CN109740722A - A kind of network representation learning method based on Memetic algorithm - Google Patents
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Abstract
The present invention discloses a kind of network representation learning method based on Memetic algorithm, comprising: real coding individual composition initial population P is randomly generated according to network node number n and vector dimension d0；Evaluate initial population P0The fitness function value of real coding individual；It uses Memetic algorithm, be foundation to initial population P with the fitness function value of real coding individual0Each real coding individual is iterated optimization；The highest real coding individual of fitness function value in population after iteration optimization is exported to the expression vector set as network node；The iteration optimization includes successively to initial population P0In real coding individual carry out crossover probability iteration optimization, the mutation probability iteration optimization of population random number and the optimization of local search iteration；The experimental results showed that the present invention can be used for the tasks such as node-classification, community's detection and visualization effectively by network structure information, especially community structure information coding into expression vector.
Description
Technical field
Learning art field is calculated and indicated the invention belongs to community network, in particular to it is a kind of to be based on Memetic algorithm
Network representation learning method, can be used for node-classification, community detection and visualization etc. tasks.
Background technique
Network representation study is that node each in network is embedded into the dense vector space of low-dimensional, to obtain network
A kind of technology that vector indicates.Due to traditional network representation method, such as adjacency matrix, there is sparsity and be difficult to reflect section
Between point the shortcomings that potential relationship, so network representation learning art is increasingly subject to the concern of associated specialist scholars.With it is traditional
Network representation is compared, and by saving the topology information of network, internet startup disk is obtained to the dense vector space of low-dimensional
Network representation is more significant, and can be widely used in the various Complex Networks Analysis models inputted based on vector, for example save
The tasks such as point visualization, node-classification and community's detection.
The general thoughts of existing network representation learning art are to maintain the topological of network structure, Bryan Perozzi
Et al. propose a kind of network representation learning method DeepWalk based on SkipGram model and random walk, referring to
Perozzi B,Al-Rfou R,Skiena S,“DeepWalk:online learning of social
representations,”AcmSigkdd International Conference on Knowledge Discovery&
Data Mining.ACM,2014.DeepWalk obtains sequence node using random walk, then sharp with this as word sequence
Learn network with SkipGram model indicates vector.Aditya Grover et al. has further expanded DeepWalk acquisition
The mode of sequence node makes random walk mode have breadth-first search and depth-first search by introducing two parameters
Characteristic, referring specifically to Grover A, Leskovec J, " node2vec:Scalable Feature Learning for
Networks,”AcmSigkdd International Conference on Knowledge Discovery&Data
Mining.ACM,2016.These technologies only focus on the network representation vector to learn and keep single order, second order of nodes etc. low
Rank similarity；Then network analysis task is carried out using existing common machine learning method, as support vector machines is saved
Point classification.But this method obtains network representation and does not have apparent distinction, i.e. between class distance is small, this will increase following model
The difficulty of network is analyzed, and this linear sequence acquisition mode of random walk makes these methods be difficult to keep network node
Nonlinear characteristic, such as the community cultule of network.
Since above-mentioned network representation learning method only considered low order similarity, the expression vector to learn does not have apparent area
Divide property, causes the performance in network analysis task that there is limitation.Therefore, studying one kind and making network representation more has differentiation
The unsupervised network representation learning method of property is the task of top priority of the art scientific and technical personnel.
Summary of the invention
It is an object of the invention to be directed to the deficiency of above-mentioned prior art, a kind of network based on Memetic algorithm is proposed
It indicates learning method, to enhance the distinction of network representation vector, saves the community structure feature of network, extended network indicates to learn
Practise the application range of algorithm.
To achieve the above object, technical solution of the present invention includes the following:
A kind of network representation learning method based on Memetic algorithm, comprising:
Step 1: the adjacency matrix A of link information between input description network node, network node number are n, vector dimension
Degree is d；Real coding individual composition initial population P is randomly generated according to network node number n and vector dimension d0；
Step 2 evaluates initial population P0The fitness function value of real coding individual；Use Memetic algorithm, with reality
The fitness function value of number encoder individual is according to initial population P0Each real coding individual is iterated optimization；By iteration
The highest real coding individual of fitness function value exports the expression vector set as network node in population after optimization；
The iteration optimization includes successively to initial population P0In real coding individual carry out crossover probability iteration it is excellent
Change, the mutation probability iteration optimization of population random number and local search iteration optimize；
The local search iteration optimization includes being obtained according to adjacency matrix A by crossover probability iteration optimization and variation
The central node of the corresponding network node of real coding individual after probability iteration optimization, each network node are leaned on to central node
Closely.
Optionally, the central node includes neighbours' central node and generic central node；
When population iterative algebra is greater than 0.8 times of population greatest iteration algebra, the iteration of neighbours' central node is both carried out
Optimization carries out the iteration optimization of generic central node again；
When population iterative algebra is less than or equal to 0.8 times of population greatest iteration algebra, neighbours' central node is only carried out
Iteration optimization.
Optionally, neighbours' central node includes the expression vector set N and each net for obtaining each network node
The degree set D of the neighbor node of network node, and D is normalized to obtain Dnorm；To expression vector set N with weight
DnormIt is weighted summation and obtains neighbours' central node C of each network node；
Generic central node: obtaining the cluster result of current real coding individual, individual for a real coding
For gene, generic gene indicates that vector table shows with node, and the expression vector average value for calculating generic node is somebody's turn to do
The central node vector of class node is generic central node.
Optionally, the iteration optimization of neighbours' central node are as follows:C
Neighbours' central node, pbest=[pbesti] (i=1,2..., n) be that fitness value is maximum in current iteration process population
Node representated by body indicates that vector set closes,For the node after neighbours' central node iteration optimization indicate to
Duration set；
The iteration optimization of the generic central node are as follows:CΩIndicate generic central node,For by same
Node after class center node iteration optimization indicates vector；
Local search optimization parameter η1And η2, η1=0.1~0.7, η2=0.03~0.1.
Optionally, the local search iteration optimization includes:
(a) local search optimization parameter η is set1And η2, η1=0.1~0.7, η2=0.03~0.1；Initial population P0Reality
Number encoder individual successively carries out the crossover probability iteration optimization of population random number and the mutation probability iteration optimization of population random number
Obtain maximum real coding individual pbest, the pbest=[pbest of fitness function valuei] (i=1,2..., n)；In pbest
Each gene represent be each node in network expression vector；
(b) obtained from pbest according to adjacency matrix A all neighbor nodes of present node expression vector set N and
The degree set D of all neighbor nodes of present node, and D is normalized to obtain Dnorm；To indicate vector set N with
Weight DnormIt is weighted summation and obtains neighbours' central node C of present node；
Work as g > 0.8mg, g is current population iterative algebra, and mg indicates maximum population iterative algebra, executes step (c)；It is no
Then, step (d) is executed；
(c) for pbestnew1In every a kind of node, according to PΩbestThe expression vector of such node is averaged to obtain
The central node vector C of such nodeΩ, PΩbestFor the cluster result of pbest, if node i belongs to the category,
Pbest '=pbestnew2；Obtain updated optimized individual, i.e. pbest'；
(d) pbest '=pbestnew1, obtain updated optimized individual, i.e. pbest'.
Optionally, comprising:
(1) input describes the adjacency matrix A of link information between network node, and network node number is n, and vector dimension is
d；Real coding individual composition initial population P is randomly generated according to network node number n and vector dimension d0；G godfather's generation kind
Group is Pg；G is current population iterative algebra, and mg indicates maximum population iterative algebra；
(2) K mean cluster algorithm is to g godfather for population PgIn each real coding individual clustered, clustered
Results set PΩ；Utilize PΩG godfather is calculated for population PgIn each real coding individual fitness function value D, using suitable
Response functional value D and algorithm of tournament selection are operated to g godfather for population recruitment, obtain updated g godfather for population Pg'；
According to parent population P'gGenerate random number rand1If rand1< pc executes (3) step；Otherwise, g is for filial generation
Population Pchildg=P'g, execute (4) step；
(3) to updated g godfather for population P'gSimulation binary system crossover operation is carried out, obtains g for progeny population
Pchildg；
(4) random number rand is generated2If rand2< pm, then to g for progeny population PchildgIn each real coding
Individual carries out multinomial mutation operation, obtains updated g for progeny population Pchild'g；Otherwise, Pchild'g=
Pchildg；
(5) using K mean cluster algorithm to progeny population Pchild'gIn each real coding individual clustered, obtain
Cluster result set P'Ω；Obtain the highest real coding individual pbest of fitness value and fitness value highest real coding
The cluster result P of bodyΩbest, utilize cluster result PΩbestLocal search optimization is carried out to pbest with adjacency matrix A, is updated
Pbest' afterwards replaces g for progeny population Pchild' with pbest'gIn pbest；
(6) progeny population Pchild'gWith g godfather for population PgIt is selected in initial population from big to small according to fitness value
The real coding individual of same number, forms updated P "g；
(7) g=g+1 is enabled, if g≤mg, Pg=P "g-1, return step (2)；Otherwise, step (8) are executed；
(8) by g-1 for updated P "g-1In population the maximum real coding individual of fitness value as output as a result,
As the node of the network indicates that vector set closes.
Optionally, P is utilizedΩG godfather is calculated for population PgIn each real coding individual fitness function value D:
In formula, V1,V2,...,VkIt is the node set of the k classification obtained by individual, V is all node collection in network
It closes, i.e. V=V1∪V2∪...∪Vk,|Vm| it is classification VmIn node number, L (Vm,Vm) table
Show the connection number in m class node set,Indicate m class node set and its in addition to m class node set
The connection number of his node set.
Optionally, algorithm of tournament selection operation is compiled in g godfather for two real numbers are randomly choosed in population every time
Code individual is compared, and fitness function value is biggish to enter P 'gIn.
Optionally, the cluster result p of each of described individualΩ=(r1,r2,...,rn), wherein ri∈ { 1,2 ..., k },
1≤i≤n, i-th of genic value represent the category label of i-th of node.
Optionally, the individual p of the real coding, p=(p1,p2,…,pn) in each gene piTake one it is random
The d of generation ties up real vector, wherein 1≤i≤n, i-th of genic value represent the expression vector of i-th of node in network.
A kind of network representation learning system based on Memetic algorithm is run of the present invention based on Memetic algorithm
Network representation learning method device.
The present invention has the advantage that compared with prior art
1, the present invention is a kind of completely unsupervised method, does not need the data of any handmarking；
2, the present invention can make network representation preferably keep in former network structure using block density as objective function
High-order community characteristics, thus enhance indicate vector distinction.
3, the present invention optimizes objective function using Memetic algorithm, is conducive to avoid falling into locally optimal solution；
4, the present invention pointedly devises a kind of local search optimization method, accelerates optimization process, not only increases
Efficiency of evolution, and can effectively obtain optimal solution.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is the local search flow chart that the present invention designs；
Fig. 3 is one group of real network topology figure that the present invention uses；
Fig. 4 is to indicate visual simulating experimental result picture to what network shown in Fig. 3 obtained with the present invention.
Specific embodiment
What gene represented is the expression vector of each node in network, and the collection of gene is combined into real coding individual；Real number is compiled
Code group of individuals is population.The node of the same category is exactly the identical node of label in K mean cluster result.
As long as the function that the fitness function value of evaluation real coding individual can be used, which can reach, keeps community's property
Function is ok, for example can be block density function, modularity function.
Central node includes neighbours' central node and generic central node, wherein neighbours' central node: every including obtaining
The degree set D of the neighbor node for indicating vector set N and each network node of a network node, and place is normalized to D
Reason obtains Dnorm；To expression vector set N with weight DnormIt is weighted summation and obtains neighbours' central node of each network node
C。
Generic central node: current real coding individual is obtained (such as after neighbours' central node iteration optimization
Real coding individual) cluster result, the expression vector average value for calculating generic node obtains the central node of such node
Vector is generic central node.
The present invention is the network representation learning method based on Memetic algorithm, the network example pair provided below with reference to Fig. 3
The present invention clearly describes, but does not constitute any limitation of the invention, and present invention may apply to all undirected no symbols
Number homogenous network.Memetic algorithm is a kind of iteration optimization algorithms for combining population global search and individual local search, it
It can effectively avoid falling into locally optimal solution, be widely used in solving complicated optimum problem.
The invention discloses a kind of network representation learning methods based on Memetic algorithm, for current net list dendrography
Learning method lacks the problem of keeping community cultule, using block density function as objective function, devises a kind of effective local search
Strategy, it is mainly optimized two parts and is constituted by the optimization of neighbour's range and community scope, effectively maintains the low order of nodes
With high-order similitude, and optimization process is accelerated, so that the network representation vector that study comes out has more distinction, well
Maintain the community characteristics of network.
Referring to Fig.1, steps are as follows for realization of the invention:
Step 1, the adjacency matrix A of the connection relationship between input description nodes, unites to node total number n
Meter, setting indicate vector dimension d, node classification number k, local search parameter η1And η2。
The node total number n=62 of this example, then the size of adjacency matrix A is 62 × 62, and setting indicates vector dimension d=
2, node classification number k=2, local search parameter η1=0.5, η2=0.1；
Step 2, the size S of initial population is enabledpop=100, S is randomly generated according to node total number n and dimension dpopIt is a to adopt
With the individual of real coding, by this SpopIndividual composition initial population P0, P0Size be Spop×n×d；Crossover probability is set
Pc=0.9, mutation probability pm=0.1, first initial algebra g0=1, maximum algebra mg=50, current algebra g=g0, enable g godfather's generation
Population PgEqual to initial population P0, i.e. Pg=P0。
100 individuals using real coding are randomly generated according to node total number n=62 and dimension d=2 in this example,
Refer to each individual p=(p1,p2,...,p62) in each gene piTake the one-dimensional real vector generated at random, wherein 1
≤ i≤62, i-th of genic value represent the expression vector of i-th of node in network.
Step 3, using K mean cluster algorithm to g godfather for population PgIn each individual clustered, obtain cluster knot
Fruit PΩ。
Step 4, P is utilizedΩG godfather is calculated for population PgIn each individual fitness function value D:
4a) according to P in this exampleΩObtain the node set in each individual in two classifications are as follows: V1,V2；V1And V2And
Collection is the set V of all nodes in the network, and in this example
Connection number L (the V in first classification 4b) is calculated according to adjacency matrix A1,V1)。
Its from first category node set and in addition to the first kind node set 4c) is calculated according to adjacency matrix A
The connection number of his node set
4d) according to L (V obtained above1,V1) andIt calculatesWherein, | V1| it is
Node number in first kind node set.
4e) similarly repeat 4b) -4d) it is calculatedSo the fitness value of the individual
For D=D1+D2。
4f) g godfather is calculated for population P according to above-mentioned stepsgIn each individual fitness value.
Step 5, it is operated to g godfather using algorithm of tournament selection for population, is updated, obtains according to fitness function value
Updated g godfather is for population P'g。
5a) set P'gFor empty set, for storing the individual of algorithm of tournament selection；
5b) in g godfather is for population randomly choose two individuals, compare the size of fitness value, by fitness value compared with
High individual is put into P'gIn；
5c) repeat step 5b) SpopIt is secondary.
Step 6, random number rand is generated1If rand1< pc executes (7) step；Otherwise, g is for progeny population
Pchildg=P'g, execute (8) step；
Step 7, to updated g godfather for population P'gSimulation binary system crossover operation is carried out, obtains g for filial generation
Population Pchildg；
Since individual is using real coding mode in this example, present invention employs the moulds of suitable real coding
Quasi- binary system interleaved mode.
Step 8, random number rand is generated2If rand2< pm, then to g for progeny population PchildgIn each individual
Multinomial mutation operation is carried out, obtains updated g for progeny population Pchild'g；Otherwise, Pchild'g=Pchildg。
Since individual is using real coding mode in this example, present invention employs the more of suitable real coding
Item formula variation mode.
Step 9, using K mean cluster algorithm to g for progeny population Pchild'gIn each individual clustered, obtain
Cluster result P'Ω。
Step 10, g is calculated for progeny population Pchild'gIn each individual fitness value D, obtain current fitness
It is worth highest individual pbest and its cluster result PΩbest, utilize PΩbestLocal search optimization is carried out to pbest with adjacency matrix A,
Updated pbest' is obtained, replaces g for progeny population Pchild' with pbest'gIn pbest.Referring in particular to Fig. 2；
(10a) this example due to gene each in pbest represent be each node in network expression vector pbest=
(pbest1,pbest2,...,pbest62), to pbesti(i=1,2..., 62) carries out following (10b)-(10e) operation；
(10b) obtains the expression vector set N of all neighbor nodes of present node according to adjacency matrix A from pbest；
(10c) obtains the degree set D of all neighbor nodes of present node according to adjacency matrix A, and D is normalized
Processing obtains Dnorm；
(10d) is weighted summation to the N of (10b) and obtains neighbours' central point C of present node, wherein weight is (10c)
In Dnorm；
(10e)
(10f) skips to step (10g), otherwise, skips to step (10h) if current algebra g > 0.8mg；
(10g) is for pbestnew1In every a kind of node proceed as follows, first according to PΩbestTo the table of such node
Show that vector is averaged to obtain the central point vector C of such nodeΩ, vector then is indicated to node
If node i belongs to current class, with regard to being updated as follows:
Enable pbest'=pbestnew2, obtain updated optimized individual, i.e. pbest'
(10h) enables pbest'=pbestnew1, obtain updated optimized individual, i.e. pbest'.
Step 11, from Pchild'gAnd PgIn select preceding S from big to small according to fitness valuepopIndividual, with these individuals
Form updated P "g。
P is enabled in this examplenewFor Pchild'gAnd PgUnion, according to the size of fitness value to PnewIn individual carry out
Preceding S is selected in descending sortpopIndividual constitutes new population and is assigned to P "g。
Step 12, g=g+1 is enabled, if g≤mg, Pg=P "g-1, return step (3)；Otherwise, step (13) are executed；
Step 13, by g-1 for updated population P "g-1The middle maximum individual of fitness value is as output as a result, being
The node of the network indicates that vector set closes.
Effect of the invention can be further illustrated by following emulation:
1. simulated conditions and evaluation index:
It is transported under 10 system of Intel (R) Core (TM) i5-3210M CPU 2.5GHz Windows with Python3.5
It is carried out on row platform.
This experimental selection normalized mutual information NMI network representation that evaluation experimental method obtains respectively is detected applied to community
The quality of task.
2. emulation experiment content and result
Emulation one is indicated study to network shown in Fig. 3 with the method for the present invention, and passes through to obtained network representation
T-SNE dimensionality reduction is visualized to two-dimensional surface, as a result as shown in figure 4, the true classification of node on behalf of different shapes is not in Fig. 4
Together.
Fig. 4 and Fig. 3 comparison can see, after the expression dimension reduction and visualization that the present invention acquires in the example network of Fig. 3
Same category of node compares concentration, and different classes of node differentiation is obvious, it can easily be seen that there are two types of network tools
The node of classification.
In addition, community's Detection task is carried out to the network using the network representation and K mean algorithm acquired, it is available to return
One changes association relationship NMI1=1, i.e., the network representation that the present invention is acquired has very high accuracy for community's Detection task.
Emulation two is indicated network shown in Fig. 3 using the DeepWalk method that Bryan Perozzi et al. is proposed
Study, and community's Detection task is carried out to the network using the network representation and K mean algorithm acquired, available normalization is mutual
Value of information NMI2=0.8888.
The normalized mutual information value NMI that DeepWalk method is obtained2=0.8888 is mutual with obtained normalization of the invention
Value of information NMI1=1 compares, as a result, it has been found that the network representation that the present invention acquires has higher standard on community's Detection task
True property.
3, the setting of local search optimization parameter:
The optimization process of local search parameter uses grid searcher strategies, and Tables 1 and 2 is fixed one of parameter, adjusts
The whole obtained NMI average value of another parameter, wherein NMI value is bigger, and the effect for representing detection is better.
The verification test data of parameter optimization are specifically shown in Tables 1 and 2.
Table 1
| Parameter η 1 | 0.1-0.2 | 0.2-0.3 | 0.3-0.4 | 0.4-0.5 | 0.5-0.6 | 0.6-0.7 | 0.7-0.8 | 0.8-0.9 |
| The NMI value of community's detection | 1 | 1 | 1 | 1 | 1 | 1 | 0.8888 | 0.8888 |
Table 2
As it can be seen from table 1 working as parameter η1In 0.1~0.7 value range, the obtained network representation of the present invention to
Amount is done well on community's Detection task, will appear performance decline by a small margin in the range of being greater than 0.7；It similarly can from table 2
To find out, as parameter η2In 0.03~0.1 value range, the obtained result of the present invention is more satisfactory.
Claims (10)
1. a kind of network representation learning method based on Memetic algorithm characterized by comprising
Step 1: the adjacency matrix A of link information between input description network node, network node number is n, and vector dimension is
d；Real coding individual composition initial population P is randomly generated according to network node number n and vector dimension d0；
Step 2 evaluates initial population P0The fitness function value of real coding individual；Use Memetic algorithm, with real coding
The fitness function value of individual is according to initial population P0Each real coding individual is iterated optimization；After iteration optimization
The highest real coding individual of fitness function value exports the expression vector set as network node in population；
The iteration optimization includes successively to initial population P0In real coding individual carry out crossover probability iteration optimization, kind
The mutation probability iteration optimization of group's random number and local search iteration optimization；
The local search iteration optimization includes being obtained according to adjacency matrix A by crossover probability iteration optimization and mutation probability
The central node of the corresponding network node of real coding individual after iteration optimization, each network node are close to central node.
2. the network representation learning method according to claim 1 based on Memetic algorithm, which is characterized in that described
Central node includes neighbours' central node and generic central node；
When population iterative algebra is greater than 0.8 times of population greatest iteration algebra, the iteration optimization of neighbours' central node is both carried out
The iteration optimization of generic central node is carried out again；
When population iterative algebra is less than or equal to 0.8 times of population greatest iteration algebra, the iteration of neighbours' central node is only carried out
Optimization.
3. the network representation learning method according to claim 1 based on Memetic algorithm, which is characterized in that
Neighbours' central node includes the neighbours for obtaining expression the vector set N and each network node of each network node
The degree set D of node, and D is normalized to obtain Dnorm；To expression vector set N with weight DnormIt is weighted and asks
With obtain neighbours' central node C of each network node；
Generic central node: the cluster result of current real coding individual is obtained, for the gene of a real coding individual
For, generic gene indicates that vector table shows with node, and the expression vector average value for calculating generic node obtains such section
The central node vector of point is generic central node.
4. the network representation learning method according to claim 1 based on Memetic algorithm, which is characterized in that described
The iteration optimization of neighbours' central node are as follows:C neighbours' central node, pbest=
[pbesti] (i=1,2..., n) be current iteration process population in fitness value it is maximum individual representated by node indicate to
Duration set,Indicate that vector set closes for the node after neighbours' central node iteration optimization；
The iteration optimization of the generic central node are as follows:CΩ
Indicate generic central node,Vector is indicated for the node after generic central node iteration optimization；
Local search optimization parameter η1And η2, η1=0.1~0.7, η2=0.03~0.1.
5. the network representation learning method according to claim 1 based on Memetic algorithm, which is characterized in that described
Local search iteration optimization includes:
(a) local search optimization parameter η is set1And η2, η1=0.1~0.7, η2=0.03~0.1；Initial population P0Real number compile
The mutation probability iteration optimization of crossover probability iteration optimization and population random number that code individual successively carries out population random number obtains
Maximum real coding individual pbest, the pbest=[pbest of fitness function valuei] (i=1,2..., n)；It is every in pbest
What a gene represented is the expression vector of each node in network；
(b) the expression vector set N of all neighbor nodes of present node and current is obtained from pbest according to adjacency matrix A
The degree set D of all neighbor nodes of node, and D is normalized to obtain Dnorm；To expression vector set N with weight
DnormIt is weighted summation and obtains neighbours' central node C of present node；
When g > 0.8mg, g are current population iterative algebra, mg indicates maximum population iterative algebra, executes step (c)；Otherwise,
It executes step (d)；
(c) for pbestnew1In every a kind of node, according to PΩbestThe expression vector of such node is averaged to obtain such
The central node vector C of nodeΩ, PΩbestFor the cluster result of pbest, if node i belongs to the category,
Pbest '=pbestnew2；Obtain updated optimized individual, i.e. pbest '；
(d) pbest '=pbestnew1, obtain updated optimized individual, i.e. pbest '.
6. the network representation learning method according to claim 1 based on Memetic algorithm characterized by comprising
(1) input describes the adjacency matrix A of link information between network node, and network node number is n, vector dimension d；Root
Real coding individual composition initial population P is randomly generated according to network node number n and vector dimension d0；G godfather is for population
Pg；G is current population iterative algebra, and mg indicates maximum population iterative algebra；
(2) K mean cluster algorithm is to g godfather for population PgIn each real coding individual clustered, obtain cluster result collection
Close PΩ；Utilize PΩG godfather is calculated for population PgIn each real coding individual fitness function value D, utilize fitness letter
Numerical value D and algorithm of tournament selection are operated to g godfather for population recruitment, obtain updated g godfather for population P 'g；
According to parent population P 'gGenerate random number rand1If rand1< pc executes (3) step；Otherwise, g is for filial generation kind
Group Pchildg=P 'g, execute (4) step；
(3) to updated g godfather for population P 'gSimulation binary system crossover operation is carried out, obtains g for progeny population
Pchildg；
(4) random number rand is generated2If rand2< pm, then to g for progeny population PchildgIn each real coding
Body carries out multinomial mutation operation, obtains updated g for progeny population Pchild 'g；Otherwise, Pchild 'g=Pchildg；
(5) using K mean cluster algorithm to progeny population Pchild 'gIn each real coding individual clustered, clustered
Results set P 'Ω；Obtain the highest real coding individual pbest of fitness value and fitness value highest real coding individual
Cluster result PΩbest, utilize cluster result PΩbestLocal search optimization is carried out to pbest with adjacency matrix A, is obtained updated
Pbest ' replaces g for progeny population Pchild ' with pbest 'gIn pbest；
(6) progeny population Pchild 'gWith g godfather for population PgIt is selected from big to small according to fitness value identical in initial population
The real coding individual of number, forms updated P "g；
(7) g=g+1 is enabled, if g≤mg, Pg=P "g-1, return step (2)；Otherwise, step (8) are executed；
(8) by g-1 for updated P "g-1The maximum real coding individual of fitness value is as output as a result, being in population
The node of the network indicates that vector set closes.
7. the network representation learning method according to claim 6 based on Memetic algorithm, which is characterized in that utilize PΩ
G godfather is calculated for population PgIn each real coding individual fitness function value D:
In formula, V1, V2..., VkIt is the node set of the k classification obtained by individual, V is all node sets, i.e. V in network
=V1∪V2∪...∪Vk,1≤m≤k, | Vm| it is classification VmIn node number, L (Vm, Vm) indicate m class
Connection number in node set,Indicate m class node set and other node collection in addition to m class node set
The connection number of conjunction.
8. the network representation learning method according to claim 6 based on Memetic algorithm, which is characterized in that described
Algorithm of tournament selection operation, i.e., be compared in .g godfather for two real coding individuals are randomly choosed in population every time, adapts to
Functional value is biggish enters P ' for degreegIn.
9. the network representation learning method according to claim 6 based on Memetic algorithm, which is characterized in that described
The cluster result P of each individualΩ=(r1, r2..., rn), wherein ri∈ { 1,2 ..., k }, 1≤i≤n, i-th of genic value generation
The category label of i-th of node of table.
10. the network representation learning method according to claim 1 based on Memetic algorithm, which is characterized in that described
The individual p of real coding, p=(p1, p2..., pn) in each gene piThe d generated at random a dimension real vector is taken,
In, 1≤i≤n, i-th of genic value represents the expression vector of i-th of node in network.
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| CN112150285A (en) * | 2020-09-23 | 2020-12-29 | 哈尔滨工业大学（威海） | Abnormal financial organization hierarchy dividing system based on neighborhood topological structure and working method thereof |
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