Predicting the Robustness of Undirected Network Controllability

Robustness of the network controllability reflects how well a networked system can maintain its controllability against destructive attacks. The measure of the network controllability robustness is quantified by a sequence of values that record the remaining controllability of the network after a sequence of node-removal or edge-removal attacks. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming. In this paper, an improved method for predicting the controllability robustness of undirected networks is developed based on machine learning using a convolutional neural network. This approach is motivated by the following observations: 1) there is no clear correlation between the topological features and the controllability robustness of a general undirected network, 2) the adjacency matrix of a network can be represented as a gray-scale image, 3) the convolutional neural network technique has proved successful in image processing without human intervention. In the new framework, preprocessing and filtering are embedded, and a sufficiently large number of training datasets generated by simulations are used to train several convolutional neural networks for classification and prediction, respectively. Extensive experimental studies were carried out, which demonstrate that the proposed framework for predicting the controllability robustness of undirected networks is more accurate and reliable than the conventional single convolutional neural network predictor.