CN109194509A - A method of the prediction network based on path strong or weak relation and community information connects side - Google Patents
A method of the prediction network based on path strong or weak relation and community information connects side Download PDFInfo
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Abstract
A method of the prediction network based on path strong or weak relation and community information connects side, establish network model, network is divided into several communities using community's partitioning algorithm, the sum of all common neighbor node weights constitute strong relationship between two nodes, strong relationship between calculate node, take path length between node be 3 and 4 all intermediate node weight products and constitute weak relationship, weak relationship between calculate node, and it is punished with penalty coefficient, reflect the influence of community information according to company side of the company between node when being internal connect or between community, calculate similarity indices between the two, by whether there is or not the similarity scores even between mid-side node pair to arrange in descending order, corresponding two nodes of h index are prediction even side before taking.The present invention, which is examined, to be combined and is considered by path and node strong and weak influence and be extracted community information, is effectively utilized the correlation information of network, precision of prediction is higher.
Description
Technical field
The present invention relates to network and link prediction field, particularly relate to a kind of based on path strong or weak relation and community information
Prediction network connects the method on side.
Background technique
Network is seen everywhere with us, from biosystem, arrives transportation network；From well known internet, postal is arrived
Political affairs net, television signals network, it almost covers the various aspects such as our study, work, lives.Online is learnt, data
The work such as inquiry on needs, look for a job, buy house, the needs in life such as shopping are watched movie, the amusement such as customization of tourism
On needs.More and more people obtain external information by internet, to understand social dynamic.In real life we
Exchange with each other constitutes social networks, and online continuous shopping forms the network of e-commerce, and traffic trip constitutes
Transportation network.The research of big data and deep learning further promotes the development of network, also provides more for our life
More conveniences.
In recent years, with the fast development of Network Science, theoretic achievement is that link prediction has built a research
Platform so that the research of link prediction and the structure of network are closely linked with evolution.Link prediction is based in network
Nodal community, topology information, related communities information etc. predict that any two in complex network are not connected with the link probability of node.
In social networks, e-commerce can create considerable value in the miscellaneous network such as data mining and bio-networks.
The topological structure that link prediction is mainly based upon network provides our similarity scores algorithm, further according to AUC or Precision
Index and other classic algorithms such as CN, RA and AA etc. are compared the superiority-inferiority for judging algorithm.For link prediction algorithm, I
Not only to consider its accuracy, consider its computation complexity be also it is necessary, not with network size and data volume
Disconnected to increase, the time needed for algorithm is also continuously increased, and how to combine the accuracy of algorithm and computation complexity is very
Important.
Summary of the invention
In order to which the acquisition network information for the method for overcoming existing prediction network to connect side is not comprehensive, precision of prediction is lower, no
Foot, in order to more fully obtain the network information, promotes the estimated performance of existing algorithm, the present invention proposes that a kind of accuracy is higher
A method of the prediction network based on path strong or weak relation and community information connects side.
The technical solution adopted by the present invention to solve the technical problems is:
A method of the prediction network based on path strong or weak relation and community information connects side, includes the following steps:
Step 1: constructing the Undirected networks G (V, E) with N number of node, and V is node, and E is to connect side, adjacency matrix A
It indicates, it is the two-dimensional array of a N × N, A if there is even side between node i and j if twoijIt is 1, otherwise is 0；
Step 2: network G is divided into several communities using community's partitioning algorithm, one of community refers to network
In with the like attribute one kind node and its even subnet that is constituted of side；
Step 3: two node is and j without even side, the public adjacent node between i and j are known as in any selection network G
Their common neighbours, take all common neighbor node weights between node i and node j and constitute strong relationship, the power of node i
It reusesIt indicates, kiIndicate that the degree of node i, the degree of a node refer to the quantity of the connected neighbor node of the node；
Step 4: i is calculated, the strong relationship between j node:
Wherein πij(t) it indicates the transition probability between i and j, refers to node i to the probability for walking arrival node j by t；πi
(t)=PTπi(t-1), t >=0 and πi(0)=ex,exIndicate the vector of N × 1, wherein i-th of element is 1, other are 0；P is one
The transition probability matrix of N × N,PTThe transposition of representing matrix P；πji(t) it indicates the transition probability between j and i, is
Finger joint point j reaches the probability of node i to walking by t；πj(t)=PTπj(t-1), t >=0 and πj(0)=ex；
Step 5: the weak relationship between calculate node i, j
Wherein, n is node i, the quantity in the path that all length is 3 and 4 between j, and MP (g) is in wherein g paths
The set of node in addition to node i and j, α are punishment parameters；
Step 6: two node is are calculated, the similarity scores index between j:
Wherein t is the value of step number；
Step 7: if node i, j belongs to the same community, then connects side inside the Lian Bianwei lacked between them,If node i, j in different communities, then the company lacked between them while for community Jian Lian,
Step 8: traverses network repeats step 3 to step 7, calculates for all two not be connected directly nodes
Corresponding CSW index is as, there may be the evaluation index on even side, CSW index is higher, node pair between not connected node pair
Between more there may be even side, by the CSW index between the node pair not being connected directly all in network according to from high to low
Sequence arrangement, the corresponding node of h CSW index is to for possible prediction company side before taking, h≤H, and wherein H is does not have in network
Directly connect the sum of the node pair on side.
Technical concept of the invention are as follows: the sum of the degree that two internode paths are 2 all public neighbours is utilized and constitutes by force
Influence, between 3,4 path of length all node degree products and constitute weak influence, use community's partitioning algorithm to extract effectively letter
Breath, improves the accuracy of prediction algorithm.
The invention has the benefit that emphasizing to influence by force in conjunction with the attribute information of two not connected internode paths, punish
Weak influence, and optimize it more with related communities information, precision of prediction is higher, and complexity is lower.
Detailed description of the invention
Fig. 1 is the schematic diagram of local path, and black dot is that there is no the nodes pair for directly connecting side, is labeled as 1 white
Dot is the common neighbours of node pair, and the white nodes for being labeled as 2 are the intermediate node set for being 3 to the path j from node i, mark
The white nodes that note is 3 are the intermediate node set for being 4 to the path j from node i.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
Referring to Fig.1, a method of the prediction network based on path strong or weak relation and community information connects side, including walks as follows
It is rapid:
Step 1: constructing the Undirected networks G (V, E) with N number of node, and V is node, and E is to connect side, adjacency matrix A
It indicates, it is the two-dimensional array of a N × N, A if there is even side between node i and j if twoijIt is 1, otherwise is 0；
Step 2: network G is divided into several communities using community's partitioning algorithm, one of community refers to network
In with the like attribute one kind node and its even subnet that is constituted of side；Mutually interconnection side between community's interior joint is closer,
It is then loose company side between community；
Wherein, community's partitioning algorithm uses the quick partitioning algorithm of Newman, it is a kind of fast community hair based on greed
Existing algorithm, the thought of algorithm is: each node of network being then combined with two modularities as an independent community first
The maximum community of Q increment；Termination condition is when the vertex in network belongs to the same community.If network has n node, m side,
Merging community's number each time is r, forms r*r a matrix e, matrix element eijIt indicates to connect between community i and community's j interior joint
Ratio of the number on side in the total number of edges of network.Its process is as follows:
(1): initialization network, starting network has n community, the e of initializationijAnd aiFor eijIf between=1/2m i and j
It is otherwise 0, a in the presence of even sidei=ki；
(2) merge two maximum communities of modularity Q increment, and calculate the modularity increment Delta Q after merging:
Δ Q=eij+eji-2aiaj=2 (eij-aiaj)
(3) merge community to later modification to community symmetrical matrix e and the corresponding ranks of community i and j；
(4) step (2) and (3) are repeated, constantly merging community, when each node of network is belonged to a community
Algorithm stops；
Step 3: two node is and j without even side, the public adjacent node between i and j are known as in any selection network G
Their common neighbours are labeled as 1 node in as Fig. 1, take all common neighbor node weights between node i and node j
And constitute strong relationship, the weight of node i is usedIt indicates, kiIndicate that the degree of node i, the degree of a node refer to the node
Connected neighbor node quantity；
Step 4: i is calculated, the strong relationship between j node:
Wherein πij(t) it indicates the transition probability between i and j, refers to node i to the probability for walking arrival node j by t；πi
(t)=PTπi(t-1), t >=0 and πi(0)=ex,exIndicate the vector of N × 1, wherein i-th of element is 1, other are 0；P is one
The transition probability matrix of N × N,PTThe transposition of representing matrix P；πji(t) it indicates the transition probability between j and i, is
Finger joint point j reaches the probability of node i to walking by t；πj(t)=PTπj(t-1), t >=0 and πj(0)=ex；
Step 5: the weak relationship between calculate node i, j
Wherein, n is node i, the quantity in the path that all length is 3 and 4 between j；MP (g) is in wherein g paths
The set of node in addition to node i and j, the product of the intermediate node weight in the path that computational length is 3, as Fig. 1 acceptance of the bid
Note is the product of 2 node degrees, and the product of the intermediate node weight in the path that computational length is 4 is labeled as 3 nodes in as Fig. 1
The product of degree, and the two is added, α is punishment parameter；
Step 6: two node is are calculated, the similarity scores index between j:
Wherein t is the value of step number, can take 3,4,5；
Step 7: if node i, j belongs to the same community, then connects side inside the Lian Bianwei lacked between them,If node i, j in different communities, then the company lacked between them while for community Jian Lian,
Step 8: traverses network repeats step 3 to step 7, calculates for all two not be connected directly nodes
Corresponding CSW index is as, there may be the evaluation index on even side, CSW index is higher, between node pair more between node pair
There may be even sides, by the CSW index between the node pair not being connected directly all in network according to sequence from high to low
Arrangement, the corresponding node of h CSW index connects side to for possible prediction before taking, and h≤H, wherein H is not connect directly in network
The sum of the node pair on side.
As described above, the specific implementation step that this patent is implemented is more clear the present invention.In spirit and power of the invention
In the protection scope that benefit requires, to any modifications and changes that the present invention makes, protection scope of the present invention is both fallen within.
Claims (1)
1. a kind of prediction network based on path strong or weak relation and community information connects the method on side, it is characterised in that: including as follows
Step:
Step 1: constructing the Undirected networks G (V, E) with N number of node, and V is node, and E is even side, adjacency matrix with indicating,
It is the two-dimensional array of a N × N, is 1 if there is even side between node i and j if two, otherwise is 0；
Step 2: network G is divided into several communities using community's partitioning algorithm, one of community refers to having in network
There is like attribute one kind node and its connects the subnet that side is constituted；
Step 3: two node is and j without even side, the public adjacent node between i and j are known as them in any selection network G
Common neighbours, take all common neighbor node weights between node i and node j and constitute strong relationship, the weight of node i is usedIt indicates, kiIndicate that the degree of node i, the degree of a node refer to the quantity of the connected neighbor node of the node；
Step 4: i is calculated, the strong relationship between j node:
Wherein πij(t) it indicates the transition probability between i and j, refers to node i to the probability for walking arrival node j by t；πi(t)=
PTπi(t-1), t >=0 and πi(0)=ex,exIndicate the vector of N × 1, wherein i-th of element is 1, other are 0；P is a N × N's
Transition probability matrix,PTThe transposition of representing matrix P；πji(t) it indicates the transition probability between j and i, refers to node j
To the probability for walking arrival node i by t；πj(t)=PTπj(t-1), t >=0 and πj(0)=ex；
Step 5: the weak relationship between calculate node i, j:
Wherein, n is node i, the quantity in the path that all length is 3 and 4 between j；MP (g) saves to remove in wherein g paths
The set of node except point i and j, α are punishment parameters；
Step 6: two node is are calculated, the similarity scores index between j:
Wherein t is the value of step number；
Step 7: if node i, j belongs to the same community, then connects side inside the Lian Bianwei lacked between them,If node i, j in different communities, then the company lacked between them while for community Jian Lian,
Step 8: traverses network repeats step 3 to step 7, calculates corresponding for all two not be connected directly nodes
CSW index as, there may be the evaluation index on even side, CSW index is higher, more may between node pair between node pair
In the presence of even side, the CSW index between the node pair not being connected directly all in network is arranged according to sequence from high to low,
The corresponding node of h CSW index connects side to for possible prediction before taking, and h≤H, wherein H is not have directly to connect the section on side in network
The sum of point pair.
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