A Learning Convolutional Neural Network Approach for Network Robustness Prediction.

Network robustness is critical for various societal and industrial networks against malicious attacks. In particular, connectivity robustness and controllability robustness reflect how well a networked system can maintain its connectedness and controllability against destructive attacks, which can be quantified by a sequence of values that record the remaining connectivity and controllability of the network after a sequence of node- or edge-removal attacks. Traditionally, robustness is determined by attack simulations, which are computationally very time-consuming or even practically infeasible for large-scale networks. In this article, an improved method for network robustness prediction is developed based on learning feature representation using the convolutional neural network (LFR-CNN). In this scheme, the higher-dimensional network data are compressed into lower-dimensional representations, which are then passed to a convolutional neural network to perform robustness prediction. Extensive experimental studies on both synthetic and real-world networks, both directed and undirected, demonstrate that: 1) the proposed LFR-CNN performs better than other two state-of-the-art prediction methods, with significantly smaller prediction errors; 2) LFR-CNN is insensitive to the variation of the input network size, which significantly extends its applicability; 3) although LFR-CNN needs more time to perform feature learning, it can achieve accurate prediction faster than attack simulations; and 4) LFR-CNN not only accurately predicts the network robustness, but also provides a good indicator for connectivity robustness, better than the classical spectral measures.

Classification-based prediction of network connectivity robustness.

Today, there is an increasing concern about malicious attacks on various networks in society and industry, against which the network robustness is critical. Network connectivity robustness, in particular, is of fundamental importance, which is generally measured by a sequence of calculated values that indicate the connectedness of the remaining network after a sequence of attacks by means of node- or edge-removal. It is computationally time-consuming, however, to measure and evaluate the network connectivity robustness using the conventional attack simulations, especially for large-scale networked systems. In the present paper, an efficient robustness predictor based on multiple convolutional neural networks (mCNN-RP) is proposed for predicting the network connectivity robustness, which is an natural extension of the single CNN-based predictor. In mCNN-RP, one CNN works as the classifier, while each of the rest CNNs works as an estimator for predicting the connectivity robustness of every classified network category. The network categories are classified according to the available prior knowledge. A data-based filter is installed for predictive data refinement. Extensive experimental studies on both synthetic and real-world networks, including directed and undirected as well as weighted and unweighted topologies, verify the effectiveness of mCNN-RP. The results demonstrate that the average prediction error is lower than the standard deviation of the tested data, which outperforms the single CNN-based framework. The runtime in assessing network connectivity robustness is significantly reduced by using the CNN-based technique. The proposed mCNN-RP not only can accurately predict the connectivity robustness of various complex networks, but also provides an excellent indicator for the connectivity robustness, better than other existing prediction measures.