Difference between revisions of "Programs & Data"

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(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...")
 
 
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==Basic restricted Boltzmann machine to learn letter patterns==
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[[MLreview2013]]
  
clear; nh=100;  nepochs=150;  lrate=0.01;
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* [[MLreview2013#RBM|Basic Restricted Boltzman Machine (RBM)]]
%load data from text file and rearrange into matrix
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* [[MLreview2013#MLP|Multi-Layer Perceptron (MLP)]]
load pattern1.txt;
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* [[MLreview2013#SVM|Support Vector Machine (SVM)]]
letters = permute( reshape( pattern1, [12 26 13]), [1 3 2]);
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* [[MLreview2013#MDP|Policy Iteration]]
 
%%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
 
  
 
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[[Fundamentals of Computational Neuroscience (2nd Edition): Programs]]
==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);
 

Latest revision as of 15:17, 30 December 2012