Regularization by Intrinsic Plasticity and Its Synergies with Recurrence for Random Projection Methods

Affiliation(s)

Research Institute for Cognition and Robotics (CoR-Lab), Bielefeld University, Bielefeld, Germany..

Research Institute for Cognition and Robotics (CoR-Lab), Bielefeld University, Bielefeld, Germany..

ABSTRACT

Neural networks based on high-dimensional random feature generation have become popular under the notions extreme learning machine (ELM) and reservoir computing (RC). We provide an in-depth analysis of such networks with respect to feature selection, model complexity, and regularization. Starting from an ELM, we show how recurrent connections increase the effective complexity leading to reservoir networks. On the contrary, intrinsic plasticity (IP), a biologically inspired, unsupervised learning rule, acts as a task-specific feature regularizer, which tunes the effective model complexity. Combing both mechanisms in the framework of static reservoir computing, we achieve an excellent balance of feature complexity and regularization, which provides an impressive robustness to other model selection parameters like network size, initialization ranges, or the regularization parameter of the output learning. We demonstrate the advantages on several synthetic data as well as on benchmark tasks from the UCI repository providing practical insights how to use high-dimensional random networks for data processing.

Neural networks based on high-dimensional random feature generation have become popular under the notions extreme learning machine (ELM) and reservoir computing (RC). We provide an in-depth analysis of such networks with respect to feature selection, model complexity, and regularization. Starting from an ELM, we show how recurrent connections increase the effective complexity leading to reservoir networks. On the contrary, intrinsic plasticity (IP), a biologically inspired, unsupervised learning rule, acts as a task-specific feature regularizer, which tunes the effective model complexity. Combing both mechanisms in the framework of static reservoir computing, we achieve an excellent balance of feature complexity and regularization, which provides an impressive robustness to other model selection parameters like network size, initialization ranges, or the regularization parameter of the output learning. We demonstrate the advantages on several synthetic data as well as on benchmark tasks from the UCI repository providing practical insights how to use high-dimensional random networks for data processing.

Cite this paper

K. Neumann, C. Emmerich and J. Steil, "Regularization by Intrinsic Plasticity and Its Synergies with Recurrence for Random Projection Methods,"*Journal of Intelligent Learning Systems and Applications*, Vol. 4 No. 3, 2012, pp. 230-246. doi: 10.4236/jilsa.2012.43024.

K. Neumann, C. Emmerich and J. Steil, "Regularization by Intrinsic Plasticity and Its Synergies with Recurrence for Random Projection Methods,"

References

[1] Y. Miche, B. Schrauwen and A. Lendasse, “Machine Learning Techniques Based on Random Projections,” In Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2010, pp. 295-302.

[2] Y.-H. Pao, G.-H. Park and D. J. Sobajic, “Learning and Generalization Characteristics of the Random Vector Functional-Link Net,” Neurocomputing, Vol. 6, No. 2, 1994, pp. 163-180. doi:10.1016/0925-2312(94)90053-1

[3] D. S. Broomhead and D. Lowe, “Multivariable Functional Interpolation and Adaptive Networks,” Complex Systems, Vol. 2, No. 1, 1988, pp. 321-355.

[4] G.-B. Huang, Q.-Y. Zhu and C.-K. Siew, “Extreme Learning Machine: A New Learning Scheme of Feedforward Neural Networks,” Proceedings of International Joint Conferences on Artificial Intelligence, Budapest, July 2004, pp. 489-501.

[5] G.-B. Huang, Q.-Y. Zhu and C.-K. Siew, “Extreme Learning Machine: Theory and Applications,” Neurocomputing, Vol. 70, No. 1-3, 2006, pp. 489-501.

[6] L. P. Wang and C. R. Wan, “Comments on the Extreme Learning Machine,” IEEE Transactions on Neural Networks, Vol. 19, No. 8, 2008, pp. 1494-1495.

[7] M. Lukosevicius and H. Jaeger, “Reservoir Computing Approaches to Recurrent Neural Network Training,” Computer Science Review, Vol. 3, No. 3, 2009, pp. 127-149.

[8] M. Hermans and B. Schrauwen, “Recurrent Kernel Machines: Computing with Infinite Echo State Networks,” Neural Computation, Vol. 24, No. 6, 2011, pp. 104-133.

[9] D. Verstraeten, B. Schrauwen and D. Stroobandt, “Reservoir-Based Techniques for Speech Recognition,” International Joint Conference on Neural Networks, Vancouver, 16-21 July 2006, pp. 1050-1053.

[10] M. D. Skowronski and J. G. Harris, “Automatic Speech Recognition Using a Predictive Echo State Network Classifer,” Neural Networks, Vol. 20, No. 3, 2007, pp. 414-423. doi:10.1016/j.neunet.2007.04.006

[11] E. A. Antonelo, B. Schrauwen and D. Stroobandt, “Event Detection and Localization for Small Mobile Robots Using Reservoir Computing,” Neural Networks, Vol. 21, No. 6, 2008, pp. 862-871.

[12] M. Rolf, J. J. Steil and M. Gienger, “Effcient Exploration and Learning of Full Body Kinematics,” IEEE 8th International Conference on Development and Learning, Shanghai, 5-7 June 2009, pp. 1-7.

[13] R. F. Reinhart and J. J. Steil, “Reaching Movement Generation with a recurrent neural network based on Learning Inverse Kinematics for the Humanoid Robot Icub,” Proceedings of IEEE-RAS International Conference on Humanoid Robots, Paris, 7-10 December 2009, pp. 323-330. doi:10.1109/ICHR.2009.5379558

[14] P. Buteneers, B. Schrauwen, D. Verstraeten and Dirk Stroobandt, “Real-Time Epileptic Seizure Detection on Intra-Cranial Rat Data Using Reservoir Computing,” Advances in Neuro-Information Processing, Vol. 5506, 2009, pp. 56-63.

[15] B. Noris, M. Nobile, L. Piccinini, M. Berti, M. Molteni, E. Berti, F. Keller, D. Campolo and A. Billard, “Gait Analysis of Autistic Children with Echo State Networks,” Workshop on Echo State Networks and Liquid State Machines, Whistler, December 2006.

[16] A.F. Krause, B.Bl?sing, V.r Dürr and T. Schack, “Direct Control of an Active Tactile Sensor Using Echo State Networks,” Human Centered Robot Systems, Vol. 6, 2009, pp. 11-21.

[17] M. J. Embrechts and L. Alexandre, “Reservoir Computing for Static Pattern Recognition,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2009, pp. 245-250.

[18] X. Dutoit, B. Schrauwen and H. Van Brussel, “NonMarkovian Processes Modeling with Echo State Networks,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2009, pp. 233-238.

[19] F. R. Reinhart and J. J. Steil, “Attractor-Based Computation with Reservoirs for Online Learning of Inverse Kinematics,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2009, pp. 257-262.

[20] C. Emmerich, R. F. Reinhart and J. J. Steil, “Recurrence Enhances the Spatial Encoding of Static Inputs in Reservoir Networks,” Proceedings of the International Conference on Artificial Neural Networks (ICANN), Thessaloniki, September 2010, Vol. 6353, pp. 148-153. doi:10.1007/978-3-642-15822-3_19

[21] G. Feng, G.-B. Huang, Q. P. Lin and R. Gay, “Error Minimized Extreme Learning Machine with Growth of Hidden Nodes and Incremental Learning,” IEEE Transactions on Neural Networks, Vol. 20, No. 8, 2009, pp. 1352-1357.

[22] G.-B. Huang, L. Chen and C.-K. Siew, “Universal Approximation Using Incremental Constructive Feedforward Networks with Random Hidden Nodes,” IEEE Transactions on Neural Networks, Vol. 17, No. 4, 2006, pp. 879-892. doi:10.1109/TNN.2006.875977

[23] Y. Miche, A. Sorjamaa, P. Bas, O. Simula, C. Jutten and A. Lendasse, “OPELM: Optimally Pruned Extreme Learning Machine,” IEEE Transactions on Neural Networks, Vol. 21, No. 1, 2009, pp. 158-162. doi:10.1109/TNN.2009.2036259

[24] A. N. Tikhonov, “Solution of Incorrectly Formulated Problems and the Regularization Method,” W. H. Winston, Washington DC, 1977.

[25] S. Geman, E. Bienenstock and R. Doursat, “Neural Networks and the Bias/Variance Dilemma,” Neural Computation, Vol. 4, No. 1, 1992, pp. 1-58.

[26] F. Girosi, M. Jones and T. Poggio, “Regularization Theory and Neural Networks Architectures,” Neural Computation, Vol. 7, No. 2, 1995, pp. 219-269. doi:10.1162/neco.1995.7.2.219

[27] W. Y. Deng, Q. H. Zheng and L. Chen, “Regularized Extreme Learning Machine,” Proceedings of IEEE Symposium on Computational Intelligence and Data Mining, Nashville, 30 March-2 April 2009, pp. 389-395. doi:10.1109/CIDM.2009.4938676

[28] B. Schrauwen, D. Verstraeten and J. Van Campenhout, “An Overview of Reservoir Computing: Theory, Applications and Implementations,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, 2005, pp. 471-482.

[29] J. Triesch, “A Gradient Rule for the Plasticity of a Neuron’s Intrinsic Excitability,” Proceedings of International Conference on Artificial Neural Networks, Warsaw, September 2005, pp. 65-79.

[30] N.-Y. Liang, G. B. Huang, P Saratchandran and N Sundararajan, “A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks,” Proceedings of IEEE Transactions on Neural Networks, Vol. 17, No. 6, 2006, pp. 1411-1423.

[31] Q. Zhu, A. Qin, P. Suganthan and G.-B. Huang, “Evolutionary Extreme Learning Machine,” Pattern Recognition, Vol. 38, No. 10, 2005, pp. 1759-1763.

[32] V. N. Vapnik, “The Nature of Statistical Learning Theory,” Springer-Verlag Inc., New York, 1995.

[33] C. M. Bishop, “Training with Noise Is Equivalent to Tikhonov Regularization,” Neural Computation, Vol. 7, 1994, pp. 108-116.

[34] C. M. Bishop, “Pattern Recognition and Machine Learning,” Springer, New York, 2007.

[35] K. Neumann and J. J. Steil, “Optimizing Extreme Learning Machines via Ridge Regression and Batch Intrinsic Plasticity,” Neurocomputing, 2012, in Press. doi:10.1016/j.neucom.2012.01.041

[36] M. Rolf, J. J. Steil and M. Gienger, “Learning Exible Full Body Kinematics for Humanoid Tool Use,” International Conference on Emerging Security Technologies, Canterbury, 6-7 September 2010, pp. 171-176.

[37] A. Frank and A. Asuncion, “Uci Machine Learning Repository,” Amherst, 2010.

[38] J. J. Steil, “Online Reservoir Adaptation by Intrinsic Plasticity for Backpropagation—Decorrelation and Echo State Learning,” Neural Networks, Vol. 20, No. 3, 2007, pp. 353-364. doi:10.1016/j.neunet.2007.04.011

[39] B. Schrauwen, M. Wardermann, D. Verstraeten, J. J. Steil and D. Stroobandt, “Improving Reservoirs Using Intrinsic Plasticity,” Neurocomputing, Vol. 71, No. 7-9, 2008 pp. 1159-1171.

[40] J. Triesch, “The combination of stdp and intrinsic plasticity yields complex dynamics in recurrent spiking networks,” Proceedings of International Conference on Artificial Neural Networks, Athens, 2006, pp. 647-652.

[41] A. N. Tikhonov and V. Y. Arsenin, “Solutions of IllPosed Problems,” Soviet Mathematics—Doklady, Vol. 4, 1963, pp. 1035-1038.

[42] H. Jaeger, “Adaptive Nonlinear System Identification with Echo State Networks,” Proceedings of Neural Information Processing Systems, Vancouver, September 2002, pp. 593-600.

[43] H. Jaeger, “The Echo State Approach to Analysing and Training Recurrent Neural Networks,” 2001.

[1] Y. Miche, B. Schrauwen and A. Lendasse, “Machine Learning Techniques Based on Random Projections,” In Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2010, pp. 295-302.

[2] Y.-H. Pao, G.-H. Park and D. J. Sobajic, “Learning and Generalization Characteristics of the Random Vector Functional-Link Net,” Neurocomputing, Vol. 6, No. 2, 1994, pp. 163-180. doi:10.1016/0925-2312(94)90053-1

[3] D. S. Broomhead and D. Lowe, “Multivariable Functional Interpolation and Adaptive Networks,” Complex Systems, Vol. 2, No. 1, 1988, pp. 321-355.

[4] G.-B. Huang, Q.-Y. Zhu and C.-K. Siew, “Extreme Learning Machine: A New Learning Scheme of Feedforward Neural Networks,” Proceedings of International Joint Conferences on Artificial Intelligence, Budapest, July 2004, pp. 489-501.

[5] G.-B. Huang, Q.-Y. Zhu and C.-K. Siew, “Extreme Learning Machine: Theory and Applications,” Neurocomputing, Vol. 70, No. 1-3, 2006, pp. 489-501.

[6] L. P. Wang and C. R. Wan, “Comments on the Extreme Learning Machine,” IEEE Transactions on Neural Networks, Vol. 19, No. 8, 2008, pp. 1494-1495.

[7] M. Lukosevicius and H. Jaeger, “Reservoir Computing Approaches to Recurrent Neural Network Training,” Computer Science Review, Vol. 3, No. 3, 2009, pp. 127-149.

[8] M. Hermans and B. Schrauwen, “Recurrent Kernel Machines: Computing with Infinite Echo State Networks,” Neural Computation, Vol. 24, No. 6, 2011, pp. 104-133.

[9] D. Verstraeten, B. Schrauwen and D. Stroobandt, “Reservoir-Based Techniques for Speech Recognition,” International Joint Conference on Neural Networks, Vancouver, 16-21 July 2006, pp. 1050-1053.

[10] M. D. Skowronski and J. G. Harris, “Automatic Speech Recognition Using a Predictive Echo State Network Classifer,” Neural Networks, Vol. 20, No. 3, 2007, pp. 414-423. doi:10.1016/j.neunet.2007.04.006

[11] E. A. Antonelo, B. Schrauwen and D. Stroobandt, “Event Detection and Localization for Small Mobile Robots Using Reservoir Computing,” Neural Networks, Vol. 21, No. 6, 2008, pp. 862-871.

[12] M. Rolf, J. J. Steil and M. Gienger, “Effcient Exploration and Learning of Full Body Kinematics,” IEEE 8th International Conference on Development and Learning, Shanghai, 5-7 June 2009, pp. 1-7.

[13] R. F. Reinhart and J. J. Steil, “Reaching Movement Generation with a recurrent neural network based on Learning Inverse Kinematics for the Humanoid Robot Icub,” Proceedings of IEEE-RAS International Conference on Humanoid Robots, Paris, 7-10 December 2009, pp. 323-330. doi:10.1109/ICHR.2009.5379558

[14] P. Buteneers, B. Schrauwen, D. Verstraeten and Dirk Stroobandt, “Real-Time Epileptic Seizure Detection on Intra-Cranial Rat Data Using Reservoir Computing,” Advances in Neuro-Information Processing, Vol. 5506, 2009, pp. 56-63.

[15] B. Noris, M. Nobile, L. Piccinini, M. Berti, M. Molteni, E. Berti, F. Keller, D. Campolo and A. Billard, “Gait Analysis of Autistic Children with Echo State Networks,” Workshop on Echo State Networks and Liquid State Machines, Whistler, December 2006.

[16] A.F. Krause, B.Bl?sing, V.r Dürr and T. Schack, “Direct Control of an Active Tactile Sensor Using Echo State Networks,” Human Centered Robot Systems, Vol. 6, 2009, pp. 11-21.

[17] M. J. Embrechts and L. Alexandre, “Reservoir Computing for Static Pattern Recognition,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2009, pp. 245-250.

[18] X. Dutoit, B. Schrauwen and H. Van Brussel, “NonMarkovian Processes Modeling with Echo State Networks,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2009, pp. 233-238.

[19] F. R. Reinhart and J. J. Steil, “Attractor-Based Computation with Reservoirs for Online Learning of Inverse Kinematics,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, April 2009, pp. 257-262.

[20] C. Emmerich, R. F. Reinhart and J. J. Steil, “Recurrence Enhances the Spatial Encoding of Static Inputs in Reservoir Networks,” Proceedings of the International Conference on Artificial Neural Networks (ICANN), Thessaloniki, September 2010, Vol. 6353, pp. 148-153. doi:10.1007/978-3-642-15822-3_19

[21] G. Feng, G.-B. Huang, Q. P. Lin and R. Gay, “Error Minimized Extreme Learning Machine with Growth of Hidden Nodes and Incremental Learning,” IEEE Transactions on Neural Networks, Vol. 20, No. 8, 2009, pp. 1352-1357.

[22] G.-B. Huang, L. Chen and C.-K. Siew, “Universal Approximation Using Incremental Constructive Feedforward Networks with Random Hidden Nodes,” IEEE Transactions on Neural Networks, Vol. 17, No. 4, 2006, pp. 879-892. doi:10.1109/TNN.2006.875977

[23] Y. Miche, A. Sorjamaa, P. Bas, O. Simula, C. Jutten and A. Lendasse, “OPELM: Optimally Pruned Extreme Learning Machine,” IEEE Transactions on Neural Networks, Vol. 21, No. 1, 2009, pp. 158-162. doi:10.1109/TNN.2009.2036259

[24] A. N. Tikhonov, “Solution of Incorrectly Formulated Problems and the Regularization Method,” W. H. Winston, Washington DC, 1977.

[25] S. Geman, E. Bienenstock and R. Doursat, “Neural Networks and the Bias/Variance Dilemma,” Neural Computation, Vol. 4, No. 1, 1992, pp. 1-58.

[26] F. Girosi, M. Jones and T. Poggio, “Regularization Theory and Neural Networks Architectures,” Neural Computation, Vol. 7, No. 2, 1995, pp. 219-269. doi:10.1162/neco.1995.7.2.219

[27] W. Y. Deng, Q. H. Zheng and L. Chen, “Regularized Extreme Learning Machine,” Proceedings of IEEE Symposium on Computational Intelligence and Data Mining, Nashville, 30 March-2 April 2009, pp. 389-395. doi:10.1109/CIDM.2009.4938676

[28] B. Schrauwen, D. Verstraeten and J. Van Campenhout, “An Overview of Reservoir Computing: Theory, Applications and Implementations,” Proceedings of European Symposium on Artificial Neural Networks, Bruges, 2005, pp. 471-482.

[29] J. Triesch, “A Gradient Rule for the Plasticity of a Neuron’s Intrinsic Excitability,” Proceedings of International Conference on Artificial Neural Networks, Warsaw, September 2005, pp. 65-79.

[30] N.-Y. Liang, G. B. Huang, P Saratchandran and N Sundararajan, “A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks,” Proceedings of IEEE Transactions on Neural Networks, Vol. 17, No. 6, 2006, pp. 1411-1423.

[31] Q. Zhu, A. Qin, P. Suganthan and G.-B. Huang, “Evolutionary Extreme Learning Machine,” Pattern Recognition, Vol. 38, No. 10, 2005, pp. 1759-1763.

[32] V. N. Vapnik, “The Nature of Statistical Learning Theory,” Springer-Verlag Inc., New York, 1995.

[33] C. M. Bishop, “Training with Noise Is Equivalent to Tikhonov Regularization,” Neural Computation, Vol. 7, 1994, pp. 108-116.

[34] C. M. Bishop, “Pattern Recognition and Machine Learning,” Springer, New York, 2007.

[35] K. Neumann and J. J. Steil, “Optimizing Extreme Learning Machines via Ridge Regression and Batch Intrinsic Plasticity,” Neurocomputing, 2012, in Press. doi:10.1016/j.neucom.2012.01.041

[36] M. Rolf, J. J. Steil and M. Gienger, “Learning Exible Full Body Kinematics for Humanoid Tool Use,” International Conference on Emerging Security Technologies, Canterbury, 6-7 September 2010, pp. 171-176.

[37] A. Frank and A. Asuncion, “Uci Machine Learning Repository,” Amherst, 2010.

[38] J. J. Steil, “Online Reservoir Adaptation by Intrinsic Plasticity for Backpropagation—Decorrelation and Echo State Learning,” Neural Networks, Vol. 20, No. 3, 2007, pp. 353-364. doi:10.1016/j.neunet.2007.04.011

[39] B. Schrauwen, M. Wardermann, D. Verstraeten, J. J. Steil and D. Stroobandt, “Improving Reservoirs Using Intrinsic Plasticity,” Neurocomputing, Vol. 71, No. 7-9, 2008 pp. 1159-1171.

[40] J. Triesch, “The combination of stdp and intrinsic plasticity yields complex dynamics in recurrent spiking networks,” Proceedings of International Conference on Artificial Neural Networks, Athens, 2006, pp. 647-652.

[41] A. N. Tikhonov and V. Y. Arsenin, “Solutions of IllPosed Problems,” Soviet Mathematics—Doklady, Vol. 4, 1963, pp. 1035-1038.

[42] H. Jaeger, “Adaptive Nonlinear System Identification with Echo State Networks,” Proceedings of Neural Information Processing Systems, Vancouver, September 2002, pp. 593-600.

[43] H. Jaeger, “The Echo State Approach to Analysing and Training Recurrent Neural Networks,” 2001.