CN107578136A - The overlapping community discovery method extended based on random walk with seed - Google Patents
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Abstract
The present invention relates to a kind of overlapping community discovery method extended based on random walk with seed, random walk selected seed community, Similarity Measure and optimization auto-adaptive function community has been used to extend, the community discovery on extensive social networks is realized, is comprised the following steps：1st, initial data is read, obtains network structure and node neighbor information；2nd, according to the transition probability matrix of node, rating matrix and node and the similarity of community, the set of seed community is obtainedSeeds；3rd, according to society's similarity between intervals optimization seed community setSeeds；4th, according to the similarity and adaptive fitness function expansions community of seed and community；5th, the free node in network is handled with community's similarity and society's similarity between intervals according to node and merges similar community；6th, network overlapped community structure is exported.This method efficient, accurate can must find overlapping community.
Description
Technical Field
The invention relates to the technical field of overlapping community discovery on a social network, in particular to an overlapping community discovery method based on random walk and seed expansion.
Background
In real life, many complex network structures exist, such as social networks, scientist collaboration networks, literature citation networks, protein collaboration networks, and online social networks. The most critical characteristics of these complex networks can be abstracted as consisting of a number of nodes and edges, wherein the nodes represent individuals in the network, the edges represent the connections between the individuals, and the edges can be assigned with weight values. Communities in a complex network typically require close point connections within a community, while point connections between communities are sparse. Community discovery is one of the key technologies for studying complex network structures. The purpose of community discovery is to efficiently and accurately discover these tight communities from a complex network structure.
The community structure is an important structure in a complex network, how to efficiently and accurately dig out the structure and information hidden in the community is still a difficult point, and in recent years, a lot of people are attracted to carry out deep research on the community structure. At present, a plurality of global community discovery algorithms based on network structure division are proposed, including hierarchical clustering algorithm, spectrum method, cluster-based method, edge clustering, label propagation and the like. The global community discovery algorithm needs to perform overall cognition on the structural information of the whole network, and some defects exist in a complex network with a large scale or incomplete scale, so that the local community discovery algorithm based on seed expansion exists. The local community discovery algorithm based on seed expansion usually starts from a seed node in a network, and utilizes local information of a community to continuously add nodes in the network to discover a community structure.
The existing seed expansion-based local community discovery algorithm has achieved certain achievements in community discovery, but still has the following problems: firstly, the time and space complexity of the algorithm is relatively high, and the algorithm has defects when processing a large-scale network; secondly, the algorithm usually selects nodes as seed nodes only through a certain simple strategy, so that the accuracy of community expansion mining is influenced; finally, the closeness of the node added into the community cannot be considered from multiple aspects in the community expansion stage, and the discovered community quality is not high.
Disclosure of Invention
The invention aims to provide an overlapping community discovery method based on random walk and seed expansion, which can efficiently and accurately discover overlapping communities.
In order to achieve the purpose, the technical scheme of the invention is as follows: an overlapping community discovery method based on random walk and seed expansion comprises the following steps:
step 1: reading original data, and acquiring network structure and node neighbor information;
step 2: acquiring seed community set according to the transition probability matrix and the scoring matrix of the nodes and the similarity between the nodes and the communities;
and step 3: optimizing seed community set according to the similarity among communities;
and 4, step 4: expanding the community according to the similarity between the seed and the community and a self-adaptive fitness function;
and 5: processing free nodes in the network according to the similarity between the nodes and the communities and the similarity between the communities and combining similar communities;
step 6: and outputting the network overlapping community structure.
Further, in step 2, according to the transition probability matrix and the score matrix of the node and the similarity between the node and the community, the method for obtaining the seed community set is as follows:
step 2.1: adjacency matrix A according to networkuvAnd node degree kvTo obtain a transition probability matrix Puv：
Puv＝Auv/kv(1)
PuvThe middle element represents the probability that the node u randomly walks one step to reach the node v;
further obtaining a transition probability matrix P after the random walk t stepst uv：
Step 2.2: according to the transition probability matrix P after t steps of walkingt uvObtaining a scoring matrix B:
wherein T represents a threshold number of steps of random walk;
each element in the score matrix B represents a score obtained when the node u moves t steps to reach the node v, and is represented by B (u, v), and the closer the two nodes are connected, the higher the score is between the two nodes;
step 2.3: sorting B (u, v) in a descending order, and taking out the first nodes with larger scoring values to form an initial seed list B-list;
step 2.4: calculating the similarity between each node in the B-list as the node of the initial seed community and the neighbor node thereof and the community NC-SIM (v, C)i) When the similarity is larger than a set threshold value, adding the neighbor node into the seed community to finally obtain a seed community set Seeds;
wherein, v represents a node point,is node v and community CiDegree of associated edge, kvDegree for node v; NC _ SIM (v, C)i) The larger the value, the more likely it is that node v belongs to community Ci。
Further, in step 3, the method for optimizing the seed community set Seeds according to the inter-community similarity is as follows:
step 3.1: traversing each seed community in the seed community set Seeds, and calculating the similarity CC _ SIM (C) between the community intervalsi,Cj)；
Wherein, | overlap (C)i,Cj) I is Community CiAnd community CjNumber of nodes in common, | CiI is Community CiNumber of nodes, | CjI is Community CjThe number of nodes of (a); CC _ SIM (C)i,Cj) The larger the size, the community C is indicatediAnd community CjThe more similar the structure of (2), when exceeding the set threshold epsilon, merging the two communities into one community;
step 3.2: and if the similarity of the community intervals is greater than the threshold epsilon, merging the two communities to obtain the optimized seed community set Seeds'.
Further, in step 4, the method for expanding communities according to the similarity between the seeds and the communities and the adaptive fitness function is as follows:
step 4.1: obtaining the neighbor set NBSet of the seed community optimized in the step 3, traversing the NBSet, and calculating the NBSetNode-to-community similarity NC _ SIM (v, C) of each neighbor node and seed communityi)；
Step 4.2: taking out the first nodes with larger similarity to form a candidate node list C-list;
step 4.3: calculating an adaptive function fitness for adding the candidate nodes in the C-list into the community, adding the nodes which can increase the fitness into the community, and otherwise, setting the nodes as free nodes; the adaptive function fitness is calculated as follows:
wherein,andthe total values of the internal degree and the external degree of the subgraph g are respectively, and the parameter α is a positive real number and is used for controlling the discovered community scale;
step 4.4: updating the NBSet, and then repeating the steps until the NBSet is empty;
step 4.5: and obtaining an initial network overlapping community set C.
Further, in step 5, the method for processing free nodes in the network and merging similar communities according to the similarity between the nodes and the communities and the similarity between the communities is as follows:
step 5.1: calculating node-to-community similarity CC _ SIM (C) from free node to community in networki,Cj) Adding the free node into the community with the highest similarity, and updating an overlapped community set C;
step 5.2: calculating similarity between communities in overlapping community set C CC _ SIM (C)i,Cj) Merging communities with similarity greater than threshold epsilonAnd obtaining a new overlapped community set C'.
Further, in step 6, the method for outputting the network overlapping community structure includes: and obtaining a new overlapped community set C 'according to the optimization, wherein each element in the set C' represents a community, and then outputting the generated network overlapped community structure.
The method has the advantages that the random walk strategy, the similarity calculation and the optimization adaptive function are combined, and the method is applied to community discovery of a large-scale network, so that the structure division of the overlapped communities in the network can be effectively obtained, and beneficial supplement is provided for the development of network clustering in the direction of overlapped community discovery.
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FIG. 1 is a flow chart of an implementation of an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
The invention discloses an overlapping community discovery method based on random walk and seed expansion, which adopts random walk to select seed communities, similarity calculation and optimized adaptive function community expansion to realize community discovery on a large-scale social network, and comprises the following steps as shown in figure 1:
step 1: and reading the original data, and acquiring the network structure and node neighbor information.
Step 2: and obtaining seed community set according to the transition probability matrix and the scoring matrix of the nodes and the similarity between the nodes and the communities. The specific method comprises the following steps:
step 2.1: adjacency matrix A according to networkuvAnd node degree kvTo obtain a transition probability matrix Puv：
Puv＝Auv/kv(1)
PuvThe middle element represents the probability that the node u randomly walks one step to reach the node v;
further obtaining a transition probability matrix P after the random walk t stepst uv：
Step 2.2: according to the transition probability matrix P after t steps of walkingt uvObtaining a scoring matrix B:
wherein T represents a threshold number of steps of random walk;
each element in the score matrix B represents a score obtained when the node u moves t steps to reach the node v, and is represented by B (u, v), and the closer the two nodes are connected, the higher the score is between the two nodes;
step 2.3: sorting B (u, v) in a descending order, and taking out the first nodes with larger scoring values to form an initial seed list B-list;
step 2.4: calculating the similarity between each node in the B-list as the node of the initial seed community and the neighbor node thereof and the community NC-SIM (v, C)i) When the similarity is larger than a set threshold value, adding the neighbor node into the seed community to finally obtain a seed community set Seeds;
wherein, v represents a node point,is node v and community CiDegree of associated edge, kvDegree for node v; NC _ SIM (v, C)i) The larger the value, the more likely it is that node v belongs to community Ci。
And step 3: and optimizing seed community set according to the inter-community similarity. The specific method comprises the following steps:
step 3.1: traversing each seed community in the seed community set Seeds, and calculating the similarity CC _ SIM (C) between the community intervalsi,Cj)；
Wherein, | overlap (C)i,Cj) I is Community CiAnd community CjNumber of nodes in common, | CiI is Community CiNumber of nodes, | CjI is Community CjThe number of nodes of (a); CC _ SIM (C)i,Cj) The larger the size, the community C is indicatediAnd community CjThe more similar the structure of (2), when exceeding the set threshold epsilon, merging the two communities into one community;
step 3.2: and if the similarity of the community intervals is greater than the threshold epsilon, merging the two communities to obtain the optimized seed community set Seeds'. In the present embodiment, the threshold value ∈ takes 0.5.
And 4, step 4: and expanding the community according to the similarity of the seed and the community and an adaptive fixness function. The specific method comprises the following steps:
step 4.1: obtaining the neighbor set NBSet of the seed community optimized in the step 3, traversing the NBSet, and calculating the node-community similarity NC _ SIM (v, C) of each neighbor node and the seed communityi) Calculating a formula shown in formula (4);
step 4.2: taking out the first nodes with larger similarity to form a candidate node list C-list;
step 4.3: calculating an adaptive function fitness for adding the candidate nodes in the C-list into the community, adding the nodes which can increase the fitness into the community, and otherwise, setting the nodes as free nodes; the adaptive function fitness is calculated as follows:
wherein,andthe total values of the internal degree and the external degree of the subgraph g are respectively, and the parameter α is a positive real number and is used for controlling the discovered community scale;
step 4.4: updating the NBSet, and then repeating the steps until the NBSet is empty;
step 4.5: and obtaining an initial network overlapping community set C.
And 5: and processing free nodes in the network according to the similarity between the nodes and the communities and the similarity between the communities and merging similar communities. The specific method comprises the following steps:
step 5.1: calculating node-to-community similarity CC _ SIM (C) from free node to community in networki,Cj) Adding the free node into the community with the highest similarity, and updating an overlapped community set C;
step 5.2: calculating similarity between communities in overlapping community set C CC _ SIM (C)i,Cj) And merging communities with the similarity larger than the threshold epsilon to obtain a new overlapped community set C'.
Step 6: and outputting the network overlapping community structure. The specific method comprises the following steps: and obtaining a new overlapped community set C 'according to the optimization, wherein each element in the set C' represents a community, and then outputting the generated network overlapped community structure.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (6)
1. An overlapping community discovery method based on random walk and seed expansion is characterized by comprising the following steps:
step 1: reading original data, and acquiring network structure and node neighbor information;
step 2: acquiring seed community set according to the transition probability matrix and the scoring matrix of the nodes and the similarity between the nodes and the communities;
and step 3: optimizing seed community set according to the similarity among communities;
and 4, step 4: expanding the community according to the similarity between the seed and the community and a self-adaptive fitness function;
and 5: processing free nodes in the network according to the similarity between the nodes and the communities and the similarity between the communities and combining similar communities;
step 6: and outputting the network overlapping community structure.
2. The method for discovering overlapping communities based on random walks and seed expansions as claimed in claim 1, wherein in step 2, the method for obtaining seed community set Seeds according to the transition probability matrix and the score matrix of the nodes and the similarity between the nodes and the communities is as follows:
step 2.1: adjacency matrix A according to networkuvAnd node degree kvTo obtain a transition probability matrix Puv：
Puv＝Auv/kv(1)
PuvThe middle element represents the probability that the node u randomly walks one step to reach the node v;
further obtaining a transition probability matrix P after the random walk t stepst uv：
Step 2.2: according to the transition probability matrix P after t steps of walkingt uvObtaining a scoring matrix B:
<mrow> <mi>B</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msubsup> <mi>P</mi> <mrow> <mi>u</mi> <mi>v</mi> </mrow> <mi>t</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
wherein T represents a threshold number of steps of random walk;
each element in the score matrix B represents a score obtained when the node u moves t steps to reach the node v, and is represented by B (u, v), and the closer the two nodes are connected, the higher the score is between the two nodes;
step 2.3: sorting B (u, v) in a descending order, and taking out the first nodes with larger scoring values to form an initial seed list B-list;
step 2.4: calculating the similarity between each node in the B-list as the node of the initial seed community and the neighbor node thereof and the community NC-SIM (v, C)i) When the similarity is larger than a set threshold value, adding the neighbor node into the seed community to finally obtain a seed community set Seeds;
<mrow> <mi>N</mi> <mi>C</mi> <mo>_</mo> <mi>S</mi> <mi>I</mi> <mi>M</mi> <mrow> <mo>(</mo> <mi>v</mi> <mo>,</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msubsup> <mi>k</mi> <mi>v</mi> <msub> <mi>C</mi> <mi>i</mi> </msub> </msubsup> <msub> <mi>k</mi> <mi>v</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
wherein, v represents a node point,is node v and community CiDegree of associated edge, kvDegree for node v; NC _ SIM (v, C)i) The larger the value, the more likely it is that node v belongs to community Ci。
3. The method for discovering overlapping communities based on random walks and seed expansions as claimed in claim 2, wherein in step 3, the method for optimizing seed community set Seeds according to inter-community similarity is as follows:
step 3.1: traversing each seed community in the seed community set Seeds, and calculating the similarity CC _ SIM (C) between the community intervalsi,Cj)；
<mrow> <mi>C</mi> <mi>C</mi> <mo>_</mo> <mi>S</mi> <mi>I</mi> <mi>M</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mi>o</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>l</mi> <mi>a</mi> <mi>p</mi> <mrow> <mo>(</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mrow> <mi>min</mi> <mrow> <mo>(</mo> <mo>|</mo> <msub> <mi>C</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>,</mo> <mo>|</mo> <msub> <mi>C</mi> <mi>j</mi> </msub> <mo>|</mo> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Wherein, | overlap (C)i,Cj) I is Community CiAnd community CjNumber of nodes in common, | CiI is Community CiNumber of nodes, | CjI is Community CjThe number of nodes of (a); CC _ SIM (C)i,Cj) The larger the size, the community C is indicatediAnd community CjThe more closely, when a set threshold e is exceeded,merging the two communities into one community;
step 3.2: and if the similarity of the community intervals is greater than the threshold epsilon, merging the two communities to obtain the optimized seed community set Seeds'.
4. The method for discovering overlapping communities based on random walks and seed expansion as claimed in claim 3, wherein in step 4, the method for expanding communities according to the similarity between seeds and communities and the adaptive fitness function is as follows:
step 4.1: obtaining the neighbor set NBSet of the seed community optimized in the step 3, traversing the NBSet, and calculating the node-community similarity NC _ SIM (v, C) of each neighbor node and the seed communityi)；
Step 4.2: taking out the first nodes with larger similarity to form a candidate node list C-list;
step 4.3: calculating an adaptive function fitness for adding the candidate nodes in the C-list into the community, adding the nodes which can increase the fitness into the community, and otherwise, setting the nodes as free nodes; the adaptive function fitness is calculated as follows:
<mrow> <msub> <mi>f</mi> <mi>g</mi> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>k</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> <mi>g</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>k</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> <mi>g</mi> </msubsup> <mo>+</mo> <msubsup> <mi>k</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> <mi>g</mi> </msubsup> <mo>)</mo> </mrow> <mi>&alpha;</mi> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
wherein,andthe total values of the internal degree and the external degree of the subgraph g are respectively, and the parameter α is a positive real number and is used for controlling the discovered community scale;
step 4.4: updating the NBSet, and then repeating the steps until the NBSet is empty;
step 4.5: and obtaining an initial network overlapping community set C.
5. The method for discovering overlapping communities based on random walk and seed expansion as claimed in claim 4, wherein in step 5, the method for processing free nodes in the network and merging similar communities according to the similarity between nodes and communities and the similarity between communities is as follows:
step 5.1: calculating node-to-community similarity CC _ SIM (C) from free node to community in networki,Cj) Adding the free node into the community with the highest similarity, and updating an overlapped community set C;
step 5.2: calculating similarity between communities in overlapping community set C CC _ SIM (C)i,Cj) And merging communities with the similarity larger than the threshold epsilon to obtain a new overlapped community set C'.
6. The method for discovering overlapping communities based on random walk and seed expansion according to claim 1, wherein in step 6, the method for outputting the network overlapping community structure is as follows: and obtaining a new overlapped community set C 'according to the optimization, wherein each element in the set C' represents a community, and then outputting the generated network overlapped community structure.
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