CN102684912B - Community structure mining method based on network potential energy - Google Patents
Community structure mining method based on network potential energy Download PDFInfo
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- CN102684912B CN102684912B CN201210104303.9A CN201210104303A CN102684912B CN 102684912 B CN102684912 B CN 102684912B CN 201210104303 A CN201210104303 A CN 201210104303A CN 102684912 B CN102684912 B CN 102684912B
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Abstract
The invention provides a community structure mining method based on network potential energy. The community structure mining method comprises the following steps of: introducing a physical concept of potential energy into a complex network, defining node potential energy and network potential energy of the complex network, dividing the complex network by virtue of an optimal potential function, and finally mining a community structure in the complex network. Because the network potential energy can better utilize topological information of the network to reflect the closeness of a topological structure of the whole network, the community structure mining method can be used for greatly improving the detection precision of the community structure.
Description
Technical field
What the present invention relates to is the method for the data mining in a kind of complex network field, the specifically community structure method for digging of complex network.
Background technology
Complex network is a kind of abstraction form of complication system in real world, node in complex network represents the individuality in complication system, the connection between node in representative system between individuality according to a kind of relation of certain regular self-assembling formation or arteface.At present, complex network has been widely used in characterizing the various complication systems such as neural net, electric power networks, the Internet, social relationships net.
Complex network comprises important topological property, i.e. a community structure.That is to say, whole complex network is made up of several community structures, and the node of each community structure inside connects very tight, and the connection between community structure is relatively sparse.Community structure is corresponding to the functional unit or the organizations etc. that have common feature in reality, for example in the Internet, community structure is exactly that the number of site of common topic is discussed, and community structure is exactly a group that has people's composition of common interest hobby in social relationships net.Therefore the community structure of, excavating in complex network has important practical significance.
Through literature search, M.E.J.Newman and M.Girvan are at article " Community structure in social and biological networks[J] " (" community structure in society and bio-networks ") (Proc.Natl.Acad.Sci.USA 99, 7821-7826 (2001)) in a kind of community mining method based on shortest path has been proposed, be specially: by the shortest path between any two points in computing network, obtain the shortest path table of whole network, utilize number of times that every limit of this table statistics passed through by the shortest path weights as this limit, remove the limit of weights maximum in network, then recalculate the weights on each limit in whole network, repeat above step, until whole network is divided into rational community structure.But it is not very high problem that the method exists accuracy of detection.
Find through retrieval again, Tyler has proposed a kind of community mining method based on local shortest path in article " Email as spectroscopy:Automated discovery of community structure within organizations " (" using Email as frequency spectrum: automatically find in-house community structure ") (The Information Society 21 (2), 143-153 (2005)).Its method is, shortest path in computing network between any two points, and only calculating and record length are less than the shortest path of set threshold value T, so just obtain a local shortest path table, recycle the number of times that passed through by shortest path on every limit of this table statistics weights as this limit, remove the limit of weights maximum in network, then recalculate the weights on each limit in whole network, repeat above step, until whole network is divided into rational community structure.The method can improve the speed of method, and the memory space that reduction method is required still can cause the reduction of accuracy of detection.
Find through retrieval again, the people such as Filippo Radicchi and Claudio Castellano have proposed a kind of community mining method based on Local network topology structure in article " Defining and identifying communities in networks[J] " (" community structure in definition recognition network ") (Proc.Natl.Acad.Sci.USA 101,2658-2663 (2004)).Its method is: by the local topology feature of community structure in Analysis of Complex network, propose using the triangular structure in network as the most basic structure of Web Community, the quantity of the triangular structure being subordinated to by every limit in statistics network is as the weights on this limit, remove the limit of weights maximum in network, then recalculate the weights on each limit in whole network, repeat above step, until whole network is divided into rational community structure.The method has been considered the local features of network topology structure, but also exists the problem that community structure accuracy of detection is not high.
Summary of the invention
The present invention is directed to the deficiency that above-mentioned prior art exists, a kind of community mining method of potential energy Network Based is provided, the concept of potential energy in physics is incorporated in Complex Networks Analysis, the definition of network potential energy has been proposed, and by the potential-energy function of peak optimizating network, reach the object of excavating community structure in complex network.
The present invention is achieved through the following technical solutions, the present invention includes following steps:
The first step, for complex network G=(V, E), V represents the set of node, E represents the set on limit.The adjacency matrix A of input network G does data preliminary treatment, obtains pretreated network adjacent matrix A '.
Described data preliminary treatment, refers to that removing network moderate is 1 node, removes the row and column that this point is corresponding in the adjacency matrix of network input.
The degree of described node, refers to the number of other nodes that are connected with this node.
Second step, for pretreated network adjacent matrix A ', analyzes topology of networks.Retrieve other nodes in whole network for each node with the searching method of breadth-first, obtain the distance between any two nodes, thereby set up Distance matrix D.
Described breadth-first, refer to that when search is from start node, all nodes that retrieval is connected with start node, obtain the node of ground floor, and then start from the node of ground floor all nodes that retrieval is connected with the node of ground floor, obtain the node of the second layer, by that analogy, until traveled through all nodes in network.
Distance between described any two nodes, refers to the limit number that in network, between 2, shortest path comprises.
The 3rd step, the distance matrix of node Network Based, calculates whole network of network potential energy.Each node in network is regarded as to the source of a gravitational field, can be obtained the potential energy between any two nodes in network
computing formula is as follows:
Wherein, R is a constant, can be set as a positive number, and D is the distance matrix obtaining in second step.
The network potential energy of whole network G is the potential energy sum between all nodes of comprising of network, and computing formula is as follows:
The 4th step, for every limit e in network
k, sub-network G after calculating deletion this edge
k=G-{e
knetwork potential energy and the network potential energy difference of former network G
computing formula is as follows:
The 5th step, removes
be worth maximum limit, and check whether generated independently sub-network.If no, get back to the 4th step; If there is independently sub-network to produce, whether the sub-network that inspection division generates meets predefined strong and weak community structure.If result of calculation meets strong and weak community structure, turn the first step, method continues; If result of calculation does not meet strong and weak community structure, method finishes, and turns the 6th step.
Described independently sub-network, refers to that set of node and limit collection are all contained in former network, and other node in node and former network does not exist the network of connection.
Described strong community structure, refers to the topological structure that meets following condition: for each node of inside, community, all meet with the linking number of community's interior nodes and be greater than and the linking number of community's exterior node.
Described weak community structure, refers to the topological structure that meets following condition: the linking number of inside, community is greater than the external linking number in community.
The 6th step, the result obtaining for the 5th step, re-constructs primitive network figure.The node that preliminary treatment in the first step is fallen, rejoins in primitive network figure, and belongs to the community structure at the node place being directly connected with it.
The present invention is incorporated into the concept of potential energy in physics in complex network, has defined node potential energy, the network potential energy of complex network, by optimization potential-energy function, complex network is divided, and finally excavates the community structure in complex network.Because network potential energy can utilize the topology information of network preferably, reflect the tightness degree of whole network topology structure, so the precision of the method improves greatly.
Brief description of the drawings
Fig. 1 is the community mining method flow diagram of potential energy Network Based;
Fig. 2 is the adjacency matrix schematic diagram of complex network;
Fig. 3 is the community structure figure of karate club.
For foregoing of the present invention can be become apparent, preferred embodiment cited below particularly, and accompanying drawing shown in coordinating, be described in detail below.
Embodiment
Below embodiments of the invention are elaborated, the present embodiment is implemented under taking technical solution of the present invention as prerequisite, provided detailed execution mode and concrete operating process, but protection scope of the present invention is not limited to following embodiment.
The present embodiment adopts the karate club data set of the classical data set Zachary in community network, and this network is processed according to flow process shown in Fig. 1 of the present invention, and concrete steps are as follows:
First step S11, does data preliminary treatment for the adjacency matrix A of karate club network G, and the node 12 that is 1 for network moderate removes in network, in the adjacency matrix of network input, removes the 12nd row and 12 row.
Second step S12, for pretreated network A ', analyze topology of networks.Retrieve other nodes in whole network for each node with the searching method of breadth-first, obtain the distance between any two nodes, thereby set up Distance matrix D.
The 3rd step S13, according to the distance matrix of network, calculates whole network of network potential energy.Each node in network is regarded as to the source of a gravitational field, can be obtained the potential energy between any two nodes in network
computing formula is as follows:
Wherein, R is set as positive integer 1, and D is the distance matrix obtaining in second step.
Whole network of network potential energy is the potential energy sum between all nodes of comprising of network, and computing formula is as follows:
Thereby, can calculate the network potential energy of whole network G before iteration
The 4th step S14, for every limit e in network
k, sub-network G after calculating deletion this edge
k=G-{e
knetwork potential energy and the network potential energy difference of former network G
computing formula is as follows:
The 5th step S15, removes
the limit of value maximum, upgrade Distance matrix D, and check whether generated independently sub-network.If no, get back to the 4th step; If there is independently sub-network to produce, whether the sub-network that inspection division generates meets predefined strong and weak community structure.If result of calculation meets strong and weak community structure, turn the first step, method continues; If result of calculation does not meet strong and weak community structure, circulation finishes, and turns the 6th step.
Described independently sub-network, refers to that set of node and limit collection are all contained in former network, and other node in node and former network does not exist the network of connection.
Described strong community structure, refers to the topological structure that meets following condition: for each node of inside, community, all meet with the linking number of community's interior nodes and be greater than and the linking number of community's exterior node.
Described weak community structure, refers to the topological structure that meets following condition: the linking number of inside, community is greater than the external linking number in community.
The 6th step S16, the result obtaining for the 5th step, re-constructs primitive network figure.The node that preliminary treatment in the first step is fallen, rejoins in primitive network figure, and belongs to the community at the node place being directly connected with it.
More than experiment is used typical network data collection, calculating to method flow of the present invention and network potential energy is illustrated, the background knowledge of experimental result and data is basically identical, as shown in Figure 3, be divided the node ratio that enters correct community structure and reached 97.05%, thereby verified validity and the accuracy of this method.
Although the present invention discloses as above with preferred embodiment; so it is not in order to limit the present invention, anyly has the knack of this skill person, without departing from the spirit and scope of the present invention; when doing a little change and retouching, therefore protection scope of the present invention is when being as the criterion depending on the claim person of defining.
Claims (3)
1. a community structure method for digging for potential energy Network Based, is characterized in that, the method comprises the steps:
The first step, does data preliminary treatment to network adjacent matrix, and the degree of deleting nodes is not more than the corresponding row and column of node of given threshold value, obtains pretreated network adjacent matrix;
The degree of described node, refers to the number of other nodes that are connected with this node;
Described threshold value is the parameter of setting for data preliminary treatment;
Second step, for pretreated network data, analyzes topology of networks, sets up distance matrix;
The 3rd step, the distance matrix of node Network Based, calculates whole network of network potential energy.Each node in network is regarded as to the source of a gravitational field, can be obtained the potential energy between any two nodes in network
computing formula is as follows:
Wherein, R is a constant, can be set as a positive number, and D is the distance matrix obtaining in second step;
The network potential energy of whole network G is the potential energy sum between all nodes of comprising of network, and computing formula is as follows:
The 4th step, for every limit e in network
k, sub-network G after calculating deletion this edge
k=G-{e
knetwork potential energy and the network potential energy difference of former network G
computing formula is as follows:
The 5th step, removes
be worth maximum limit, and check whether generated independently sub-network; If no, get back to the 4th step; If there is independently sub-network to produce, whether the sub-network that inspection division generates meets predefined strong and weak community structure; If result of calculation meets strong and weak community structure, turn the first step, method continues; If result of calculation does not meet strong and weak community structure, method finishes, and turns the 6th step;
Wherein, described independently sub-network, refers to that set of node and limit collection are all contained in former network, and other node in node and former network does not exist the network of connection;
Described strong community structure, refers to the topological structure that meets following condition: for each node of inside, community, all meet with the linking number of community's interior nodes and be greater than and the linking number of community's exterior node;
Described weak community structure, refers to the topological structure that meets following condition: the linking number of inside, community is greater than the external linking number in community;
The 6th step, the result obtaining for the 5th step, re-constructs primitive network figure, and the node that preliminary treatment in the first step is deleted rejoins in primitive network figure, and belongs to the community at the node place being directly connected with it.
2. the community structure method for digging of potential energy Network Based according to claim 1, is characterized in that, is that data preliminary treatment is that to remove the degree of nodes be 1 node described in the first step, in the adjacency matrix of network input, removes the row and column that this point is corresponding.
3. the community structure method for digging of potential energy Network Based according to claim 1, it is characterized in that, second step concrete steps are: analyze topology of networks, retrieve other nodes in whole network for each node with the searching method of breadth-first, obtain the distance between any two nodes, thereby set up distance matrix.
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| CN101272328A (en) * | 2008-02-29 | 2008-09-24 | 吉林大学 | Dispersion type community network clustering method based on intelligent proxy system |
| CN101383748A (en) * | 2008-10-24 | 2009-03-11 | 北京航空航天大学 | Community division method in complex network |
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| CN101272328A (en) * | 2008-02-29 | 2008-09-24 | 吉林大学 | Dispersion type community network clustering method based on intelligent proxy system |
| CN101383748A (en) * | 2008-10-24 | 2009-03-11 | 北京航空航天大学 | Community division method in complex network |
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