A Convolutional Neural Network Approach to Predicting Network Connectedness Robustness

Abstract

To quantitatively measure the connectedness robustness of a complex network, a sequence of values that record the remaining connectedness of the network after a sequence of node-or edge-removal attacks can be used. However, it is computationally time-consuming to measure the network connectedness robustness by attack simulations for large-scale networked systems. In the present paper, an efficient method based on convolutional neural network (CNN) is proposed to train for estimating the network connectedness robustness. The new approach is motivated by the facts that 1) the adjacency matrix of a network can be converted to a gray-scale image and CNN is very powerful for image processing, and 2) CNN has proved very effective in predicting the controllability robustness of complex networks. Extensive experimental studies on directed and undirected, as well as synthetic and real-world networks suggest that: 1) the proposed CNN-based methodology performs excellently in the prediction of the connectedness robustness of complex networks as a process; 2) it performs fairly well as the indicator for the connectedness robustness, compared to other predictive measures.

Gaze Tracking Using an Unmodified Web Camera and Convolutional Neural Network

“…Deep learning is a powerful technique that has developed fast and is widely used in many applications [25,26] including computer vision [27] and gaze estimation [28,29]. Furthermore, there have been several open-source datasets for gaze estimation from the research community, for instance, MPIIGaze [22], GazeCapture [30], TabletGaze [31], including head pose and gaze database [32], ETH-XGaze [33], and RT-GENE [34].…”

A Learning Convolutional Neural Network Approach for Network Robustness Prediction

“…The network connectivity is fundamentally important for a network to function, affecting particularly the network controllability [18] and synchronizability [21]. It is easy to see that good controllability requires good connectivity, but good connectivity does not necessarily guarantee good controllability [22]. In fact, network connectivity and controllability have very different characteristics and measures: the former is guaranteed by a sufficient number of edges, while the later further requires a proper organization of the sufficient number of edges.…”

“…Today, malicious attacks and random failures widely exist in many engineering and technological facilities and processes, which degrade or even destroy certain network functions typically through destructing the network connectivity. Therefore, it is essential to strengthen the network connectivity against such attacks and failures [22]- [29]. In general, destructive attacks and failures take place in the forms of node-and edge-removals, which may cause significant degeneration of network connectivity and controllability.…”

“…For both connectivity and controllability robustness enhancements, deep neural networks [46]- [48] provide a useful tool for computation, optimization and analysis. Successful deep learning applications on complex networks include network robustness prediction using convolutional neural networks (CNNs) [22], [49]- [52], and critical node identification using deep reinforcement learning [27] and graph attention networks [29]. Main advantages of CNN-based approaches for robustness prediction include: 1) the method is straightforward, where the adjacency matrix of a complex network is treated as a gray-scale image, and then the classification (if any) and regression tasks are same as in image processing.…”

“…2) The performance of CNN-based approach is stable and reliable: all types of network adjacency matrices are acceptable as input, which is also shift-invariant [53], namely shuffling and transposing pixels of an image (while keeping the network topology unchanged) does not degrade the performance of the prediction [22], [52]. In addition, it has been experimentally demonstrated that CNN is tolerable to slightly changes of the network size.…”