Research On Link Prediction In Complex Brain Networks Based On Hierarchical Random Graph Model

In order to find the potential relationship between brain areas, we need topredict links between nodes of various brain regions in the complex brain neuralnetworks. Link prediction of brain networks attempts to estimate the likelihoodof the existence of links between nodes based on the available brain networkinformation, such as nodes attributes and the observed links. In addition, thedata of known brain network may be blurred or disorder. Link predictionalgorithm not only can be used to identify observed link, but can correct thewrong links, which is of great importance to the reconfiguration, structuraloptimization and evolution of brain networks.At present, link prediction algorithms are mainly divided into threecategories: probability model algorithm, similarity definition algorithm, andmaximum likelihood estimation algorithm. Early methods and researches of linkprediction were mainly based on probability model. This kind of algorithm ismainly used to machine learning and data mining areas, and suitable for thelarge-scale data set networks. However, due to the high computational complexity and non-universal parameters, its application range is limited; Forthe similarity method based on network topology properties, it only applies tothe simple undirected network with nodes similarity, and its computationalefficiency is low in the real network without nodes similarity; The third methodis based on the maximum likelihood estimation of network structure. Thealgorithm is suitable for networks of composite structure. Especially for themaximum likelihood estimation algorithm based on hierarchical random graphmodel, it has good accuracy in deal with hierarchical structure networks. Thebrain network is a kind of typical complex system, so the connection can be seenas a reflection of internal hierarchy. The most effective and intuitive method ofestablishing and expressing hierarchy is to adopt hierarchical random graphmodel. Therefore, this article selects hierarchical random graph model toconstruct networks and predict links.The main idea of algorithm was as follows: Firstly, this algorithm usedbrain networks data to create the hierarchical random graph model. Secondly, itsampled the space of all possible dendrograms using the improved Markovchain Monte Carlo algorithm. Thirdly, it calculated the average connectionprobability. It also evaluated by the evaluation index. To start with, This paperused fMRI data of normal human to construct brain networks under the scale of5%to40%sparsity(5per step), and networks data under eight different scaleswere constructed random graph models. Then, Markov chain Monte Carloalgorithm was applied to the bayesian theory. For the Markov Chain to be in equilibrium, the best HRG seed model was collected. The dendrogram spacewith proportional likelihood was collected, which was base on the seed model.Finally, the average of edge probabilities in brain networks were computed byadopting dendrogram samples, and results were analyzed withevaluation indexes. This algorithm overcome poor problems of traditionalmethods and improves the accuracy of model construction. The dendrogramsample space comes true probability average of edges.The algorithm performed real brain network data. Results showed that thealgorithm exhibited best result in brain network between different hierarchicalnetworks. In addition, compared with the traditional methods based on similarity,it obtained the good effect, and experienced reasonable computing complexity.This paper puts forward a new method of hierarchical random graph model usedin brain network, which has achieved good results. The research on brainnetwork links has certain reference value.