 5 is a block diagram showing the functional configuration of the information processing device 100 according to an embodiment of the present disclosure. As shown in FIG. 5, the information processing device 100 includes an acquisition unit 110, a superimposition unit 120, and an extraction unit 130. Each functional unit of the acquisition unit 110, the superimposition unit 120, and the extraction unit 130 may be realized by a computer program stored in the memory device 103 of the information processing device 100 being executed by the processor 104.

[0031] The acquisition unit 110 acquires a plurality of networks. Specifically, the acquisition unit 110 acquires layer information regarding each network to be superimposed that can be modeled as a graph structure. For example, for the additional layer L A and the base layer L B consider a case where a multi-layer network M is composed. Here, the additional layer L A and the base layer L B are LA =(V A , E A ), and L B =(V B , E B ), where V A and V B are the node sets of the additional layer L A and the base layer L B respectively, and E A and E B are the edge sets of the additional layer L A and the base layer L B respectively. The acquisition unit 110 can acquire L A =(V B =(V A , E A ), E A ), and L B =(V B , E B ) as the layer information between the additional layer L

[0032] Also, for the node v of the additional layer L A and the base layer L B , the object a represented by the node is called an actor. For example, the additional layer L A and the base layer L B can be modeled as the flight networks (transportation networks between airports) of airlines A and B, that is, with airports as nodes and non-stop flights between airports as edges. The set of actors of the additional layer L A is defined as

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[0033] The superimposing unit 120 superimposes a plurality of networks according to the reflectance to generate a multi-layer network. Specifically, the superimposing unit 120 superimposes the additional layer L A and the base layer L B to generate a multi-layer network M as follows.

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[0034] Also, regarding the actor set of the multi-layer network,

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[0035] When a certain actor has nodes in both the additional layer L A and the base layer L B such an actor is called a shared actor.

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[0036] Also, regarding the conversion between nodes and actors,

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[0037] Regarding the reflectivity parameter r, as shown in FIG. 7, the overlapping part 120 weights r for all edges e A of the additional layer L A ∈E A and weights 1 - r for all edges e B of the base layer L B ∈E B

[0038] The extraction unit 130 extracts the community of seed nodes in the multi - layer network. Here, the community C A with the node v

Number

[0039] Also, for the seed node v M (s) corresponding to the seed actor s in the multi - layer network M, the set of the top k nodes with the highest closeness is represented as T M (s,k). The reflectivity index regarding the seed actor s to the multi - layer network M is

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[0040] Also, for the reflectivity parameter r,

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[0041] Such a reflectivity index TKS changes such that as r approaches 0, it gets closer to the community of the seed actor s in the base layer L B and as r approaches 1, it gets closer to the community of the seed actor s in the additional layer L A .

[0042] Also, TKS i (s) The difference between the maximum value and the minimum value is defined as the reflection width (WR).

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[0043] The reflectivity defined in this way is based on the premise of using Degree-Normalized PPR (DNPPR) as the closeness index, and the shared actor

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[0044] For example, the extraction unit 130 may use the known community extraction algorithm APPR (Reid Andersen, Fan Chung, and Kevin Lang. Local graph partitioning using pagerank vectors. In 2006 47 th Annual IEEE Symposium on Foundations of Computer Science (FOCS ’06), pp. 475-486, 2006). As shown in Algorithm 1 of FIG. 8, in APPR, a PPR vector with the seed node u obtained by performing a random walk as in Algorithm 2

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[0045] PPR and the weight degree can be made variable by the weight on the edge, and DNPPR can also be made variable by the weight. Here, how PPR changes with weighting is described in Algorithm 2. PPR is the visit probability of each node in the random walk. The random walk is a model in which a random walker starts from the starting point, transitions to any of the adjacent nodes with probability α, and returns to the starting point with probability 1 - α. The probability p v (x) from a certain node v to an adjacent node x is

Number

[0046] In this embodiment, for all edges e A of the additional layer L A ∈ E A and for all edges e B of the base layer L B ∈ E B weights r and 1 - r are respectively assigned, and for all nodes v ∈ V M of the multi - layer network M, a starting - point return edge from a node v M (s) to the seed node v is introduced, and the reflectivity TKS is controlled according to Algorithm 3 shown in FIG. 9.

[0047] When considering the community of the shared actor

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[0048] Here, the closer r is to 0, the closer d w M (v M (a)) is to d w B (v B (a)), and the closer r is to 1, the closer d w M (v M (a)) is to d w A (v A (a)). Furthermore, the closer r is to 0, the smaller PPR s,A (a) becomes, so PPR s,M (a) approaches PPR s,B (a), and the closer r is to 1, the smaller PPR s,B (a) becomes, so PPR s,M (a) approaches PPR s,A (a). It can be seen.

[0049] This means that depending on the value of r, d w M (v M (a)) is close to the degree in the additional layer L A or the base layer LB close to the degree in s,M (a) is the additional layer L A close to the PPR in B It means that it can continuously control whether it is close to the PPR in the base layer L or close to the PPR in the additional layer L. For example, [Number] if it is the case that [Number] can be approximated to. This means that the DNPPR after superposition is approximated to the DNPPR calculated only by the additional layer L. Conversely, when 0 < r << 1, the DNPPR after superposition is also approximated to the DNPPR calculated only by the base layer L. In this way, by increasing the weight of the layer for which a high reflectance is desired, the influence of the other layer on the PPR and the weighted degree can be relatively reduced, and the DNPPR after superposition can be continuously changed to a value close to the DNPPR of the additional layer L A or to a value close to the base layer L. B or to a value close to the base layer L. A of the additional layer L B or to a value close to the base layer L.

[0050] The extraction unit 130 can determine nodes with a predetermined degree of closeness or more in the multi-layer network M superimposed according to the reflectance as described above, and extract the community of the seed nodes based on the determined node group.

[0051] Note that for the eigenactor, there may be a case where the value of the DNPPR cannot be reduced by the reflectance parameter r. For this reason, the extraction unit 130 introduces a starting point regression edge, and the reflectance can also be controlled to a small value in the eigenactor.

[0052] For example, for the shared actor, the approximation of the DNPPR as described above is possible, but this is [Number] This is because it becomes [the following]. On the other hand, when a is the eigen-actor of the base layer L A this approximation does not hold, [Number] and it becomes [the following]. In this equation, although the PPR s,B (a) in the numerator and (1 - r)·d w B (v B (a)) in the denominator become small, since both the numerator and the denominator become small values, it cannot be determined in advance whether the overall DNPPR will increase or decrease. Although one wants to lower the reflectance of the base layer L B and raise the reflectance of the additional layer L A nevertheless, in M of the actor a that has nodes only in the base layer L B the DNPPR of the node v M (a) may enter the result C M where it increases. As a result, there is a possibility that the reflectance of the base layer L B increases and the reflectance of the additional layer L A decreases. This means that the reflectance cannot be controlled.

[0053] In one embodiment, the extraction unit 130 may introduce start - regression edges from the seed node to all the nodes of the multi - layer network M and extract the community of the seed node. Regarding the eigen - actor, the PPR s,B (a) and (1 - r)·d w B (v B (a)) which should have a small influence cannot be relativized by the PPR s,A (a) and r·d w A (v A (a)) as is different from the case of the shared actor.

[0054] The start - regression edge, as shown in FIG. 9, is an edge from an arbitrary node v ∈ V M on the multi - layer network M to the seed node v M(s) generates edges with weight r and directed edges with weight 1 - r. By generating γ edges with weight r and γ directed edges with weight 1 - r respectively, the weight degree can also be relativized in the eigenvector. Thus, DNPPR can be defined as follows.

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[0055] As a result, the following is obtained.

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[0056] According to the above-described embodiments, by introducing the reflectivity parameter r, it is possible to control whether the DNPPR in the multi-layer network approaches the value of the DNPPR of the additional layer or the value of the DNPPR of the base layer. Thereby, the community of the seed nodes in the multi-layer network can be adjusted. Also, by introducing the starting point return edge, the reflectivity can be controlled even in the eigenvector. As a result, it is possible to realize the reflectivity TKS, the monotonic increase degree FMI, and the wide reflection width WR.

[0057] In the above-described embodiments, an example of superimposing airline networks of different airlines has been described. However, the present disclosure is not limited to this, and it is also applicable to cases where a plurality of services having different databases such as SNS and messaging services store a common node (for example, an account, a file, etc.). When the attributes of the node are known, applications such as friend recommendations on SNS and music recommendations on streaming services can be executed between different services by community extraction, and the specific form of its realization can also be controlled depending on which attribute is focused on.

[0058] The common node described here includes the following four patterns. · A case where a globally uniquely identifiable ID is pre-assigned (IATA 3-letter code in an airline network, URL in an Internet network) · A case where, although it cannot be globally identified, different IDs are pre-assigned and can be identified as being the same by some kind of naming (accounts set with different email addresses on multiple SNSs but belonging to the same person) · A case where, although no ID is originally assigned, by assigning an ID, the identity can be identified (entities within a physical space such as a tourist destination) · A combination of the above three patterns (for example, a case where a globally uniquely identifiable ID is assigned in one network but no ID is assigned in the other network)

[0059] As described above in detail for the embodiments of the present disclosure, the present disclosure is not limited to the specific embodiments described above, and various modifications and changes are possible within the scope of the gist of the present disclosure described in the claims.

Explanation of Signs

[0060] 100 Information processing apparatus 110 Acquisition unit 120 Superimposing unit 130 Extraction unit

Claims

1. An acquisition unit that acquires a first network and a second network; An overlay unit that overlays the first network and the second network according to a reflectivity to generate a third network; An extraction unit that extracts a community of seed nodes in the third network; It has, The community to be extracted expands or contracts according to a change in the reflectivity, an information processing apparatus.

2. The overlay unit generates the third network by weighting the first network and the second network according to the reflectivity, The extraction unit adds a regression edge between the seed node and each node of the third network, the information processing apparatus according to claim 1.

3. The extraction unit extracts the community based on the regression edge, the information processing apparatus according to claim 2.

4. The extraction unit controls the nodes of the community between a first community of the first network and a second community of the second network according to the reflectivity, the information processing apparatus according to claim 1.

5. Acquiring a first network and a second network; Overlaying the first network and the second network according to a reflectivity to generate a third network; Having extracting a community of seed nodes in the third network, The community to be extracted expands or contracts according to a change in the reflectivity, an information processing method executed by one or more computers.

6. Acquiring a first network and a second network; Overlaying the first network and the second network according to a reflectivity to generate a third network; Causing one or more computers to execute extracting a community of seed nodes in the third network, The community to be extracted expands or contracts according to a change in the reflectivity, a program.

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