Knowledge-Based Prediction of Network Controllability Robustness

Network controllability robustness reflects how well a networked system can maintain its controllability against destructive attacks. Its measure 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 studied only for directed networks and is determined by attack simulations, which is computationally time consuming or even infeasible. In the present paper, an improved method for predicting the controllability robustness of undirected networks is developed based on machine learning using a group of convolutional neural networks (CNNs). In this scheme, a number of training data generated by simulations are used to train the group of CNNs for classification and prediction, respectively. Extensive experimental studies are carried out, which demonstrate that 1) the proposed method predicts more precisely than the classical single-CNN predictor; 2) the proposed CNN-based predictor provides a better predictive measure than the traditional spectral measures and network heterogeneity.

[1]  Wen-Xu Wang,et al.  Exact controllability of complex networks , 2013, Nature Communications.

[2]  Guanrong Chen,et al.  Naming Game: Models, Simulations and Analysis , 2018 .

[3]  Guanrong Chen,et al.  Enhancing Controllability Robustness of q-Snapback Networks through Redirecting Edges , 2019, Research.

[4]  Albert-Lszl Barabsi,et al.  Network Science , 2016, Encyclopedia of Big Data.

[5]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[6]  Guanrong Chen,et al.  Advances in Network Controllability , 2019, IEEE Circuits and Systems Magazine.

[7]  Jing Liu,et al.  Evolution of network robustness under continuous topological changes , 2016 .

[8]  Tao Wang,et al.  End-to-end text recognition with convolutional neural networks , 2012, Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012).

[9]  Yoshua Bengio,et al.  Deep Sparse Rectifier Neural Networks , 2011, AISTATS.

[10]  Jing Liu,et al.  A Multi-Objective Evolutionary Algorithm for Promoting the Emergence of Cooperation and Controllable Robustness on Directed Networks , 2018, IEEE Transactions on Network Science and Engineering.

[11]  Ryo Nakamura,et al.  On the Predictability of Network Robustness from Spectral Measures , 2019, 2019 IEEE 43rd Annual Computer Software and Applications Conference (COMPSAC).

[12]  Hans J. Herrmann,et al.  Mitigation of malicious attacks on networks , 2011, Proceedings of the National Academy of Sciences.

[13]  Xiang Li,et al.  Fundamentals of Complex Networks: Models, Structures and Dynamics , 2015 .

[14]  Albert-László Barabási,et al.  Control Principles of Complex Networks , 2015, ArXiv.

[15]  S. Havlin,et al.  The extreme vulnerability of interdependent spatially embedded networks , 2012, Nature Physics.

[16]  Hiroki Sayama,et al.  Optimization of robustness and connectivity in complex networks. , 2003, Physical review letters.

[17]  Jing Liu,et al.  Designing comprehensively robust networks against intentional attacks and cascading failures , 2019, Inf. Sci..

[18]  Fabio Pasqualetti,et al.  Benchmarking Measures of Network Controllability on Canonical Graph Models , 2017, Journal of Nonlinear Science.

[19]  Petter Holme,et al.  Onion structure and network robustness , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  白亮,et al.  Optimization of robustness of network controllability against malicious attacks , 2014 .

[21]  Hussein A. Abbass,et al.  Evolving Robust Networks Using Evolutionary Algorithms , 2018, Evolutionary Computation and Complex Networks.

[22]  Beom Jun Kim,et al.  Attack vulnerability of complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Wen-Xu Wang,et al.  Multiplex congruence network of natural numbers , 2015, Scientific Reports.

[24]  Lin Wang,et al.  Controllability of networked MIMO systems , 2015, Autom..

[25]  Ying-Cheng Lai,et al.  Physical controllability of complex networks , 2017, Scientific Reports.

[26]  Xiaomeng Wang,et al.  The evolution of network controllability in growing networks , 2019, Physica A: Statistical Mechanics and its Applications.

[27]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[28]  Harry Eugene Stanley,et al.  Robustness of onion-like correlated networks against targeted attacks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Guanrong Chen,et al.  Further on the controllability of networked MIMO LTI systems , 2018 .

[30]  Derek Ruths,et al.  Robustness of Network Controllability under Edge Removal , 2013, CompleNet.

[31]  Lao Songyang,et al.  Enhancing Complex Network Controllability by Rewiring Links , 2013, 2013 Third International Conference on Intelligent System Design and Engineering Applications.

[32]  Guanrong Chen,et al.  Predicting Network Controllability Robustness: A Convolutional Neural Network Approach , 2020, IEEE transactions on cybernetics.

[33]  Kishan G. Mehrotra,et al.  Multi-objective Optimization to Improve Robustness in Networks , 2018, Multi-Objective Optimization.

[34]  Yuan Zhang,et al.  Controllability Analysis for a Networked Dynamic System With Autonomous Subsystems , 2017, IEEE Transactions on Automatic Control.

[35]  Yangyong Zhu,et al.  GraphInception: Convolutional Neural Networks for Collective Classification in Heterogeneous Information Networks , 2019, IEEE Transactions on Knowledge and Data Engineering.

[36]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[37]  Gang Hua,et al.  A convolutional neural network cascade for face detection , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[38]  Lin Wang,et al.  Toward Stronger Robustness of Network Controllability: A Snapback Network Model , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  Lin Wang,et al.  Towards Optimal Robustness of Network Controllability: An Empirical Necessary Condition , 2020, IEEE Transactions on Circuits and Systems I: Regular Papers.

[40]  Yukio Hayashi,et al.  Onion-like networks are both robust and resilient , 2018, Scientific Reports.

[41]  Cunlai Pu,et al.  Robustness analysis of network controllability , 2012 .

[42]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[43]  Leman Akoglu,et al.  Optimizing network robustness by edge rewiring: a general framework , 2016, Data Mining and Knowledge Discovery.

[44]  Albert-László Barabási,et al.  Control Centrality and Hierarchical Structure in Complex Networks , 2012, PloS one.

[45]  Guanrong Chen,et al.  Controllability of networked higher-dimensional systems with one-dimensional communication , 2017, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[46]  白亮,et al.  Smart Rewiring： Improving Network Robustness Faster , 2015 .

[47]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.

[48]  Xiang Zhang,et al.  Character-level Convolutional Networks for Text Classification , 2015, NIPS.

[49]  Mathias Niepert,et al.  Learning Convolutional Neural Networks for Graphs , 2016, ICML.

[50]  Andrew Zisserman,et al.  Very Deep Convolutional Networks for Large-Scale Image Recognition , 2014, ICLR.

[51]  Ginestra Bianconi,et al.  Network controllability is determined by the density of low in-degree and out-degree nodes. , 2014, Physical review letters.

[52]  Albert-László Barabási,et al.  Effect of correlations on network controllability , 2012, Scientific Reports.

[53]  Jun Zhao,et al.  Recurrent Convolutional Neural Networks for Text Classification , 2015, AAAI.

[54]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[55]  Guanrong Chen,et al.  A Comparative Study on Controllability Robustness of Complex Networks , 2019, IEEE Transactions on Circuits and Systems II: Express Briefs.

[56]  Hai Zhao,et al.  Improving controllability of complex networks by rewiring links regularly , 2014, The 26th Chinese Control and Decision Conference (2014 CCDC).

[57]  P. ERDbS.  ON THE STRENGTH OF CONNECTEDNESS OF A RANDOM GRAPH , 2001 .

[58]  Shi-Jinn Horng,et al.  Deep Air Quality Forecasting Using Hybrid Deep Learning Framework , 2018, IEEE Transactions on Knowledge and Data Engineering.