脉冲神经网络之Tempotron（二）
脉冲神经网络之Tempotron代码示例
上一篇从原理的角度大致介绍了脉冲神经网络的神经元模型以及Tempotron监督学习方法，这一章记录了Tempotron的代码实现。这份代码是使用matlab编写，用脉冲神经网络实现对26个字母分类，我们从细节去解释该代码：
function TempotronClassify()
% Tempotron: a neuron that learns spike timing-based decisions
% Rober Gutig 2006 Nature Neuroscience
clear; clc;
NumImages=26;
for i=1:NumImages
ImageName=strcat('Icon16X16\Letter-',char('A'+i-1),'-black-icon');% 从icon16X16文件夹中读取所有图片
ImageMatrix=imread(ImageName,'bmp');% 读取图片为灰度图，保存在矩阵中，取反
ImageMatrix=~ImageMatrix; % make the white pixel be 0, and black be 1;
TrainPtns(:,i)=image2ptn(ImageMatrix);
end
%% convert a image to a spike train saved in a vector
RandParts=1;
spikeTrain=zeros(32,1);
if RandParts==1
loadR=1;
AR=A(:);
if loadR==0
R = randperm(size(A,1)*size(A,2));
save('RandIndex','R');
else
load('RandIndex','R');
end
numRandNeus=32;
for i=1:numRandNeus
IndexR=R((1+(i-1)*8):(8+(i-1)*8));
Bits=AR(IndexR);
Bits=Bits';
spikeTime=bi2de(Bits,'left-msb'); % 二进制转十进制
if spikeTime==0
spikeTime=2^8; % put 0 to the end of the interval
end
spikeTrain(i)=spikeTime;
end
endTrainPtns=TrainPtns*1e-3; % scale to ms
nAfferents = size(TrainPtns,1);
nPtns = NumImages;
%nOutputs = 1; %%%%%%%%%% 1
nOutputs = 5;TrainPtns是32*26的矩阵，也就是将所有转换后的spikeTrain拼接一起。nAfferents代表了输入脉冲数量，这里就是32，由这32个输入确定一个输出（字母）。输出就定义为5，也就是5个二进制数表示一个字母的编号。
loadData=0;% 是否载入已保存的模型
V_thr = 1; V_rest = 0;
T = 256e-3; % pattern duration ms
dt = 1e-3;
tau_m = 20e-3; % tau_m = 15e-3;？？？
tau_s = tau_m/4;
% K(t?ti)=V0(exp[?(t?ti)/τ]–exp[?(t?ti)/τs])
aa = exp(-(0:dt:3*tau_m)/tau_m)-exp(-(0:dt:3*tau_m)/tau_s);
V0 = 1/max(exp(-(0:dt:3*tau_m)/tau_m)-exp(-(0:dt:3*tau_m)/tau_s));
lmd = 2e-2;%1e-2/V0; % optimal performance lmd=3e-3*T/(tau_m*nAfferents*V0) 1e-4/V0;
maxEpoch = 200;
mu = 0.99; % momentum factorK(t-ti)=V0(exp[-(t-ti)/τ]–exp[-(t-ti)/τs])if loadData ==0 %初始化网络
weights = 1e-2*randn(nAfferents,nOutputs); % 1e-3*randn(nAfferents,1);
save('weights0','weights');
else
load('weights0','weights');
endClass = de2bi(1:26,'left-msb'); Class=Class';
correctRate=zeros(1,maxEpoch);
dw_Past=zeros(nAfferents,nPtns,nOutputs); % momentum for accelerating learning.上一个权重的更新，用于动量计算
for epoch=1:maxEpoch
Class_Tr = false(nOutputs,nPtns); % actual outputs of training
for pp=1:nPtns
for neuron=1:nOutputs
Vmax=0; tmax=0;
fired=false;
Vm1=zeros(1,256); indx1= 1; % trace pattern 1
for t=dt:dt:T
Vm = 0;
if fired==false
Tsyn=find(TrainPtns(:,pp)<=t+0.1*dt); % no cut window
else
Tsyn=find(TrainPtns(:,pp)<=t_fire+0.1*dt); % shut down inputs
end
if ~isempty(Tsyn)
A1=TrainPtns(:,pp);
A2=A1(Tsyn);
K =V0*(exp(-(t-A2)/tau_m)-exp(-(t-A2)/tau_s)); % the kernel value for each fired afferent
A1=weights(:,neuron);
firedWeights=A1(Tsyn);
Vm = Vm + firedWeights'*K ;
end
Vm = Vm + V_rest;
if Vm>=V_thr && fired==false % fire
fired=true;
t_fire=t;
Class_Tr(neuron,pp)=true;
end
if Vm>Vmax
Vmax=Vm; tmax=t;
end
%if pp==1
Vm1(indx1)=Vm;
indx1=indx1+1;
%end
end
%if pp==1
figure(1); plot(dt:dt:T,Vm1);
title(strcat('Image ',char('A'+pp-1),'; neuron: ',num2str(neuron))); drawnow;
%end
if Vmax<=0
tmax=max(TrainPtns(:,pp));
end
if Class_Tr(neuron,pp)~=Class(neuron,pp) % error
Tsyn=find(TrainPtns(:,pp)<=tmax+0.1*dt);
if ~isempty(Tsyn)
A1=TrainPtns(:,pp);
A2=A1(Tsyn);
K =V0*(exp(-(tmax-A2)/tau_m)-exp(-(tmax-A2)/tau_s)); % the kernel value for each fired afferent
A1=weights(:,neuron);
dwPst=dw_Past(:,pp,neuron);
if fired==false % LTP
Dw=lmd*K;
else % LTD
Dw=-1.1*lmd*K;
end
A1(Tsyn) = A1(Tsyn) + Dw + mu*dwPst(Tsyn);
weights(:,neuron)=A1;
dwPst(Tsyn)=Dw;
dw_Past(:,pp,neuron) = dwPst;
end
end
end % end of one neuron computation
end % end of one image
%CC=isequal(Class,Class_Tr);
%correctRate(epoch)=sum(Class==Class_Tr)/length(Class);
CC = bi2de(Class_Tr','left-msb');
end
save('TrainedWt','weights');
figure(2); plot(1:maxEpoch,correctRate,'-b.');
end对整个时间窗口计算完后，将Vm加上复位电压，如果该值超过了阈值电压，则发放脉冲；若该值超过了已有的Vmax，则更新Vmax。之后进入判断语句：
if Class_Tr(neuron,pp)~=Class(neuron,pp) 神经元的输出和实际输出不相符时，分为两个情况：
（1）实际输出为0，但发放了脉冲。
此时应该抑制脉冲发放，于是权重应该减小：
Dw=-1.1*lmd*K;
（2）实际输出为1，但没有发放脉冲：
此时应该增大神经元的刺激，权重应该增加：
Dw=lmd*K;
最后保存此次循环的权重。于是单层的脉冲神经网路监督学习就这样完成了。下面附上完整代码：
function TempotronClassify()
% Tempotron: a neuron that learns spike timing-based decisions
% Rober Gutig 2006 Nature Neuroscience
clear; clc;
NumImages=26;
for i=1:NumImages
ImageName=strcat('Icon16X16\Letter-',char('A'+i-1),'-black-icon');% 从icon16X16文件夹中读取所有图片
ImageMatrix=imread(ImageName,'bmp');% 读取图片为灰度图，保存在矩阵中，取反
ImageMatrix=~ImageMatrix; % make the white pixel be 0, and black be 1;
TrainPtns(:,i)=image2ptn(ImageMatrix);
end
TrainPtns=TrainPtns*1e-3; % scale to ms
nAfferents = size(TrainPtns,1);
nPtns = NumImages;
%nOutputs = 1; %%%%%%%%%% 1
nOutputs = 5;
loadData=0;% 是否载入已保存的模型
V_thr = 1; V_rest = 0;
T = 256e-3; % pattern duration ms
dt = 1e-3;
tau_m = 20e-3; % tau_m = 15e-3;？？？
tau_s = tau_m/4;
% K(t?ti)=V0(exp[?(t?ti)/τ]–exp[?(t?ti)/τs])
aa = exp(-(0:dt:3*tau_m)/tau_m)-exp(-(0:dt:3*tau_m)/tau_s);
V0 = 1/max(exp(-(0:dt:3*tau_m)/tau_m)-exp(-(0:dt:3*tau_m)/tau_s));
lmd = 2e-2;%1e-2/V0; % optimal performance lmd=3e-3*T/(tau_m*nAfferents*V0) 1e-4/V0;
maxEpoch = 200;
mu = 0.99; % momentum factor
% generate patterns (each pattern consists one spik-e per afferent)
if loadData ==0 %初始化网络
weights = 1e-2*randn(nAfferents,nOutputs); % 1e-3*randn(nAfferents,1);
save('weights0','weights');
else
load('weights0','weights');
end
%Class = logical(eye(nOutputs)); % desired class label for each pattern
%Class = false(1,26); Class(26)=true;
Class = de2bi(1:26,'left-msb'); Class=Class';
correctRate=zeros(1,maxEpoch);
dw_Past=zeros(nAfferents,nPtns,nOutputs); % momentum for accelerating learning.上一个权重的更新，用于动量计算
for epoch=1:maxEpoch
Class_Tr = false(nOutputs,nPtns); % actual outputs of training
for pp=1:nPtns
% Class_Tr = false(nOutputs,1); % actual outputs of training
for neuron=1:nOutputs
Vmax=0; tmax=0;
fired=false;
Vm1=zeros(1,256); indx1= 1; % trace pattern 1
for t=dt:dt:T
Vm = 0;
if fired==false
Tsyn=find(TrainPtns(:,pp)<=t+0.1*dt); % no cut window
else
Tsyn=find(TrainPtns(:,pp)<=t_fire+0.1*dt); % shut down inputs
end
if ~isempty(Tsyn)
A1=TrainPtns(:,pp);
A2=A1(Tsyn);
K =V0*(exp(-(t-A2)/tau_m)-exp(-(t-A2)/tau_s)); % the kernel value for each fired afferent
A1=weights(:,neuron);
firedWeights=A1(Tsyn);
Vm = Vm + firedWeights'*K ;
end
Vm = Vm + V_rest;
if Vm>=V_thr && fired==false % fire
fired=true;
t_fire=t;
Class_Tr(neuron,pp)=true;
end
if Vm>Vmax
Vmax=Vm; tmax=t;
end
%if pp==1
Vm1(indx1)=Vm;
indx1=indx1+1;
%end
end
%if pp==1
figure(1); plot(dt:dt:T,Vm1);
title(strcat('Image ',char('A'+pp-1),'; neuron: ',num2str(neuron))); drawnow;
%end
if Vmax<=0
tmax=max(TrainPtns(:,pp));
end
if Class_Tr(neuron,pp)~=Class(neuron,pp) % error
Tsyn=find(TrainPtns(:,pp)<=tmax+0.1*dt);
if ~isempty(Tsyn)
A1=TrainPtns(:,pp);
A2=A1(Tsyn);
K =V0*(exp(-(tmax-A2)/tau_m)-exp(-(tmax-A2)/tau_s)); % the kernel value for each fired afferent
A1=weights(:,neuron);
dwPst=dw_Past(:,pp,neuron);
if fired==false % LTP
Dw=lmd*K;
else % LTD
Dw=-1.1*lmd*K;
end
A1(Tsyn) = A1(Tsyn) + Dw + mu*dwPst(Tsyn);
weights(:,neuron)=A1;
dwPst(Tsyn)=Dw;
dw_Past(:,pp,neuron) = dwPst;
end
end
end % end of one neuron computation
end % end of one image
%CC=isequal(Class,Class_Tr);
%correctRate(epoch)=sum(Class==Class_Tr)/length(Class);
CC = bi2de(Class_Tr','left-msb');
end
save('TrainedWt','weights');
figure(2); plot(1:maxEpoch,correctRate,'-b.');
end
%%将图片编码为脉冲序列并保存在向量中
function spikeTrain=image2ptn(A)
%% convert a image to a spike train saved in a vector
RandParts=1;
% A1=A';
% B=[A1(:);A(:)];
% numPixels=length(B);
% numInputNeurons=numPixels/8; % 64 neurons
% spikeTrain=zeros(numInputNeurons,1);
% for i=1:numInputNeurons
% Bits=B((1+(i-1)*8):(8+(i-1)*8));
% Bits=Bits';
% spikeTime=bi2de(Bits,'left-msb');
% if spikeTime==0
% spikeTime=2^8; % put 0 to the end of the interval
% end
% spikeTrain(i)=spikeTime;
% end
spikeTrain=zeros(32,1);
if RandParts==1
loadR=1;
AR=A(:);
if loadR==0
R = randperm(size(A,1)*size(A,2));
save('RandIndex','R');
else
load('RandIndex','R');
end
numRandNeus=32;
for i=1:numRandNeus
IndexR=R((1+(i-1)*8):(8+(i-1)*8));
Bits=AR(IndexR);
Bits=Bits';
spikeTime=bi2de(Bits,'left-msb'); % 二进制转十进制
if spikeTime==0
spikeTime=2^8; % put 0 to the end of the interval
end
spikeTrain(i)=spikeTime;
end
end
end