神经元集群小波—聚类编码的研究
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摘要
研究目的：
本论文研究记忆脑区(海马)神经元集群电活动的小波—聚类编码，研究它编码外界刺激的效能，以期在“细貌”上“划分”编码特定刺激的功能的神经元集群。本论文的研究对象是记忆关键脑区海马CA3区的功能神经元集群，期望从神经元放电及其各个小波尺度的细貌上“划分”编码特定刺激的功能神经元集群，探索在不同小波尺度上对刺激的编码效能，特别是在同时输入两类刺激时，研究在某个特定小波尺度上的“细貌”编码在编码两个以上刺激的优越性。
研究方法：
1．建立脉冲耦合神经网络(pulse coupled neural network，PCNN)模型，仿真在不同刺激模式(记忆任务)下，海马CA3区神经元群体电活动的时空序列。
根据海马解剖结构的特点，海马CA3区的120个神经元分为兴奋性神经元和抑制性神经元，其数量比为5：1；在CA3区，平均每个兴奋性神经元与75％的同一层其他神经元相连。抑制性神经元为全连接，用于调节CA3区神经元集群的稀疏放电；神经元之间的权重为高斯分布；只有兴奋性神经元有输出，神经元群体的输出为稀疏发放，群体的平均发放率小于10％(稀疏发放)。
PCNN模型的输入为几类典型的刺激模式：(1)Gaussian分布随机刺激，周期为0.2sec的正弦刺激以及以上两类刺激以不同权重的线性叠加；(2)正弦整流刺激，余弦整流刺激以及两类刺激的线性叠加。PCNN模型在三类刺激下神经元集群中每个神经元放电的仿真序列中，获取其ISI时空序列。
2．对仿真神经元群体的放电进行聚类编码：
1)对PCNN模型在不同刺激下的仿真ISI时空序列，应用自组织竞争神经网络的聚类来划分出功能神经元集群；
2)根据海马神经元群体发放ISI时空序列的FFT频谱分布，确定小波分解的尺度为5，对ISI序列进行小波分解，对各个尺度上的ISI子分量进行聚类，划分在输入以上三类刺激时，特别是在两种刺激同时输入时编码刺激的功能神经元集群。
研究结果：
1．PCNN模型可以有效地仿真海马不同刺激下神经元群体发放的稀疏时空序列，为本论文研究小波—聚类编码提供了仿真数据。
2．应用自组织竞争神经网络对神经元群体发放的聚类编码表达：
(1) PCNN模型输入Gaussian随机刺激，正弦刺激和以上两类刺激线性叠加时输出ISI序列的编码结果：
1)聚类编码
①．Gaussian分布的随机刺激下，聚类后的神经元集群中有20个神经元，编号分别为(10，11，14，24，25，27，35，36，37，45，48，50，55，57，61，70，77，90，92，99)；
②．正弦刺激下，聚类后的神经元集群中有34个神经元，编号为(2，6，8，9，13，19，20，26，28，29，30，32，34，40，41，46，50，51，52，53，54，55，57，59，60，61，63，65，71，75，83，85，86，87)。
③．在两类刺激叠加输入模式下，聚类后的神经元集群中有22个神经元，编号为(1，3，4，5，6，8，10，11，12，14，15，17，1 8，19，20，21，22，24，25，26，29，31，33，34，41，42，44，45，46，47，49，50，52，55，56，57，59，60，61，64，67，71，73，75，76，77，78，79，80，81，84，85，87，88，89，91，92，93，94，95，96，97，98，99)。
2)小波—聚类编码：
在第五尺度神经元集群放电的小波—聚类编码效果最好，对应神经元编号为
①．在Gaussian随机刺激下，第五尺度聚类神经元编号为(1，2，54，69，74，81，85，95)：
②．在余弦刺激下，第五尺度聚类神经元编号为(9，11，12，15，16，17，18，20，21，23，32，36，37，39，41，43，44，56，57，59，63，66，70，74，75，83，86，95，97)；
③．在两类刺激叠加输入模式下，第五尺度神经元编号为(1，2，9，12，13，16，17，18，23，32，36，37，39，41，43，44，45，46，54，56，57，69，74，81，83，85，86，63，66，70，74，75，95)；
(2) PCNN模型输入正弦整流刺激、余弦整流刺激和以上两类刺激线性叠加下输出ISI序列的编码结果
1)聚类编码结果：
①．在正弦整流刺激下，聚类神经元编号为(3，12，16，18，19，21，23，24，28，30，31，32，35，38，39，40，46，51，54，55，58，59，62，64，68，71，73，74，75，76，78，79，81，82，84，86，87，91，92，95，97，99)；
②．在余弦整流刺激下，聚类神经元编号为(2，3，6，9，10，11，12，14，15，22，23，24，26，30，31，32，33，34，39，40，42，49，50，55，57，59，62，63，64，66，73，76，79，80，81，88，89，90，94，95，96)：
③．在两类刺激叠加输入模式下，聚类神经元编号为(2，3，4，5，6，8，10，12，13，15，21，22，23，25，28，29，30，31，35，37，39，40，41，42，46，47，48，50，52，54，55，56，57，58，59，60，61，65，67，68，69，72，73，74，75，76，78，79，80，81，85，86，91，92，93，95，97，98)：
2)小波—聚类编码结果为
在第二尺度神经元集群放电的小波—聚类编码效果最好，对应神经元编号为
①．在正弦整流刺激下，聚类神经元编号为(1，7，8，10，22，23，33，41，43，51，57，65，77，87)：
②．在余弦整流刺激下，聚类神经元编号为(15，20，28，32，38，43，53，54，58，61，70，72，83，84，97，100)：
③．在两类刺激叠加输入模式下，聚类神经元编号为(7，8，12，15，17，20，21，22，23，24，25，26，28，30，31，32，33，34，36，38，39，40，41，43，46，47，52，56，59，61，64，65，67，70，72，73，75，77，78，79，80，83，84，86，87，90，91，93，95，97，100)；
研究结论：
1．PCNN模型可以有效仿真在三类输入刺激模式下，海马CA3区神经元群体的稀疏发放(平均发放率小于10％)。
2．聚类编码信息的效能：在(1)Gaussian随机刺激下和正弦刺激；(2)正弦整流刺激和余弦整流刺激下，神经元集群ISI序列聚类编码可以划分表征不同单个刺激的神经元集群；但对于划分两类刺激的叠加效能不明显。
3．小波—聚类编码信息的效能：(1)在Gaussian随机刺激和正弦刺激下，在第五尺度可以划分表征两类刺激的特征神经元集群，且编码效果优于聚类编码信息的效能；(2)在正弦整流刺激和余弦整流刺激下，在第二尺度可以划分表征两类刺激的特征神经元集群。
Objective
This paper aims to study the coding of neural ensembles relating to memory (hippocampus) with wavelet-clustering method, so as to discriminate specific functional neural ensembles in the detail. The study probes into the key structure of memory hippocampus CA3 area, with wavelet decomposition, expecting to discriminate functional neural ensembles under different wavelet scales, evaluate the coding efficiency, especially with two simultaneous inputs, the priority of certain wavelet scale over other scales.
Methods
1. Establish pulse coupled neural network (PCNN) model, simulate spatial temporal activity of neural population in hippocampus CA3 area under different stimulus (memory tasks).
According to the anatomical characteristics of hippocampus, the PCNN model is composed of 120 neurons, of which 100 is excitatory and 20 inhibitory. In CA3 area, each excitatory neuron is connected to about 75% of other neurons in the same layer. The inhibitory neurons are all-to-all connected and is related to the sparse firings in the area. The synaptic weight among neurons is set Gaussian distribution; only excitatory neurons output to other layers with sparse activity (less than 10%).
PCNN model is given different typical patterns of stimuli: (1) random input with Gaussian distribution, sinusoidal input (T=0.2sec), and the linear superimpose of above two signals; (2) Rectified sinusoidal input, rectified cosinusoidal input, and the linear superimpose of above two signals.. The output of PCNN is the time series of spikings of each neuron in the ensemble, from which we acquire inter-spike interval (ISI) series of the neural population.
2. Cluster coding the simulation data of neural ensembles:
1) Analyze ISI series of neural population under three different stimuli, discriminate functional neural ensembles with self organizing map;
2) According to the FFT spectrum of ISI series, the scale of wavelet is set to 5. Code the ISI series with self organizing map at each scale of wavelet, discriminate different functional ensembles relating to the specific input.
Results
1. PCNN model can simulate the sparse activity of hippocampus neural population under different stimuli, it provides simulation data for the further study of waveletcluster coding in this paper.
2. Cluster coding of neural population with the application of self organizing map:
(1) Results for Gaussian input, sSinusoidal input and superimpose of the two inputs:
1) Results of cluster coding:
①. Under random stimulus with Gaussian distribution, the clusterd neurons are (10, 11, 14, 24, 25, 27, 35, 36, 37, 45, 48, 50, 55, 57, 61, 70, 77, 90, 92,99);
②. Under sinusoidal input, the clusterd neurons are (2, 6, 8, 9, 13, 19, 20, 26, 28, 29, 30, 32, 34, 40, 41, 46, 50, 51, 52, 53, 54, 55, 57, 59, 60, 61, 63, 65, 71, 75, 83, 85, 86, 87)
③. Under the stimulation of both the above inputs, the clustered neurons are ( 1, 3, 4, 5, 6, 8, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 29, 31, 33, 34, 41, 42, 44, 45, 46, 47, 49, 50, 52, 55, 56, 57, 59, 60, 61, 64, 67, 71, 73, 75, 76, 77, 78, 79, 80, 81, 84, 85, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99).
2) Results of wavelet-cluster coding:
For the wavelet-clustering coding, the best results are shown on scale-5, the clustered neurons under three different stimuli are as follows:
1) Under random stimulus with Gaussian distribution, the clusterd neurons on scale-5 are (1, 2, 54, 69, 74, 81, 85, 95);
2) Under sinusoidal stimulus with Gaussian distribution, the clusterd neurons on scale-5 are (9, 11, 12, 15, 16, 17, 18, 20, 21, 23, 32, 36, 37, 39, 41, 43, 44, 56, 57, 59, 63, 66, 70, 74, 75, 83, 86, 95, 97);
3) Under the stimulation of both the above inputs, the clustered neurons are (1, 2, 9, 12, 13, 16, 17, 18, 23, 32, 36, 37, 39, 41, 43, 44, 45, 46, 54, 56, 57, 69, 74, 81, 83, 85, 86, 63, 66, 70, 74, 75, 95).
(2) Results for sinusoidal input, cosinusoidal input and superimpose of the two inputs:
1) Results of cluster coding:
①. Under the stimulation of sinusoidal input, the clustered neurons are (3, 12, 16, 18, 19, 21, 23, 24, 28, 30, 31, 32, 35, 38, 39, 40, 46, 51, 54, 55, 58, 59, 62, 64, 68, 71, 73, 74, 75, 76, 78, 79, 81, 82, 84, 86, 87, 91, 92, 95, 97, 99);
②. Under the stimulation of cosinusoidal input, the clustered neurons are (2, 3, 6, 9, 10, 11, 12, 14, 15, 22, 23, 24, 26, 30, 31, 32, 33, 34, 39, 40, 42, 49, 50, 55, 57, 59, 62, 63, 64, 66, 73, 76, 79, 80, 81, 88, 89, 90, 94, 95, 96);
③. Under the stimulation of both the above inputs, the clustered neurons are (2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 21, 22, 23, 25, 28, 29, 30, 31, 35, 37, 39, 40, 41, 42, 46, 47, 48, 50, 52, 54, 55, 56, 57, 58, 59, 60, 61, 65, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 85, 86, 91, 92, 93, 95, 97, 98);
2) Results of wavelet-cluster coding..
For the wavelet-clustering coding, the best results are shown on scale-2, the clustered neurons under three different stimuli are as follows:
①. Under the stimulation of sinusoidal input, the clustered neurons are (1, 7, 8, 10, 22, 23, 33, 41, 43, 51, 57, 65, 77, 87);
②. Under the stimulation of cosinusoidal input, the clustered neurons are (15, 20, 28, 32, 38, 43, 53, 54, 58, 61, 70, 72, 83, 84, 97, 100);
③. Under the stimulation of both the above inputs, the clustered neurons are (7, 8, 12, 15, 17, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 43, 46, 47, 52, 56, 59, 61, 64, 65, 67, 70, 72, 73, 75, 77, 78, 79, 80, 83, 84, 86, 87, 90, 91, 93, 95, 97, 100).
Conclusions
1. The sparse output of PCNN model efficiently simulated firing patterns of hippocampus CA3 area neurons under three different stimuli.
2. The cluster coding of neural ensemble under (1) Gaussian distributed random stimulus and sinusoidal stimulus; (2) rectified sinusoidal and rectified cosinusoidal input show little overlap over each other, on the whole , different stimuli can be discriminated with cluster coding neural ensembles. But under the above two stimuli simultaneously, the cluster coding is not very effective.
3. The wave-cluster coding can discriminate different input stimulus on most of the scales, this is best shown (1) on scale-5 for Gaussian random input and sinusoidal input; (2) on scale-2 for rectified sinusoidal input and rectified cosinusoidal input. Under the superimpose of both the stimulus, wave-clustering on specific scale show better result than cluster coding.
本论文研究记忆脑区(海马)神经元集群电活动的小波—聚类编码，研究它编码外界刺激的效能，以期在“细貌”上“划分”编码特定刺激的功能的神经元集群。本论文的研究对象是记忆关键脑区海马CA3区的功能神经元集群，期望从神经元放电及其各个小波尺度的细貌上“划分”编码特定刺激的功能神经元集群，探索在不同小波尺度上对刺激的编码效能，特别是在同时输入两类刺激时，研究在某个特定小波尺度上的“细貌”编码在编码两个以上刺激的优越性。
研究方法：
1．建立脉冲耦合神经网络(pulse coupled neural network，PCNN)模型，仿真在不同刺激模式(记忆任务)下，海马CA3区神经元群体电活动的时空序列。
根据海马解剖结构的特点，海马CA3区的120个神经元分为兴奋性神经元和抑制性神经元，其数量比为5：1；在CA3区，平均每个兴奋性神经元与75％的同一层其他神经元相连。抑制性神经元为全连接，用于调节CA3区神经元集群的稀疏放电；神经元之间的权重为高斯分布；只有兴奋性神经元有输出，神经元群体的输出为稀疏发放，群体的平均发放率小于10％(稀疏发放)。
PCNN模型的输入为几类典型的刺激模式：(1)Gaussian分布随机刺激，周期为0.2sec的正弦刺激以及以上两类刺激以不同权重的线性叠加；(2)正弦整流刺激，余弦整流刺激以及两类刺激的线性叠加。PCNN模型在三类刺激下神经元集群中每个神经元放电的仿真序列中，获取其ISI时空序列。
2．对仿真神经元群体的放电进行聚类编码：
1)对PCNN模型在不同刺激下的仿真ISI时空序列，应用自组织竞争神经网络的聚类来划分出功能神经元集群；
2)根据海马神经元群体发放ISI时空序列的FFT频谱分布，确定小波分解的尺度为5，对ISI序列进行小波分解，对各个尺度上的ISI子分量进行聚类，划分在输入以上三类刺激时，特别是在两种刺激同时输入时编码刺激的功能神经元集群。
研究结果：
1．PCNN模型可以有效地仿真海马不同刺激下神经元群体发放的稀疏时空序列，为本论文研究小波—聚类编码提供了仿真数据。
2．应用自组织竞争神经网络对神经元群体发放的聚类编码表达：
(1) PCNN模型输入Gaussian随机刺激，正弦刺激和以上两类刺激线性叠加时输出ISI序列的编码结果：
1)聚类编码
①．Gaussian分布的随机刺激下，聚类后的神经元集群中有20个神经元，编号分别为(10，11，14，24，25，27，35，36，37，45，48，50，55，57，61，70，77，90，92，99)；
②．正弦刺激下，聚类后的神经元集群中有34个神经元，编号为(2，6，8，9，13，19，20，26，28，29，30，32，34，40，41，46，50，51，52，53，54，55，57，59，60，61，63，65，71，75，83，85，86，87)。
③．在两类刺激叠加输入模式下，聚类后的神经元集群中有22个神经元，编号为(1，3，4，5，6，8，10，11，12，14，15，17，1 8，19，20，21，22，24，25，26，29，31，33，34，41，42，44，45，46，47，49，50，52，55，56，57，59，60，61，64，67，71，73，75，76，77，78，79，80，81，84，85，87，88，89，91，92，93，94，95，96，97，98，99)。
2)小波—聚类编码：
在第五尺度神经元集群放电的小波—聚类编码效果最好，对应神经元编号为
①．在Gaussian随机刺激下，第五尺度聚类神经元编号为(1，2，54，69，74，81，85，95)：
②．在余弦刺激下，第五尺度聚类神经元编号为(9，11，12，15，16，17，18，20，21，23，32，36，37，39，41，43，44，56，57，59，63，66，70，74，75，83，86，95，97)；
③．在两类刺激叠加输入模式下，第五尺度神经元编号为(1，2，9，12，13，16，17，18，23，32，36，37，39，41，43，44，45，46，54，56，57，69，74，81，83，85，86，63，66，70，74，75，95)；
(2) PCNN模型输入正弦整流刺激、余弦整流刺激和以上两类刺激线性叠加下输出ISI序列的编码结果
1)聚类编码结果：
①．在正弦整流刺激下，聚类神经元编号为(3，12，16，18，19，21，23，24，28，30，31，32，35，38，39，40，46，51，54，55，58，59，62，64，68，71，73，74，75，76，78，79，81，82，84，86，87，91，92，95，97，99)；
②．在余弦整流刺激下，聚类神经元编号为(2，3，6，9，10，11，12，14，15，22，23，24，26，30，31，32，33，34，39，40，42，49，50，55，57，59，62，63，64，66，73，76，79，80，81，88，89，90，94，95，96)：
③．在两类刺激叠加输入模式下，聚类神经元编号为(2，3，4，5，6，8，10，12，13，15，21，22，23，25，28，29，30，31，35，37，39，40，41，42，46，47，48，50，52，54，55，56，57，58，59，60，61，65，67，68，69，72，73，74，75，76，78，79，80，81，85，86，91，92，93，95，97，98)：
2)小波—聚类编码结果为
在第二尺度神经元集群放电的小波—聚类编码效果最好，对应神经元编号为
①．在正弦整流刺激下，聚类神经元编号为(1，7，8，10，22，23，33，41，43，51，57，65，77，87)：
②．在余弦整流刺激下，聚类神经元编号为(15，20，28，32，38，43，53，54，58，61，70，72，83，84，97，100)：
③．在两类刺激叠加输入模式下，聚类神经元编号为(7，8，12，15，17，20，21，22，23，24，25，26，28，30，31，32，33，34，36，38，39，40，41，43，46，47，52，56，59，61，64，65，67，70，72，73，75，77，78，79，80，83，84，86，87，90，91，93，95，97，100)；
研究结论：
1．PCNN模型可以有效仿真在三类输入刺激模式下，海马CA3区神经元群体的稀疏发放(平均发放率小于10％)。
2．聚类编码信息的效能：在(1)Gaussian随机刺激下和正弦刺激；(2)正弦整流刺激和余弦整流刺激下，神经元集群ISI序列聚类编码可以划分表征不同单个刺激的神经元集群；但对于划分两类刺激的叠加效能不明显。
3．小波—聚类编码信息的效能：(1)在Gaussian随机刺激和正弦刺激下，在第五尺度可以划分表征两类刺激的特征神经元集群，且编码效果优于聚类编码信息的效能；(2)在正弦整流刺激和余弦整流刺激下，在第二尺度可以划分表征两类刺激的特征神经元集群。
Objective
This paper aims to study the coding of neural ensembles relating to memory (hippocampus) with wavelet-clustering method, so as to discriminate specific functional neural ensembles in the detail. The study probes into the key structure of memory hippocampus CA3 area, with wavelet decomposition, expecting to discriminate functional neural ensembles under different wavelet scales, evaluate the coding efficiency, especially with two simultaneous inputs, the priority of certain wavelet scale over other scales.
Methods
1. Establish pulse coupled neural network (PCNN) model, simulate spatial temporal activity of neural population in hippocampus CA3 area under different stimulus (memory tasks).
According to the anatomical characteristics of hippocampus, the PCNN model is composed of 120 neurons, of which 100 is excitatory and 20 inhibitory. In CA3 area, each excitatory neuron is connected to about 75% of other neurons in the same layer. The inhibitory neurons are all-to-all connected and is related to the sparse firings in the area. The synaptic weight among neurons is set Gaussian distribution; only excitatory neurons output to other layers with sparse activity (less than 10%).
PCNN model is given different typical patterns of stimuli: (1) random input with Gaussian distribution, sinusoidal input (T=0.2sec), and the linear superimpose of above two signals; (2) Rectified sinusoidal input, rectified cosinusoidal input, and the linear superimpose of above two signals.. The output of PCNN is the time series of spikings of each neuron in the ensemble, from which we acquire inter-spike interval (ISI) series of the neural population.
2. Cluster coding the simulation data of neural ensembles:
1) Analyze ISI series of neural population under three different stimuli, discriminate functional neural ensembles with self organizing map;
2) According to the FFT spectrum of ISI series, the scale of wavelet is set to 5. Code the ISI series with self organizing map at each scale of wavelet, discriminate different functional ensembles relating to the specific input.
Results
1. PCNN model can simulate the sparse activity of hippocampus neural population under different stimuli, it provides simulation data for the further study of waveletcluster coding in this paper.
2. Cluster coding of neural population with the application of self organizing map:
(1) Results for Gaussian input, sSinusoidal input and superimpose of the two inputs:
1) Results of cluster coding:
①. Under random stimulus with Gaussian distribution, the clusterd neurons are (10, 11, 14, 24, 25, 27, 35, 36, 37, 45, 48, 50, 55, 57, 61, 70, 77, 90, 92,99);
②. Under sinusoidal input, the clusterd neurons are (2, 6, 8, 9, 13, 19, 20, 26, 28, 29, 30, 32, 34, 40, 41, 46, 50, 51, 52, 53, 54, 55, 57, 59, 60, 61, 63, 65, 71, 75, 83, 85, 86, 87)
③. Under the stimulation of both the above inputs, the clustered neurons are ( 1, 3, 4, 5, 6, 8, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 29, 31, 33, 34, 41, 42, 44, 45, 46, 47, 49, 50, 52, 55, 56, 57, 59, 60, 61, 64, 67, 71, 73, 75, 76, 77, 78, 79, 80, 81, 84, 85, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99).
2) Results of wavelet-cluster coding:
For the wavelet-clustering coding, the best results are shown on scale-5, the clustered neurons under three different stimuli are as follows:
1) Under random stimulus with Gaussian distribution, the clusterd neurons on scale-5 are (1, 2, 54, 69, 74, 81, 85, 95);
2) Under sinusoidal stimulus with Gaussian distribution, the clusterd neurons on scale-5 are (9, 11, 12, 15, 16, 17, 18, 20, 21, 23, 32, 36, 37, 39, 41, 43, 44, 56, 57, 59, 63, 66, 70, 74, 75, 83, 86, 95, 97);
3) Under the stimulation of both the above inputs, the clustered neurons are (1, 2, 9, 12, 13, 16, 17, 18, 23, 32, 36, 37, 39, 41, 43, 44, 45, 46, 54, 56, 57, 69, 74, 81, 83, 85, 86, 63, 66, 70, 74, 75, 95).
(2) Results for sinusoidal input, cosinusoidal input and superimpose of the two inputs:
1) Results of cluster coding:
①. Under the stimulation of sinusoidal input, the clustered neurons are (3, 12, 16, 18, 19, 21, 23, 24, 28, 30, 31, 32, 35, 38, 39, 40, 46, 51, 54, 55, 58, 59, 62, 64, 68, 71, 73, 74, 75, 76, 78, 79, 81, 82, 84, 86, 87, 91, 92, 95, 97, 99);
②. Under the stimulation of cosinusoidal input, the clustered neurons are (2, 3, 6, 9, 10, 11, 12, 14, 15, 22, 23, 24, 26, 30, 31, 32, 33, 34, 39, 40, 42, 49, 50, 55, 57, 59, 62, 63, 64, 66, 73, 76, 79, 80, 81, 88, 89, 90, 94, 95, 96);
③. Under the stimulation of both the above inputs, the clustered neurons are (2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 21, 22, 23, 25, 28, 29, 30, 31, 35, 37, 39, 40, 41, 42, 46, 47, 48, 50, 52, 54, 55, 56, 57, 58, 59, 60, 61, 65, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 85, 86, 91, 92, 93, 95, 97, 98);
2) Results of wavelet-cluster coding..
For the wavelet-clustering coding, the best results are shown on scale-2, the clustered neurons under three different stimuli are as follows:
①. Under the stimulation of sinusoidal input, the clustered neurons are (1, 7, 8, 10, 22, 23, 33, 41, 43, 51, 57, 65, 77, 87);
②. Under the stimulation of cosinusoidal input, the clustered neurons are (15, 20, 28, 32, 38, 43, 53, 54, 58, 61, 70, 72, 83, 84, 97, 100);
③. Under the stimulation of both the above inputs, the clustered neurons are (7, 8, 12, 15, 17, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 43, 46, 47, 52, 56, 59, 61, 64, 65, 67, 70, 72, 73, 75, 77, 78, 79, 80, 83, 84, 86, 87, 90, 91, 93, 95, 97, 100).
Conclusions
1. The sparse output of PCNN model efficiently simulated firing patterns of hippocampus CA3 area neurons under three different stimuli.
2. The cluster coding of neural ensemble under (1) Gaussian distributed random stimulus and sinusoidal stimulus; (2) rectified sinusoidal and rectified cosinusoidal input show little overlap over each other, on the whole , different stimuli can be discriminated with cluster coding neural ensembles. But under the above two stimuli simultaneously, the cluster coding is not very effective.
3. The wave-cluster coding can discriminate different input stimulus on most of the scales, this is best shown (1) on scale-5 for Gaussian random input and sinusoidal input; (2) on scale-2 for rectified sinusoidal input and rectified cosinusoidal input. Under the superimpose of both the stimulus, wave-clustering on specific scale show better result than cluster coding.
引文
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