CN111062421A - Network node multidimensional data community division algorithm based on correlation analysis - Google Patents
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Abstract
The invention provides a network node multidimensional data community division algorithm based on correlation analysis, which analyzes the correlation of nodes by using the relationship among node attributes, and determines whether the nodes are connected with each other according to the magnitude of the correlation, thereby obtaining a complex network; then, on the basis of a Gaussian mixture model, a model is established by utilizing the self-attribute of the nodes, and the optimal partitioning result of the weighted complex network is obtained by solving the optimal solution of the model through an EM (effective electromagnetic) algorithm; the network node multidimensional data community division algorithm based on the correlation analysis highly utilizes the self attribute characteristics of the nodes and the incidence relation among the nodes, effectively improves the community division accuracy, is simple to implement, has strong operability, is not limited by established rules and reasoning models, and is suitable for various complex networks.
Description
Technical Field
The invention belongs to the technical field of network science, and particularly relates to a network node multidimensional data community division algorithm based on correlation analysis.
Background
In recent years, the academic community is not interested in researching complex networks, and many systems in the real world are presented in the form of complex networks, such as power networks, traffic networks, social networks, the internet and the like. The community structure is an important characteristic of a complex network, the connection between nodes in the communities is very close, and the connection between the communities is relatively loose. The research on the community structure of the complex network has very important theoretical significance for analyzing the internal topological structure of the complex network and the like. In an unauthorized complex network, the topological structure of the network is the main content considered when communities are divided, and the degree of association between nodes is negligible. In the weighted complex network, the edge weight among the nodes can better describe the contact tightness among the nodes, and the structure of the complex network can be expressed more truly and exhaustively; the social community time sharing considers not only whether nodes are associated but also the degree of association.
The division of complex network communities has a very important meaning for people to know real network information, so that the division of complex network community structures is an important research field. Many researchers research the community division method from various characteristics such as network topology structure and node attribute, and the complex network has the characteristics of sparse structure, node degree distribution presenting power rate distribution and long tail distribution, and the division effect of the community division algorithm based on the topology structure in the actual complex network is not ideal. The traditional community division algorithm mainly researches an unauthorized complex network, utilizes network topology to mine a community structure, but ignores the important role of information such as node self-attribute and the like in the community attribution aspect. Thus, for increasingly complex community partitioning, existing partitioning methods will become no longer applicable.
The invention patent CN107545509A discloses a community division method of a multi-relationship social network, which provides a community division method of a multi-relationship social network, and the community division method of the multi-relationship social network comprises the following steps: firstly, converting original network data into a similarity tensor, and then establishing an analysis model; and then, obtaining a decomposition result of the tensor by using a tensor decomposition method. However, the network relationship selected by the method has a great influence on community division, and further plays a decisive role in similarity tensor, and if the selected network relationship is not suitable for network data to be divided, the dividing accuracy is greatly reduced, so that the universality of the method is not high.
The invention patent CN109389179A discloses a time sequence smooth community dividing method and device based on label diffusion, the method includes: 1) acquiring a label value of each node in a network to be divided at the previous moment of the current moment; 2) judging whether the oscillation frequency is greater than a preset threshold value or not; 3) if not, acquiring a first preference weight of the node; taking the first preference value as the current preference value of the node; 4) if so, acquiring a second preference weight of the node; taking the second preference value as the current preference value of the node; 5) updating the label value of the node at the current moment; and returning to execute the step 2) until all the nodes in the network to be divided are divided into communities formed by the nodes with the same label value. According to the method, on the basis of label diffusion, nodes with the same label value are divided into the same community by combining the label values of all the nodes at a certain specified time, but the patent scheme is accidental, the accuracy of the label value cannot be guaranteed, the calculation of the label value is complex and time-consuming, and the practicability is low.
The invention patent CN106780058A discloses a method and a device for dividing communities of a dynamic network, which are implemented by obtaining network topology structures of the dynamic network at least two moments, and traversing each target node by taking each node of the plurality of nodes as the target node; calculating modularity increments of the target node and each adjacent node of the target node respectively, comparing the average modularity increments of the target node and each adjacent node, and determining the division of the target node according to the size of the modularity increments; and repeatedly traversing each target node until any two communities in each network topology structure cannot be combined continuously. In the scheme, too many traversal and repeated operations are performed, frequent and complex calculation is performed, a simple community division method is not adopted, too heavy calculation load is applied, and cost performance is not high.
Most of the existing community division methods search which community the node belongs to by traversing the attribute of the node or the commonality of the community network, so as to divide the community. These methods rely on established rules or inference models and do not perform well in the face of community division: (1) the node is attacked or data is forged, so that the type or the characteristics of the node are changed; (2) the node association is too close to precisely locate the node features.
Disclosure of Invention
The invention aims to provide a network node multidimensional data community division algorithm based on correlation analysis, aiming at the prior technical problems.
In order to solve the technical problems, the invention adopts the technical scheme that:
a network node multidimensional data community division algorithm based on correlation analysis is disclosed, the method utilizes the relationship among node attributes to carry out correlation analysis on nodes, and determines whether edges are connected among the nodes according to the magnitude of the correlation, thereby obtaining a complex network; and then, on the basis of a Gaussian mixture model, establishing a model by utilizing the self attribute of the node, and solving the optimal solution of the model through an EM (effective electromagnetic radiation) algorithm to obtain the optimal division result of the weighted complex network.
The method specifically comprises the following steps:
s1, calculating the correlation between the nodes to obtain a complex network;
and S2, modeling the node attribute data by using a Gaussian mixture model to obtain a likelihood probability model, and performing optimization processing by using an EM (effective man) algorithm to obtain a community division result.
Preferably, the step S1 specifically includes:
s11, assuming that there is at most one edge connection between two nodes, the element value of its adjacency matrix a may take 0 or not 0, i.e.:
wherein w is a weight; w is the weight set of the edge; v is a node; v is a node set; sim (v)i，vj) Is a node viAnd node vjCorrelation;
s12, recording the attribute of a certain node in a certain time window as random variationQuantity SXThe attribute of another node in the same time window is a random variable sYThen, the correlation between the nodes is calculated by adopting a Pearson coefficient:
preferably, the step S2 specifically includes:
s21, taking index attributes of all nodes in the network as a multidimensional variable X ═ X1，x2，…，xnThe probability of a node u being assigned to a community s is based on the index attribute x of the nodeuThe probability is defined as gammasx(ii) a Assuming that the gaussian mixture model consists of k gaussian models (i.e. the data contains k classes), the probability model of the gaussian mixture model is:
wherein k is the number of Gaussian models, namely the number of classes contained in the data; u is a node; x is the number ofuIs the index attribute of the node u; p (x | k) ═ N (x | μ)k，∑k) Is the probability density function of the kth Gaussian model, and can be considered as that after the kth model is selected, the model generates attribute data x of nodesiThe probability of (d); p (k) ═ pikIs the weight of the kth gaussian model, is the prior probability of selecting the kth model;
s22 Attribute data x for each nodeiThe probability generated by the kth gaussian model is:
where γ (i, k) is attribute data x for each nodeiProbability generated by the kth gaussian model; n (x)i|μk，∑k) Is node attribute data xiThe posterior probability of the kth gaussian distribution is calculated by:
wherein d is a variable dimension, namely the number of node attributes, mu is the mean value of each attribute data of the node, and sigma is a covariance matrix and represents the correlation between each attribute of the node;
s23, the likelihood probability model based on the node attribute is known from the Gaussian mixture model as follows:
wherein s is a community; gamma raysxThe probability of assigning the node u to the community s; p (s | pi, mu, sigma, x) is a likelihood probability model based on node attributes;
s24, parameters in the likelihood probability estimation model are maximized by the EM algorithm, a network containing a community structure is fitted, and then the connection probability value and the serial number of the community to which any node belongs can be obtained, namely a community division result is obtained.
The method comprises the steps of firstly calculating the correlation degree between nodes by utilizing correlation analysis; different community structures in the same network are assumed to be generated by different Gaussian models, the self-attribute of a high-dimensional node is modeled into a Gaussian mixture model, a likelihood probability model is established, the optimal solution of the model is solved by using an EM algorithm, and the optimal division result of the weighted complex network is obtained.
Compared with the prior art, the invention has the following advantages:
(1) the community division algorithm provided by the invention combines the node attribute characteristics, carries out division according to the association degree between the nodes, highly utilizes the attribute characteristics of the nodes and the association relation between the nodes, effectively improves the community division accuracy, is simple to implement, has strong operability, is not limited by established rules and reasoning models, and is suitable for various complex networks.
(2) The network node multidimensional data community division algorithm based on the correlation analysis establishes a model by utilizing a Gaussian mixture model and node attribute characteristics, so that the incidence relation in the node is quantized and recorded.
(3) According to the community division algorithm, parameters in the maximization likelihood probability estimation model of the EM algorithm are utilized, a network containing a community structure is fitted, the connection probability value and the serial number of the community to which any node belongs can be obtained, and a community division result is obtained.
Drawings
FIG. 1 is a flowchart of a network node multidimensional data community division algorithm based on correlation analysis according to the present invention.
Fig. 2 is a complex network diagram provided in embodiment 1 of the present invention.
Fig. 3 is a graph showing the community division result provided in embodiment 1 of the present invention.
Detailed Description
The technical solutions of the present invention are further described in detail with reference to the drawings and specific embodiments so that those skilled in the art can better understand the present invention and can implement the present invention, but the embodiments are not limited to the present invention.
Example 1
The method comprises the steps of automatically collecting attribute data of 50 nodes through a performance monitor, carrying out correlation calculation on the attribute data, and then carrying out community division through a Gaussian mixture model.
S1, performing correlation analysis calculation on the collected 50 node data, wherein the correlation analysis calculation method specifically comprises the following steps:
s11, assuming that there is at most one edge connection between two nodes, the element value of its adjacency matrix a may take 0 or not 0, i.e.:
wherein w is a weight; w is the weight set of the edge; v is a node; v is a node set; sim (v)i，vj) Is a node viAnd node vjCorrelation;
s12, recording the attribute of a certain node in a certain time window as a random variable SXThe attribute of another node in the same time window is a random variable sYThen correlation between nodesSex was calculated using Pearson coefficients:
obtaining a complex network diagram (such as figure 2);
s2, modeling the node attribute data by using a Gaussian mixture model to obtain a likelihood probability model, and then performing optimization processing by using an EM (effective expectation) algorithm to obtain a community division result, wherein the method specifically comprises the following steps:
s21, taking index attributes of all nodes in the network as a multidimensional variable X ═ X1，x2，…，xnThe probability of a node u being assigned to a community s is based on the index attribute x of the nodeuThe probability is defined as gammasx(ii) a Assuming that the gaussian mixture model consists of k gaussian models (i.e. the data contains k classes), the probability model of the gaussian mixture model is:
wherein k is the number of Gaussian models, namely the number of classes contained in the data; u is a node; x is the number ofuIs the index attribute of the node u; p (x | k) ═ N (x | μ)k，∑k) Is the probability density function of the kth Gaussian model, and can be considered as that after the kth model is selected, the model generates attribute data x of nodesiThe probability of (d); p (k) ═ pikIs the weight of the kth gaussian model, is the prior probability of selecting the kth model;
s22 Attribute data x for each nodeiThe probability generated by the kth gaussian model is:
where γ (i, k) is attribute data x for each nodeiProbability generated by the kth gaussian model; n (x)i|μk，Σk) Is node attribute data xiA posteriori of the k-th Gaussian distributionThe probability is calculated by the following formula:
wherein d is a variable dimension, namely the number of node attributes, mu is the mean value of each attribute data of the node, and sigma is a covariance matrix and represents the correlation between each attribute of the node;
s23, the likelihood probability model based on the node attribute is known from the Gaussian mixture model as follows:
wherein s is a community; gamma raysxThe probability of assigning the node u to the community s; p (s | pi, mu, sigma, x) is a likelihood probability model based on node attributes;
s24, utilizing parameters in the maximum likelihood probability estimation model of the EM algorithm, fitting a network containing a community structure, and obtaining a connection probability value and the number of a community to which any node belongs, namely obtaining a community division result shown in FIG 3. The 50 nodes are divided into 2 communities. The first community number is C0, which contains 26 node data, and the 26 node data are respectively represented by the numbers:
[2,3,4,7,9,10,15,16,18,19,25,26,27,28,29,30,33,34,38,39,40,42,43,44,45,48]；
the second community number is C1, which contains 24 node data, and the 24 node data are respectively represented by the numbers: [1,5,6,8,11,12,13,14,17,20,21,22,23,24,31,32,35,36,37,41,46,47,49,50].
The nodes belonging to the same community are closely connected, and the nodes not belonging to the same community are loosely connected.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by the present specification, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (3)
1. A network node multidimensional data community division algorithm based on correlation analysis is characterized in that the method utilizes the relationship among node attributes to carry out correlation analysis on nodes, and determines whether edges are connected among the nodes according to the magnitude of the correlation, so that a complex network is obtained; then, on the basis of a Gaussian mixture model, a model is established by utilizing the self-attribute of the nodes, the optimal partitioning result of the weighted complex network is obtained by solving the optimal solution of the model through an EM algorithm, and the method comprises the following steps:
s1, calculating the correlation between the nodes to obtain a complex network;
and S2, modeling the node attribute data by using a Gaussian mixture model to obtain a likelihood probability model, and performing optimization processing by using an EM (effective man) algorithm to obtain a community division result.
2. The correlation analysis-based network node multidimensional data community division algorithm according to claim 1, wherein the step S1 specifically comprises:
s11, assuming that there is at most one edge connection between two nodes, the element value of its adjacency matrix a may take 0 or not 0, i.e.:
wherein w is a weight; w is the weight set of the edge; v is a node; v is a node set; sim (v)i，vj) Is a node viAnd node vjCorrelation;
s12, recording the attribute of a certain node in a certain time window as a random variable SXThe attribute of another node in the same time window is a random variable sYThen, the correlation between the nodes is calculated by adopting a Pearson coefficient:
3. the correlation analysis-based network node multidimensional data community division algorithm according to claim 1, wherein the step S2 specifically comprises:
s21, taking index attributes of all nodes in the network as a multidimensional variable X ═ X1，x2，…，xnThe probability of a node u being assigned to a community s is based on the index attribute x of the nodeuThe probability is defined as gammasx(ii) a Assuming that the gaussian mixture model consists of k gaussian models (i.e. the data contains k classes), the probability model of the gaussian mixture model is:
wherein k is the number of Gaussian models, namely the number of classes contained in the data; u is a node; x is the number ofuIs the index attribute of the node u; p (x | k) ═ N (x | μ)k，∑k) Is the probability density function of the kth Gaussian model, and can be considered as that after the kth model is selected, the model generates attribute data x of nodesiThe probability of (d); p (k) ═ pikIs the weight of the kth gaussian model, is the prior probability of selecting the kth model;
s22 Attribute data x for each nodeiThe probability generated by the kth gaussian model is:
where γ (i, k) is attribute data x for each nodeiProbability generated by the kth gaussian model; n (x)i|μk，Σk) Is node attribute data xiThe posterior probability of the kth gaussian distribution is calculated by:
wherein d is the variable dimension, namely the number of the node attributes, mu is the mean value of each attribute data of the node,
sigma is a covariance matrix and represents the correlation among all the attributes of the nodes;
s23, the likelihood probability model based on the node attribute is known from the Gaussian mixture model as follows:
wherein s is a community; gamma raysxThe probability of assigning the node u to the community s; p (s | pi, mu, sigma, x) is a likelihood probability model based on node attributes;
s24, parameters in the likelihood probability estimation model are maximized by the EM algorithm, a network containing a community structure is fitted, and then the connection probability value and the serial number of the community to which any node belongs can be obtained, namely a community division result is obtained.
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