Predicting Network Controllability Robustness: A Convolutional Neural Network Approach

Abstract

Network controllability measures how well a networked system can be controlled to a target state, and its robustness reflects how well the system can maintain the controllability against malicious attacks by means of node-removals or edge-removals. The measure of network controllability is quantified by the number of external control inputs needed to recover or to retain the controllability after the occurrence of an unexpected attack. The measure of the network controllability robustness, on the other hand, is quantified by a sequence of values that record the remaining controllability of the network after a sequence of attacks. Traditionally, the controllability robustness is determined by attack simulations, which is computationally time consuming. In this paper, a method to predict the controllability robustness based on machine learning using a convolutional neural network is proposed, motivated by the observations that 1) there is no clear correlation between the topological features and the controllability robustness of a general network, 2) the adjacency matrix of a network can be regarded as a gray-scale image, and 3) the convolutional neural network technique has proved successful in image processing without human intervention. Under the new framework, a fairly large number of training data generated by simulations are used to train a convolutional neural network for predicting the controllability robustness according to the input network-adjacency matrices, without performing conventional attack simulations. Extensive experimental studies were carried out, which demonstrate that the proposed framework for predicting controllability robustness of different network configurations is accurate and reliable with very low overheads.

arXiv comment11 pages, 7 figures

References in corpus (21)

• Adam: A Method for Stochastic Optimization
• Very Deep Convolutional Networks for Large-Scale Image Recognition
• Efficient Estimation of Word Representations in Vector Space
• Deep Learning in Neural Networks: An Overview
• Catastrophic cascade of failures in interdependent networks
• Character-level Convolutional Networks for Text Classification
• Attack vulnerability of complex networks
• Renormalization group analysis of the small-world network model
• Universal Behavior of Load Distribution in Scale-free Networks
• Mitigation of Malicious Attacks on Networks
• Control Principles of Complex Networks
• Exact Controllability of Complex Networks
• Control centrality and hierarchical structure in complex networks
• The extreme vulnerability of interdependent spatially embedded networks
• Effect of correlations on network controllability
• Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
• Networkcontrology
• Effects of the network structural properties on its controllability
• Toward Stronger Robustness of Network Controllability: A Snapback Network Model
• Benchmarking measures of network controllability on canonical graph models
• Improving controllability of complex networks by rewiring links regularly

Cited by in corpus (6)

• Structural Robustness of Complex Networks: A Survey of A Posteriori Measures
• A Learning Convolutional Neural Network Approach for Network Robustness Prediction
• Knowledge-Based Prediction of Network Controllability Robustness
• A Framework of Hierarchical Attacks to Network Controllability
• SPP-CNN: An Efficient Framework for Network Robustness Prediction
• CNN-based Prediction of Network Robustness With Missing Edges