基于液体状态机的脑运动神经系统的建模研究
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摘要
脑机接口是一种实现大脑直接与外界环境进行沟通并进行控制的新技术。随着多通道神经元信号采集技术与计算机控制技术的日益成熟,从大脑皮层神经元群体活动中提取运动信息的解码算法是整个脑机接口系统实现脑信号与外界环境联系的关键部分。本文针对脑运动神经系统的建模与辨识问题,深入研究了从大脑运动皮层神经元脉冲序列信号中提取关于生物具体运动行为信息的解码算法。本文的实验对象是猴子运动大脑皮层脉冲数据与它的肢体运动的姿态的建模关系,对大脑运动皮层神经元脉冲序列信号的建模的工作主要是集中在对采样的各个方向运动的脉冲数据进行方向分类以及轨迹拟合。
本文首先介绍了液体状态机(Liquid State Machine,LSM)这种神经网络模型。液体状态机是一种新型的回归神经网络,采取的神经元是Leaky-Integrate-and-Fire(LIF)模型神经元。由于它能够直接接受和处理脉冲,脉冲序列不再需要像频率编码的处理模式一样转变成频率序列,使得以这种方式处理能够大幅度提高建模精度。实验结果表明对于脑神经脉冲序列的处理它是一种合适的计算模型。
为了提高实验的建模精度并且有效地避免液体状态机在随机生成时带来的问题,本文还用粒子群算法对液体状态机的中间回路的连接权值进行优化,以提高其分类能力,实验结果证实,采用PSO优化后的LSM的分类能力有了大幅度提高。
最后针对本文中问题的独特性,本文提出了改进型的液体状态机并且应用它来对本文的实验数据进行分类与建模研究。从分类问题的分类精度和轨迹拟合可以看出本文提出的改进型更能够适用于本文的特定实验。
Brain-Machine interface is a kind of new technology that makes the brain communicating with and even controlling the outside devices a reality. As the advance of the multi-channels neural signals sampling and computer control technology, the decoding of the neural activities of neurons, which are in the form of spike trains, is the key for the communication of the brain and outside devices. Aiming at the modeling of the spike trains, we take a deep look into the ways of drawing neural information from the neural signals recorded from the motor cortex. The research target of this experiment is a monkey whose brain is under some special surgery so the neural signals of the motor cortex can be recorded by some electrodes. The main purpose of the modeling of motor cortical signals is the directional classification and track fitting of the spike trains. As when the signals are recorded, the monkey is doing some arm-movement, and we just want to know the relationship between the movements—the move direction and move trajectory—and the spike trains.
The computing model we adopt is the Liquid State Machine (LSM). It is a kind of recurrent neural network but the neuron model is Leaky-Integrate-and-Fire model so it can receive and deal with the spikes directly. Doesn’t like the traditional way of dealing with the spikes, the LSM never transforms the spikes anymore, so it can get a better precision relatively. The experimental result shows that LSM is a proper way to model the spike trains.
Also we adopt the Particle Swarm Optimization (PSO) to the circuit of LSM and we find that the separation property of the circuit is greatly enhanced after the amelioration of the circuit with the PSO.
In order to apply the LSM to our experiment and get the higher model precision, we improve the LSM in a special way and we find that after the improvement we get higher modeling precision.
本文首先介绍了液体状态机(Liquid State Machine,LSM)这种神经网络模型。液体状态机是一种新型的回归神经网络,采取的神经元是Leaky-Integrate-and-Fire(LIF)模型神经元。由于它能够直接接受和处理脉冲,脉冲序列不再需要像频率编码的处理模式一样转变成频率序列,使得以这种方式处理能够大幅度提高建模精度。实验结果表明对于脑神经脉冲序列的处理它是一种合适的计算模型。
为了提高实验的建模精度并且有效地避免液体状态机在随机生成时带来的问题,本文还用粒子群算法对液体状态机的中间回路的连接权值进行优化,以提高其分类能力,实验结果证实,采用PSO优化后的LSM的分类能力有了大幅度提高。
最后针对本文中问题的独特性,本文提出了改进型的液体状态机并且应用它来对本文的实验数据进行分类与建模研究。从分类问题的分类精度和轨迹拟合可以看出本文提出的改进型更能够适用于本文的特定实验。
Brain-Machine interface is a kind of new technology that makes the brain communicating with and even controlling the outside devices a reality. As the advance of the multi-channels neural signals sampling and computer control technology, the decoding of the neural activities of neurons, which are in the form of spike trains, is the key for the communication of the brain and outside devices. Aiming at the modeling of the spike trains, we take a deep look into the ways of drawing neural information from the neural signals recorded from the motor cortex. The research target of this experiment is a monkey whose brain is under some special surgery so the neural signals of the motor cortex can be recorded by some electrodes. The main purpose of the modeling of motor cortical signals is the directional classification and track fitting of the spike trains. As when the signals are recorded, the monkey is doing some arm-movement, and we just want to know the relationship between the movements—the move direction and move trajectory—and the spike trains.
The computing model we adopt is the Liquid State Machine (LSM). It is a kind of recurrent neural network but the neuron model is Leaky-Integrate-and-Fire model so it can receive and deal with the spikes directly. Doesn’t like the traditional way of dealing with the spikes, the LSM never transforms the spikes anymore, so it can get a better precision relatively. The experimental result shows that LSM is a proper way to model the spike trains.
Also we adopt the Particle Swarm Optimization (PSO) to the circuit of LSM and we find that the separation property of the circuit is greatly enhanced after the amelioration of the circuit with the PSO.
In order to apply the LSM to our experiment and get the higher model precision, we improve the LSM in a special way and we find that after the improvement we get higher modeling precision.
引文
[1] Brown, E., Frank, L., Tang, D., Quirk, M., and Wilson, M.. A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rathippocampal place cells. J. of Neuroscience, 1998,18(18):7411~7425.
[2] Gao, Y., Black, M. J., Bienenstock, E., Shoham, S., and Donoghue, J. P.. Probabilistic inference of hand motion from neural activity in motor cortex. Advances in Neural InformationProcessing Systems, 2002, 14, The MIT Press.13~16
[3] Gelb, A., Applied Optimal Estimation.(Second Version), Massachusetts: MIT Press, 1974, 123~132
[4] Georgopoulos, A., Schwartz, A., and Kettner, R. Neural population coding of movement direction. Science, 1986, 233:1416~1419.
[5] Helms Tillery, S., Taylor, D., Isaacs, R., Schwartz, A. Online control of a prosthetic arm from motor cortical signals. Soc. for Neuroscience, 2000, Vol. 26:213~216
[6] Maynard, E., Nordhausen C., Normann, R. The Utah intracortical electrode array: A recording structure for potential brain-computer interfaces. Electroencephalography and Clinical Neuophysiology,1997, 102: 228~239.
[7] Moran, D. and Schwartz, B.. Motor cortical representation of speed and direction during reaching. J. of Neurophysiology, 1999, 82(5):2676~2692.
[8] Paninski, L., Fellows, M., Hatsopoulos, N., and Donoghue, J. P.. Temporal tuning properties for hand position and velocity in motor cortical neurons, J. of Neurophysiology, 2001, 91:515~532
[9] Serruya, M. D., Hatsopoulos, N. G., Paninski, L., Fellows, M. R., and Donoghue, J. P. Brain-machine interface: Instant neural control of a movement signal. Nature, 2002, 416:141~142.
[10] Justin Cort Sanchez , From Cortical Neural Spike Trains to Behavior: Modeling and Analysis: Dissertation for Doctor of Philosophy, University of Florida, 2004
[11] Taylor. D., Tillery, S., Schwartz, A.. Direct cortical control of 3D neuroprosthetic devices. Science, 2002, 296(5574):1829~1832.
[12] Warland, D., Reinagel, P., and Meister, M.. Decoding visual information from apopulation of retinal ganglion cells. J. of Neurophysiology, 1997,78(5):2336~2350.
[13] Welch, G. and Bishop, G.. An introduction to the Kalman filter. Technical Report TR95-041, University of North Carolina at Chapel Hill, Chapel Hill,NC 2001,275-317.
[14] Wessberg, J., Stambaugh, C., Kralik, J., M.. Real-time prediction of hand trajectory by ensemblesof cortical neurons in primates. Nature, 2000, 408:361~365.
[15] Wu, W., Black, M. J., Gao, Y., Bienenstock, E., Serruya, M., and Donoghue, J. P., Inferring hand motion from multi-cell recordings in motor cortex using a Kalman filter, SAB’02-Workshop on Motor Control in Humans and Robots: On the Interplay of Real Brains andArtificial Devices, Aug. 10, 2002, Edinburgh, Scotland, pp. 66~73.
[16] Zhang, K., Ginzburg, I., McNaughton, B., Sejnowski, T., Interpreting neuronal population activity by reconstruction: Unified framework with application to hippocampal place cells, J.Neurophysiol , 1998, 79:1017~1044
[17]何庆华,吴宝明,王禾等.脑机接口视觉刺激器的研究.中国临床康复, 2004, 8(11): 2060-2061
[18]谢水清,杨阳,杨仲乐.脑-机接口中高性能虚拟键盘的实现.中南民族大学学报(自然科学版), 2004, 23(2): 38~40
[19]杨帮华,颜国正,严荣国.脑-机接口研究进展.中国医疗器械杂志, 2005, 29(5): 353-357
[20] Birbaumer N., Kubler A., Ghanayim N., et al. The thought translation device (TTD) for completely paralyzedpatients. IEEE Trans. Rehab. Eng., 2000, 8(2): 190~193
[21] Birbaumer N., Ghanayim N., Hinterberger T., et al. A spelling device for the paralysed. Nature, 1999, 398(6725): 297~298
[22] Farwell L.A. and Donchin E. Talking off the top of your head: Toward a mental prosthesis utilizing event-related brain potential. Electroencephalography and clinical neurophysiology 1988, 70(6): 510~523
[23] Donchin E., Spencer K.M. and Wijesinghe R. The mental prosthesis: assessing the speed of a P300-basedbrain-computer interface. IEEE Trans. Rehab. Eng., 2000, 8(2): 174~179
[24] Chapin J.K., Moxon K.A., Markowitz R.S., et al. Real-time control of a robot armusing simultaneously recorded neurons in the motor cortex. Nature Neuroscience, 1999, 2(7): 664~670
[25] Chapin J.K. and Nicolelis M.A.L. Principal component analysis of neuronal ensemble activity reveals multidimensional somatosensory representations. Journal of Neuroscience Methods, 1999, 94(1): 121~140
[26] Georgopoulos A.P., Kalaska J.F., Caminiti R., et al. On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J. Neuronsci., 1982, 2(11): 1527~1537
[27] Georgopoulos A.P., Schwartz A.B. and Kettner R.E. Neuronal population coding of movement direction. Science, 1986, 233: 1416~1419
[28] Serruya M.D., Hatsopoulos N.G., Paninski L., et al. Instant neural control of a movement signal. Nature, 2002, 416: 141~142
[29] Carmena J.M., Lebedev M.A., Crist R.E., et al. Learning to Control a Brain–Machine Interface for Reaching and Grasping by Primates. Plos Biology, 2003, 1(2): 1~13
[30] Andrew B Schwartz, Dawn M Taylor, Stephen I Helms Tillery. Extraction algorithms for cortical control of arm prosthetics. Current Opinion in Neurobiology,2001,11:701~707
[31] Neuronal population coding of movement direction, A.P. Georgopoulos, A.B. Schwartz, and R.E. Kettner, Science, vol.233:1416-1419, 1986
[32] Schwartz, A. Direct cortical representation of drawing. Science, 1994, 265: 540~542.
[33] Chapin, J. K., Moxon, K. A., Markowitz, R. S. & Nicolelis, M. A. L. Real-time control of a robot arm using simultaneously recorded neurons in the motor cortex. Nature Neuroscience, 1999, 2:664~670.
[34] Humphrey, D. R., Schmidt, E. M. & Thompson, W. D. Predicting measures of motor performance from multiple cortical spike trains. Science, 1970, 170:758~762.
[35] W. Maass, T. Natschl?ger, and H. Markram. Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Computation, 2002, 14(11):2531~2560.
[36] Bohte S.M., Kok J.N. and La Poutre, Error- backpropagation in temporally encoded networks of spiking neurons. Neurocomputing, 2002, 48(1-4): 17~37
[37] Maass W., Natschlager T. &Markram,H. Fading memory and kernel properties ofgeneric cortical microcircuit models. Journal of Physiology, , 2004, 98(4):315~330
[38] Joshi, P., & Wolfgang Maass. Movement generation and control with generic neural microcircuits. In Proceedings of BIO-ADIT, 2004, 16~31.
[39] Burgsteiner H. Training networks of biological realistic spiking neurons for real-time robot control. In Proceedings of the 9th international conference on engineering applications of neural networks, 2005, 129~136.
[40] Burgsteiner H. On learning with recurrent spiking neural networks and their applications to robot control with real-world devices. Doctoral dissertation. Graz University of Technology, 2005
[41] D. Verstraeten, B. Schrauwen, D. Stroob and J. Van Campenhout, Isolated word recognition with the Liquid State Machine: a case study, Applications of Spiking Neural Networks, 2005, 95(6): 521~528
[42] Antonio Chella and Riccardo Rizzo, Time-Varying Signals Classification Using a Liquid State Machine, Biological and Artificial Intelligence Environments, Springer Netherlands, 2007, 133~139
[43] C. Fernando. Pattern recognition in a bucket: a real liquid brain. Lecture Notes on Computing Science, 2003, 2801:588-593
[44] Schwartz Doron Tal, Eric L.Computing with the leaky integrate and fire neuron: logarithmic computation and multiplication, Neural Computation, 1997, 9: 305~318
[45] H?usler S.,Markram H.,Maass W. Perspectives of the High Dimensional Dynamics of Neural Microcircuits from the Point of View of Low Dimensional Readouts, complexity, 2003, 8(4):9~50
[46] Harald B., Mark K., Alexander Leopold, Movement prediction from real-world images using a liquid state machine Applied Intelligence, 2007, 26(2):99~109
[47] Maass W, Networks of Spiking Neurons: The Third Generation of Neural Network Models, Neural Networks, 1997, 10:1659~1671
[48] Norton, D., Ventura, D. Preparing More Effective Liquid State Machines Using Hebbian Learning, 2006 International Joint Conference On Neural Network, 2006, 4243~4248
[49] Kennedy, J., Eberhart, R., Particle Swarm Optimization. Proceeding of the 1995 IEEE International Conference on Neural Network, 1995, 1942~1948
[50] Miguel A.L. Nicolelis and John K. Chapin. Controlling Robots with the Mind, Scientific American Magazine , 2002, 287:46~53
[51] Georgopoulos, A. P. Kalaska, J. F., Caminiti, R.& Massey, J. T. On the relationsbetween the direction of two-dimensional arm movements and cell discharge in primate motor cortex. Neuroscience, 1982, 2:1527~1537
[52] Johan Wessberg, Christopher R. Stambaugh, Jerald D. Kralik, etc., Real-time prediction of hand trajectory by ensembles of cortical neurons in primates, Nature , 2000, 408:361~365
[53] Fang Huijuan, Wang Yongji, Huang J., He J.P. Multi-class support vector machines for brain neural signals recognition, in Proc. of 6th World Congress on Intelligent Control and Automation, 2006, 2: 9940~9944
[54] Verstraeten, B. schrauven, Stroobandt, J.Van. Campenhout, Isolated word recognition with the Liquid State Machine: A case study, Information Processing letters, 2005, 95:521~528
[55] Wang Yongji, Wang wan, Support Vector Regression for Cortical Control of Virtual Cursor, Proceeding of 2005 First International Conference on Neural Interface and Control, 2005, 17~20
[2] Gao, Y., Black, M. J., Bienenstock, E., Shoham, S., and Donoghue, J. P.. Probabilistic inference of hand motion from neural activity in motor cortex. Advances in Neural InformationProcessing Systems, 2002, 14, The MIT Press.13~16
[3] Gelb, A., Applied Optimal Estimation.(Second Version), Massachusetts: MIT Press, 1974, 123~132
[4] Georgopoulos, A., Schwartz, A., and Kettner, R. Neural population coding of movement direction. Science, 1986, 233:1416~1419.
[5] Helms Tillery, S., Taylor, D., Isaacs, R., Schwartz, A. Online control of a prosthetic arm from motor cortical signals. Soc. for Neuroscience, 2000, Vol. 26:213~216
[6] Maynard, E., Nordhausen C., Normann, R. The Utah intracortical electrode array: A recording structure for potential brain-computer interfaces. Electroencephalography and Clinical Neuophysiology,1997, 102: 228~239.
[7] Moran, D. and Schwartz, B.. Motor cortical representation of speed and direction during reaching. J. of Neurophysiology, 1999, 82(5):2676~2692.
[8] Paninski, L., Fellows, M., Hatsopoulos, N., and Donoghue, J. P.. Temporal tuning properties for hand position and velocity in motor cortical neurons, J. of Neurophysiology, 2001, 91:515~532
[9] Serruya, M. D., Hatsopoulos, N. G., Paninski, L., Fellows, M. R., and Donoghue, J. P. Brain-machine interface: Instant neural control of a movement signal. Nature, 2002, 416:141~142.
[10] Justin Cort Sanchez , From Cortical Neural Spike Trains to Behavior: Modeling and Analysis: Dissertation for Doctor of Philosophy, University of Florida, 2004
[11] Taylor. D., Tillery, S., Schwartz, A.. Direct cortical control of 3D neuroprosthetic devices. Science, 2002, 296(5574):1829~1832.
[12] Warland, D., Reinagel, P., and Meister, M.. Decoding visual information from apopulation of retinal ganglion cells. J. of Neurophysiology, 1997,78(5):2336~2350.
[13] Welch, G. and Bishop, G.. An introduction to the Kalman filter. Technical Report TR95-041, University of North Carolina at Chapel Hill, Chapel Hill,NC 2001,275-317.
[14] Wessberg, J., Stambaugh, C., Kralik, J., M.. Real-time prediction of hand trajectory by ensemblesof cortical neurons in primates. Nature, 2000, 408:361~365.
[15] Wu, W., Black, M. J., Gao, Y., Bienenstock, E., Serruya, M., and Donoghue, J. P., Inferring hand motion from multi-cell recordings in motor cortex using a Kalman filter, SAB’02-Workshop on Motor Control in Humans and Robots: On the Interplay of Real Brains andArtificial Devices, Aug. 10, 2002, Edinburgh, Scotland, pp. 66~73.
[16] Zhang, K., Ginzburg, I., McNaughton, B., Sejnowski, T., Interpreting neuronal population activity by reconstruction: Unified framework with application to hippocampal place cells, J.Neurophysiol , 1998, 79:1017~1044
[17]何庆华,吴宝明,王禾等.脑机接口视觉刺激器的研究.中国临床康复, 2004, 8(11): 2060-2061
[18]谢水清,杨阳,杨仲乐.脑-机接口中高性能虚拟键盘的实现.中南民族大学学报(自然科学版), 2004, 23(2): 38~40
[19]杨帮华,颜国正,严荣国.脑-机接口研究进展.中国医疗器械杂志, 2005, 29(5): 353-357
[20] Birbaumer N., Kubler A., Ghanayim N., et al. The thought translation device (TTD) for completely paralyzedpatients. IEEE Trans. Rehab. Eng., 2000, 8(2): 190~193
[21] Birbaumer N., Ghanayim N., Hinterberger T., et al. A spelling device for the paralysed. Nature, 1999, 398(6725): 297~298
[22] Farwell L.A. and Donchin E. Talking off the top of your head: Toward a mental prosthesis utilizing event-related brain potential. Electroencephalography and clinical neurophysiology 1988, 70(6): 510~523
[23] Donchin E., Spencer K.M. and Wijesinghe R. The mental prosthesis: assessing the speed of a P300-basedbrain-computer interface. IEEE Trans. Rehab. Eng., 2000, 8(2): 174~179
[24] Chapin J.K., Moxon K.A., Markowitz R.S., et al. Real-time control of a robot armusing simultaneously recorded neurons in the motor cortex. Nature Neuroscience, 1999, 2(7): 664~670
[25] Chapin J.K. and Nicolelis M.A.L. Principal component analysis of neuronal ensemble activity reveals multidimensional somatosensory representations. Journal of Neuroscience Methods, 1999, 94(1): 121~140
[26] Georgopoulos A.P., Kalaska J.F., Caminiti R., et al. On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J. Neuronsci., 1982, 2(11): 1527~1537
[27] Georgopoulos A.P., Schwartz A.B. and Kettner R.E. Neuronal population coding of movement direction. Science, 1986, 233: 1416~1419
[28] Serruya M.D., Hatsopoulos N.G., Paninski L., et al. Instant neural control of a movement signal. Nature, 2002, 416: 141~142
[29] Carmena J.M., Lebedev M.A., Crist R.E., et al. Learning to Control a Brain–Machine Interface for Reaching and Grasping by Primates. Plos Biology, 2003, 1(2): 1~13
[30] Andrew B Schwartz, Dawn M Taylor, Stephen I Helms Tillery. Extraction algorithms for cortical control of arm prosthetics. Current Opinion in Neurobiology,2001,11:701~707
[31] Neuronal population coding of movement direction, A.P. Georgopoulos, A.B. Schwartz, and R.E. Kettner, Science, vol.233:1416-1419, 1986
[32] Schwartz, A. Direct cortical representation of drawing. Science, 1994, 265: 540~542.
[33] Chapin, J. K., Moxon, K. A., Markowitz, R. S. & Nicolelis, M. A. L. Real-time control of a robot arm using simultaneously recorded neurons in the motor cortex. Nature Neuroscience, 1999, 2:664~670.
[34] Humphrey, D. R., Schmidt, E. M. & Thompson, W. D. Predicting measures of motor performance from multiple cortical spike trains. Science, 1970, 170:758~762.
[35] W. Maass, T. Natschl?ger, and H. Markram. Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Computation, 2002, 14(11):2531~2560.
[36] Bohte S.M., Kok J.N. and La Poutre, Error- backpropagation in temporally encoded networks of spiking neurons. Neurocomputing, 2002, 48(1-4): 17~37
[37] Maass W., Natschlager T. &Markram,H. Fading memory and kernel properties ofgeneric cortical microcircuit models. Journal of Physiology, , 2004, 98(4):315~330
[38] Joshi, P., & Wolfgang Maass. Movement generation and control with generic neural microcircuits. In Proceedings of BIO-ADIT, 2004, 16~31.
[39] Burgsteiner H. Training networks of biological realistic spiking neurons for real-time robot control. In Proceedings of the 9th international conference on engineering applications of neural networks, 2005, 129~136.
[40] Burgsteiner H. On learning with recurrent spiking neural networks and their applications to robot control with real-world devices. Doctoral dissertation. Graz University of Technology, 2005
[41] D. Verstraeten, B. Schrauwen, D. Stroob and J. Van Campenhout, Isolated word recognition with the Liquid State Machine: a case study, Applications of Spiking Neural Networks, 2005, 95(6): 521~528
[42] Antonio Chella and Riccardo Rizzo, Time-Varying Signals Classification Using a Liquid State Machine, Biological and Artificial Intelligence Environments, Springer Netherlands, 2007, 133~139
[43] C. Fernando. Pattern recognition in a bucket: a real liquid brain. Lecture Notes on Computing Science, 2003, 2801:588-593
[44] Schwartz Doron Tal, Eric L.Computing with the leaky integrate and fire neuron: logarithmic computation and multiplication, Neural Computation, 1997, 9: 305~318
[45] H?usler S.,Markram H.,Maass W. Perspectives of the High Dimensional Dynamics of Neural Microcircuits from the Point of View of Low Dimensional Readouts, complexity, 2003, 8(4):9~50
[46] Harald B., Mark K., Alexander Leopold, Movement prediction from real-world images using a liquid state machine Applied Intelligence, 2007, 26(2):99~109
[47] Maass W, Networks of Spiking Neurons: The Third Generation of Neural Network Models, Neural Networks, 1997, 10:1659~1671
[48] Norton, D., Ventura, D. Preparing More Effective Liquid State Machines Using Hebbian Learning, 2006 International Joint Conference On Neural Network, 2006, 4243~4248
[49] Kennedy, J., Eberhart, R., Particle Swarm Optimization. Proceeding of the 1995 IEEE International Conference on Neural Network, 1995, 1942~1948
[50] Miguel A.L. Nicolelis and John K. Chapin. Controlling Robots with the Mind, Scientific American Magazine , 2002, 287:46~53
[51] Georgopoulos, A. P. Kalaska, J. F., Caminiti, R.& Massey, J. T. On the relationsbetween the direction of two-dimensional arm movements and cell discharge in primate motor cortex. Neuroscience, 1982, 2:1527~1537
[52] Johan Wessberg, Christopher R. Stambaugh, Jerald D. Kralik, etc., Real-time prediction of hand trajectory by ensembles of cortical neurons in primates, Nature , 2000, 408:361~365
[53] Fang Huijuan, Wang Yongji, Huang J., He J.P. Multi-class support vector machines for brain neural signals recognition, in Proc. of 6th World Congress on Intelligent Control and Automation, 2006, 2: 9940~9944
[54] Verstraeten, B. schrauven, Stroobandt, J.Van. Campenhout, Isolated word recognition with the Liquid State Machine: A case study, Information Processing letters, 2005, 95:521~528
[55] Wang Yongji, Wang wan, Support Vector Regression for Cortical Control of Virtual Cursor, Proceeding of 2005 First International Conference on Neural Interface and Control, 2005, 17~20