Community Extraction Method Based On The Hopfield Network

Many systems of nature and human society can be modeled by complex network. Complex network has become a hot spot of management, sociology, biology, physics, computer science and other disciplines. As for the further research of network properties, people find there are some community structures in actual network. The internal connections of nodes which in the same community are relatively close, but relatively sparse between different communities. To reveal this community structure is of great significance for insighting into the network structure and analysing the network characteristics. This thesis firstly propose the Hopfield network community extraction algorithm, and then show that the Mincut, Ratiocut, Normalizedcut, Modularity which used in Spectral algorithm can be implemented by our method in different Hopfield network weights. So, this algorithm unifies the existing method. Specific work is as follows:(1)We combine the artificial neural network with the community extraction problem and put forward an algorithm which based on the Hopfield network. Using the dynamic character of network, when the Hopfield network reaches stability, the output of the network can be used for dividing the complex network.(2) We propose and prove five propositions. These five propositions make clear that how to find the Hopfield network’s weight matrix and threshold vector which connect with the existing extraction criteria. If we change the weight matrix and threshold vector, we can get a new extraction criterion like W.(3) We conduct lots of example verifications. We put the five criteria above as the objective function and use our algorithm and Spectral algorithm to do experiment on7actual networks and an artificial network. The similarities and differences between the two methods can be showed by the objective function value and the optimal community structure. The experimental results show that our algorithm can achieve better objective value and the community structure which extracted is more reasonable. Finally, we summarize whole thesis and discuss some possible problems in further research.