3.2. Preferential Decision Model Based on Dynamic Iteration
Based on the formulas and definitions mentioned above, a new model has been proposed, which is a preferential decision model based on dynamic iteration that involves many aspects: the information propagation model, the memory similarity, preferential decision degree, the loss of information, and so on.
In real life, we make progress through continuous learning. No matter what age, we will be influenced by the surrounding environment to make decisions, which imperceptibly drives us to learn from the people or things around us. We compare the community network to a social circle. When we make decisions, we will be influenced by the people around us. Learning from the experience of others to help us make decisions is the core idea presented in this article.
There are many types of learning in different circles. Like those around us who have resources and influence and those who have a close relationship with us, we will be greatly influenced by them when making decisions. This is also true for community detection in complex networks. In the constant iterations of local communities, nodes are constantly making decisions and finally approaching stability. In our daily life, we can understand that parents have a stronger connection with us. For example, their suggestions will have a great impact on the decision of which we will settle in the future. This is one of the reasons why we want to introduce connection strength. Compared with our own past behavioral cycle, it shows that our hobbies and life rhythms are very similar. Because different people have different decision-making styles, people with identical similarities will be more likely to get together. We are closer to making this decision, which is close to the life we are exposed to. Thus, the past similarity between the two nodes is introduced to reflect the true tightness of the two nodes. In each iteration, for neighbor nodes, each node will make its own decision according to the surrounding comprehensive factors. Thus, in the end, we lead to the probability that one node chooses another node, and there is a certain choice for any node around. Some of the probabilities may approach zero, in which case the node will basically not make its own choice. In the information propagation based on dynamic iteration, the neighboring nodes are de-spreaded with a certain probability. For example, in our real life, we will pass on information, ideas, attitudes or affections to other individuals or groups in order to make resultant changes. In information dissemination, there is a possibility of information loss, which is directed by the topological features and transmitted information. Because there are always some useless or uninteresting information in real life to interfere with us, we consider the information propagation model, the past memory similarity, preferential decision degree, and the loss of information together.
The past memory similarity. Given a list of memory tags to any social network node, the higher the similarity of the past is, the closer the past behavior of the node is. This shows that the probability of interaction between two nodes is greater. In the following formula,
means the
i-th memory label list array of the node
u. In particular,
∂ is a constant, usually
, and the purpose of introducing
∂ is to prevent
from falling to zero. We have done numerous experiments to change the value of
∂ but found that the performance is the best in this case. We can define
, which is the past memory similarity between node
u and node
v, as follows:
We can identify memory labels as something that a person was interested in, and the length of the memory area represents the range of personal acceptance. The more similar the memory tags are, the greater the value of is, which means the more similar common experience between the two nodes. In real life, people with the same experience share common interests and hobbies. Because different people have different decision-making styles, people with similar experiences are more likely to get together.
Preferential decision degree. In each iteration of information propagation, each decision of the node is the result of preferential selection after comprehensive consideration. Thus, we introduce the concept of preferential decision-making degree to better represent the stability of the algorithm. When choosing community division, it is analogous to choosing to communicate with people around us in our daily life and make their own decisions. In real life, we prefer to go to communicate with people who are similar to past cycle behaviors. People who have similar interests and interests will hope to learn what they want from people who have close relationships with them. Generally, let
be the set of neighbors of node
u,
and
indicate the connection strength and the Jaccard similarity between node
u and node
v, respectively.
denotes the past memory similarity coefficient between node
u and node
v. Let
be the preferential decision degree, which is defined as follows:
The propagation of information between nodes is analogous to the exchange of information among people. Communication between people can be influenced by many factors. Knowledge and resources of a person can be regarded as the Preferential decision degree of a node. The association between the two persons can be considered as the connection strength and the Jaccard coefficient. In the process of iteration, the node will always choose the best result to make a reasonable decision.
The probability of propagation. From the above formulas, we can conclude that the node has a preferential decision degree for each neighboring node, and the higher it is, the greater the decision-making probability will be. Let
be the set of neighboring nodes of node
u, and node
belongs to
. Let
be the probability of selecting node
as deciding objects for node
u, which is defined as follows:
For the node u, all its neighbors are likely to be selected. Low Preferential decision degree indicates that the probability of being selected is small, but this does not mean that it is impossible. It can also be analogous to our real life, and sometimes we need to learn what we need from strangers.
Information loss. In our daily lives, there is always some information that will be discarded in the process of information exchange. As the number of iterations increases, the probability of information loss increases. To prevent the information exchange failure caused by the preferential decision degree between nodes, it is extremely important to introduce a threshold. The copra algorithm divides the community by introducing a label dependent coefficient and an adjustable parameter v. In this paper, a threshold is used to control nodes to make better decisions. Its threshold has a significant impact on the experimental results, which not only reduces the reference of parameters but also divides the community accurately in a better way according to its node characteristics.