Reconstruction of bifurcation diagrams using an extreme learning machine with a pruning algorithm

We describe the reconstruction of bifurcation diagrams using an extreme learning machine with a pruning algorithm. We can reconstruct the bifurcation diagram from only some time-series data by using a neural network. However, the reconstruction accuracy is influenced by the structure of the neural network. To improve reconstruction accuracy we apply a pruning algorithm to the neural network used for the reconstruction of bifurcation diagrams. In this study, we use a pruned extreme learning machine (ELM) based on sensitivity analysis. In numerical experiments, first we compare time-series predictions using the ELM with and without the pruning algorithm. Then, we show the effectiveness of the pruned extreme learning machine for the reconstruction of bifurcation diagrams.

[1]  Sawada,et al.  Measurement of the Lyapunov spectrum from a chaotic time series. , 1985, Physical review letters.

[2]  R. Preisendorfer,et al.  Principal Component Analysis in Meteorology and Oceanography , 1988 .

[3]  K Pakdaman,et al.  Reconstructing Bifurcation Diagrams of Dynamical Systems Using Measured Time Series , 2000, Methods of Information in Medicine.

[4]  I. Shimada,et al.  A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems , 1979 .

[5]  U Parlitz,et al.  Modeling parameter dependence from time series. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Makoto Kotani,et al.  Identification of Chaotic Dynamical Systems with Back-Propagation Neural Networks , 1994 .

[7]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[8]  Amaury Lendasse,et al.  Evolving fuzzy Optimally Pruned Extreme Learning Machine: A comparative analysis , 2010, International Conference on Fuzzy Systems.

[9]  Li Ying,et al.  A Pruning Algorithm for Extreme Learning Machine , 2013, IDEAL.

[10]  Kai Sun,et al.  A generalized pruning algorithm for extreme learning machine , 2015, 2015 IEEE International Conference on Information and Automation.

[11]  Ryuji Tokunaga,et al.  Reconstructing bifurcation diagrams only from time-waveforms , 1994 .

[12]  M. Adachi,et al.  Reconstructing bifurcation diagrams with Lyapunov exponents from only time-series data using an extreme learning machine , 2017 .

[13]  Erik Cambria,et al.  Fusing audio, visual and textual clues for sentiment analysis from multimodal content , 2016, Neurocomputing.

[14]  Taishin Nomura,et al.  Time series-based bifurcation diagram reconstruction , 1999 .

[15]  César Hervás-Martínez,et al.  PCA-ELM: A Robust and Pruned Extreme Learning Machine Approach Based on Principal Component Analysis , 2012, Neural Processing Letters.

[16]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[17]  Amaury Lendasse,et al.  OP-ELM: Optimally Pruned Extreme Learning Machine , 2010, IEEE Transactions on Neural Networks.

[18]  Yuanlong Yu,et al.  A new pruning algorithm for extreme learning machine , 2017, 2017 IEEE International Conference on Information and Automation (ICIA).

[19]  E. Bagarinao,et al.  Reconstructing bifurcation diagrams from noisy time series using nonlinear autoregressive models. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Masaharu Adachi,et al.  A Quantitative Method for Evaluating Reconstructed One-Dimensional Bifurcation Diagrams , 2018, J. Comput..

[21]  Baojun Zhao,et al.  Gradient-based no-reference image blur assessment using extreme learning machine , 2016, Neurocomputing.

[22]  Masaharu Adachi,et al.  Reconstruction of Bifurcation Diagrams Using Extreme Learning Machines , 2013, 2013 IEEE International Conference on Systems, Man, and Cybernetics.

[23]  Yuan Lan,et al.  An extreme learning machine approach for speaker recognition , 2012, Neural Computing and Applications.

[24]  Chee Kheong Siew,et al.  Extreme learning machine: Theory and applications , 2006, Neurocomputing.