Programs & Data - Revision history

Tt at 15:17, 30 December 2012

2012-12-30T15:17:12Z

Hallab at 22:08, 16 December 2012

2012-12-16T22:08:00Z

Hallab at 22:06, 16 December 2012

2012-12-16T22:06:57Z

Hallab: Replaced content with "MLreview2013"

2012-12-16T22:03:37Z

Replaced content with "MLreview2013"

Hallab at 18:21, 14 December 2012

2012-12-14T18:21:11Z

Hallab: Created page with "==Basic restricted Boltzmann machine to learn letter patterns== clear; nh=100; nepochs=150; lrate=0.01; %load data from text file and rearrange into matrix load pattern1.t..."

2012-12-14T16:50:19Z

Created page with "==Basic restricted Boltzmann machine to learn letter patterns== clear; nh=100; nepochs=150; lrate=0.01; %load data from text file and rearrange into matrix load pattern1.t..."

New page

==Basic restricted Boltzmann machine to learn letter patterns==

clear; nh=100; nepochs=150; lrate=0.01;
%load data from text file and rearrange into matrix
load pattern1.txt;
letters = permute( reshape( pattern1, [12 26 13]), [1 3 2]);

%%train rbm for nepochs presentations of the 26 letters
input = reshape(letters,[12*13 26])
vb =zeros(12*13,1); hb =zeros(nh,1); w =.1*randn(nh,12*13);

figure; hold on;
xlabel 'epoch'; ylabel 'error'; xlim([0 nepochs]);
for epoch=1:nepochs;
err=0;
for i=1:26
%Sample hidden units given input, then reconstruct.
v = input(:,i);
h = 1./(1 + exp(-(w *v + hb))); %sigmoidal activation
hs= h > rand(nh,1); %probabilistic sampling
vr= 1./(1 + exp(-(w'*hs+ vb))); %input reconstruction
hr= 1./(1 + exp(-(w *vr+ hb))); %hidden reconstruction

%Contrastive Divergence rule: dw ~ h*v - hr*vr
dw = lrate*(h*v'-hr*vr'); w = w +dw;
dvb = lrate*( v - vr ); vb= vb+dvb;
dhb = lrate*( h - hr ); hb= hb+dhb;
err = err + sum( (v-vr).^2 ); %reconstruction error
end
plot( epoch, err/(12*13*26), '.'); drawnow;%figure output
end

%%plot reconstructions of noisy letters
r = randomFlipMatrix(round(.2*12*13)); %(20% of bits flipped)
noisy_letters = abs(letters - reshape(r,[12 13 26]));
recon = reshape(noisy_letters, 12*13, 26); %put data in matrix
recon=recon(:,1:5); %only plot first 10
figure; set(gcf,'Position',get(0,'screensize'));

for i=0:3
for j=1:5
subplot(3+1, 5, i*5 + j);
imagesc( reshape(recon(:,j),[12 13]) ); %plot
colormap gray; axis off; axis image;

h = 1./(1 + exp(-(w *recon(:,j) + hb))); %compute hidden
hs= h > rand(nh,1); %sample hidden
recon(:,j) = 1./(1 + exp(-(w'*hs + vb)));%compute visible
recon(:,j) = recon(:,j) > rand(12*13,1); %sample visible
end
end

function r=randomFlipMatrix(n);
% returns matrix with components 1 at n random positions
r=zeros(156,26);
for i=1:26
x=randperm(156);
r(x(1:n),i)=1;
end

==An MLP with backpropagation for solving the XOR problem==
clear; clf;
N_i=2; N_h=2; N_o=1;
w_h=rand(N_h,N_i)-0.5; w_o=rand(N_o,N_h)-0.5;

% training vectors (XOR)
r_i=[0 1 0 1 ; 0 0 1 1];
r_d=[0 1 1 0];

% Updating and training network with sigmoid activation function
for trial=1:10000;
% training randomly on one pattern
i=ceil(4*rand);
r_h=1./(1+exp(-w_h*r_i(:,i)));
r_o=1./(1+exp(-w_o*r_h));
d_o=(r_o.*(1-r_o)).*(r_d(:,i)-r_o);
d_h=(r_h.*(1-r_h)).*(w_o'*d_o);
w_o=w_o+0.7*(r_h*d_o')';
w_h=w_h+0.7*(r_i(:,i)*d_h')';
% test all pattern
r_o_test=1./(1+exp(-w_o*(1./(1+exp(-w_h*r_i)))));
d(trial)=0.5*sum((r_o_test-r_d).^2);
end
plot(d)

==Using libsvm for classification==

clear; close all; figure; hold on; axis square

%% training data and training SVM
r1=2+rand(300,1); a1=2*pi*rand(300,1); polar(a1,r1,'bo');
r2=randn(300,1); a2=.5*pi*rand(300,1); polar(a2,r2,'rx');

x=[r1.*cos(a1),r1.*sin(a1);r2.*cos(a2),r2.*sin(a2)];
y=[zeros(300,1);ones(300,1)];
model=svmtrain(y,x);

%% test data and SVM predicition
r1=2+rand(300,1); a1=2*pi*rand(300,1);
r2=randn(300,1); a2=.5*pi*rand(300,1);
x=[r1.*cos(a1),r1.*sin(a1);r2.*cos(a2),r2.*sin(a2)];
yp=svmpredict(y,x,model);

figure; hold on; axis square
[tmp,I]=sort(yp);
plot(x(1:600-sum(yp),1),x(1:600-sum(yp),2),'bo');
plot(x(600-sum(yp)+1:600,1),x(600-sum(yp)+1:600,2),'rx');

==Program for the chain example using policy iteration==

% Chain example: Policy iteration

% Parameters
clear; N=10; P=0.8; gamma=0.9;

% Reward function
r = zeros(1,N) - 0.1; r(1)=-1; r(N)=1;

% Initiality random start policy and value function
policy = ceil(2*rand(1,N)); policy(1)=2; policy(N)=1;
Vpi = rand(1,N); Vpi(1)=r(1); Vpi(N)=r(N);

for iter=1:3
% Estimate V for this policy
for i=1:10
for s=2:N-1
snext = s-1+2*(policy(s)-1);
sother = s+1-2*(policy(s)-1);
Vpi(s) = r(s)+gamma*(P*Vpi(snext)+(1-P)*Vpi(sother));
end
end
%Updating policy
for s=2:N-1
[tmp, policy(s)] = max([Vpi(s-1),Vpi(s+1)]);
end
end
plot(Vpi);

← Older revision		Revision as of 15:17, 30 December 2012
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	* [[MLreview2013#SVM\|Support Vector Machine (SVM)]]		* [[MLreview2013#SVM\|Support Vector Machine (SVM)]]
	* [[MLreview2013#MDP\|Policy Iteration]]		* [[MLreview2013#MDP\|Policy Iteration]]
		+
		+	[[Fundamentals of Computational Neuroscience (2nd Edition): Programs]]

@@ Line 1: / Line 1: @@
 [[MLreview2013]]
-* [[MLreveiew2013#RBM|Basic Restricted Boltzman Machine (RBM)]]
+* [[MLreview2013#RBM|Basic Restricted Boltzman Machine (RBM)]]
-* [[MLreveiew2013#MLP|Multi-Layer Perceptron (MLP)]]
+* [[MLreview2013#MLP|Multi-Layer Perceptron (MLP)]]
-* [[MLreveiew2013#SVM|Support Vector Machine (SVM)]]
+* [[MLreview2013#SVM|Support Vector Machine (SVM)]]
-* [[MLreveiew2013#MDP|Policy Iteration]]
+* [[MLreview2013#MDP|Policy Iteration]]

← Older revision		Revision as of 22:06, 16 December 2012
Line 1:		Line 1:
	[[MLreview2013]]		[[MLreview2013]]
		+
		+	* [[MLreveiew2013#RBM\|Basic Restricted Boltzman Machine (RBM)]]
		+	* [[MLreveiew2013#MLP\|Multi-Layer Perceptron (MLP)]]
		+	* [[MLreveiew2013#SVM\|Support Vector Machine (SVM)]]
		+	* [[MLreveiew2013#MDP\|Policy Iteration]]

← Older revision		Revision as of 22:03, 16 December 2012
Line 1:		Line 1:
−	[[~~Basic RBM~~]]	+	[[MLreview2013]]
−
−	~~==Basic restricted Boltzmann machine to learn letter patterns==~~
−
−	~~clear; nh=100; nepochs=150; lrate=0.01;~~
−	~~%load data from text file and rearrange into matrix~~
−	~~load pattern1.txt;~~
−	~~letters = permute( reshape( pattern1, [12 26 13]), [1 3 2]);~~
−
−	~~%%train rbm for nepochs presentations of the 26 letters~~
−	~~input = reshape(letters,[12*13 26])~~
−	~~vb =zeros(1213,1); hb =zeros(nh,1); w =.1randn(nh,12*13);~~
−
−	~~figure; hold on;~~
−	~~xlabel 'epoch'; ylabel 'error'; xlim([0 nepochs]);~~
−	~~for epoch=1:nepochs;~~
−	~~err=0;~~
−	~~for i=1:26~~
−	~~%Sample hidden units given input, then reconstruct.~~
−	~~v = input(:,i);~~
−	~~h = 1./(1 + exp(-(w *v + hb))); %sigmoidal activation~~
−	~~hs= h > rand(nh,1); %probabilistic sampling~~
−	~~vr= 1./(1 + exp(-(w'*hs+ vb))); %input reconstruction~~
−	~~hr= 1./(1 + exp(-(w *vr+ hb))); %hidden reconstruction~~
−
−	~~%Contrastive Divergence rule: dw ~ hv - hrvr~~
−	~~dw = lrate(hv'-hr*vr'); w = w +dw;~~
−	~~dvb = lrate*( v - vr ); vb= vb+dvb;~~
−	~~dhb = lrate*( h - hr ); hb= hb+dhb;~~
−	~~err = err + sum( (v-vr).^2 ); %reconstruction error~~
−	~~end~~
−	~~plot( epoch, err/(121326), '.'); drawnow;%figure output~~
−	~~end~~
−
−	~~%%plot reconstructions of noisy letters~~
−	~~r = randomFlipMatrix(round(.21213)); %(20% of bits flipped)~~
−	~~noisy_letters = abs(letters - reshape(r,[12 13 26]));~~
−	~~recon = reshape(noisy_letters, 12*13, 26); %put data in matrix~~
−	~~recon=recon(:,1:5); %only plot first 10~~
−	~~figure; set(gcf,'Position',get(0,'screensize'));~~
−
−	~~for i=0:3~~
−	~~for j=1:5~~
−	~~subplot(3+1, 5, i*5 + j);~~
−	~~imagesc( reshape(recon(:,j),[12 13]) ); %plot~~
−	~~colormap gray; axis off; axis image;~~
−
−	~~h = 1./(1 + exp(-(w *recon(:,j) + hb))); %compute hidden~~
−	~~hs= h > rand(nh,1); %sample hidden~~
−	~~recon(:,j) = 1./(1 + exp(-(w'*hs + vb)));%compute visible~~
−	~~recon(:,j) = recon(:,j) > rand(12*13,1); %sample visible~~
−	~~end~~
−	~~end~~
−
−	~~function r=randomFlipMatrix(n);~~
−	~~% returns matrix with components 1 at n random positions~~
−	~~r=zeros(156,26);~~
−	~~for i=1:26~~
−	~~x=randperm(156);~~
−	~~r(x(1:n),i)=1;~~
−	~~end~~
−
−
−	~~==An MLP with backpropagation for solving the XOR problem==~~
−	~~clear; clf;~~
−	~~N_i=2; N_h=2; N_o=1;~~
−	~~w_h=rand(N_h,N_i)-0.5; w_o=rand(N_o,N_h)-0.5;~~
−
−	~~% training vectors (XOR)~~
−	~~r_i=[0 1 0 1 ; 0 0 1 1];~~
−	~~r_d=[0 1 1 0];~~
−
−	~~% Updating and training network with sigmoid activation function~~
−	~~for trial=1:10000;~~
−	~~% training randomly on one pattern~~
−	~~i=ceil(4*rand);~~
−	~~r_h=1./(1+exp(-w_h*r_i(:,i)));~~
−	~~r_o=1./(1+exp(-w_o*r_h));~~
−	~~d_o=(r_o.(1-r_o)).(r_d(:,i)-r_o);~~
−	~~d_h=(r_h.(1-r_h)).(w_o'*d_o);~~
−	~~w_o=w_o+0.7(r_hd_o')';~~
−	~~w_h=w_h+0.7(r_i(:,i)d_h')';~~
−	~~% test all pattern~~
−	~~r_o_test=1./(1+exp(-w_o(1./(1+exp(-w_hr_i)))));~~
−	~~d(trial)=0.5*sum((r_o_test-r_d).^2);~~
−	~~end~~
−	~~plot(d)~~
−
−	~~==Using libsvm for classification==~~
−
−	~~clear; close all; figure; hold on; axis square~~
−
−	~~%% training data and training SVM~~
−	~~r1=2+rand(300,1); a1=2pirand(300,1); polar(a1,r1,'bo');~~
−	~~r2=randn(300,1); a2=.5pirand(300,1); polar(a2,r2,'rx');~~
−
−	~~x=[r1.cos(a1),r1.sin(a1);r2.cos(a2),r2.sin(a2)];~~
−	~~y=[zeros(300,1);ones(300,1)];~~
−	~~model=svmtrain(y,x);~~
−
−	~~%% test data and SVM predicition~~
−	~~r1=2+rand(300,1); a1=2pirand(300,1);~~
−	~~r2=randn(300,1); a2=.5pirand(300,1);~~
−	~~x=[r1.cos(a1),r1.sin(a1);r2.cos(a2),r2.sin(a2)];~~
−	~~yp=svmpredict(y,x,model);~~
−
−	~~figure; hold on; axis square~~
−	~~[tmp,I]=sort(yp);~~
−	~~plot(x(1:600-sum(yp),1),x(1:600-sum(yp),2),'bo');~~
−	~~plot(x(600-sum(yp)+1:600,1),x(600-sum(yp)+1:600,2),'rx');~~
−
−
−	~~==Program for the chain example using policy iteration==~~
−
−	~~% Chain example: Policy iteration~~
−
−	~~% Parameters~~
−	~~clear; N=10; P=0.8; gamma=0.9;~~
−
−	~~% Reward function~~
−	~~r = zeros(1,N) - 0.1; r(1)=-1; r(N)=1;~~
−
−	~~% Initiality random start policy and value function~~
−	~~policy = ceil(2*rand(1,N)); policy(1)=2; policy(N)=1;~~
−	~~Vpi = rand(1,N); Vpi(1)=r(1); Vpi(N)=r(N);~~
−
−	~~for iter=1:3~~
−	~~% Estimate V for this policy~~
−	~~for i=1:10~~
−	~~for s=2:N-1~~
−	~~snext = s-1+2*(policy(s)-1);~~
−	~~sother = s+1-2*(policy(s)-1);~~
−	~~Vpi(s) = r(s)+gamma(PVpi(snext)+(1-P)*Vpi(sother));~~
−	~~end~~
−	~~end~~
−	~~%Updating policy~~
−	~~for s=2:N-1~~
−	~~[tmp, policy(s)] = max([Vpi(s-1),Vpi(s+1)]);~~
−	~~end~~
−	~~end~~
−	~~plot(Vpi);~~

← Older revision		Revision as of 18:21, 14 December 2012
Line 1:		Line 1:
		+	[[Basic RBM]]
		+
	==Basic restricted Boltzmann machine to learn letter patterns==		==Basic restricted Boltzmann machine to learn letter patterns==