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Labtask1: Generatedataset

The document contains code to generate a dataset and train a neural network. It begins by generating a dataset of 500 points, separating them into two classes based on an equation. It then trains a perceptron model on 400 points and tests it on the remaining 100 points. Next, it trains a simple neural network with one hidden layer on the XOR problem. The network has three inputs, two nodes in the hidden layer, and one output node. It runs gradient descent training over 1000 iterations to update the weights.

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Sohaib Sajid
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99 views12 pages

Labtask1: Generatedataset

The document contains code to generate a dataset and train a neural network. It begins by generating a dataset of 500 points, separating them into two classes based on an equation. It then trains a perceptron model on 400 points and tests it on the remaining 100 points. Next, it trains a simple neural network with one hidden layer on the XOR problem. The network has three inputs, two nodes in the hidden layer, and one output node. It runs gradient descent training over 1000 iterations to update the weights.

Uploaded by

Sohaib Sajid
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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GenerateDataSet

clf
% Line Plot
x1 = 0:0.1:5;
x2 = 2*x1 + 3;
plot(x1,x2)
grid on
hold on

liner = @(x1,x2) x2 - 2*x1 -3;

% Shorter Code
X = 5*rand(1,1000);
Y = max(x2)*rand(1,1000);
star = [];

% Loop check
for ii = 1:size(Y,2)
if liner(X(ii),Y(ii)) > liner(x1,x2)
scatter(X(ii),Y(ii),'ro')
star(ii) = 0;
%disp('*')
else
scatter(X(ii),Y(ii),'b*')
star(ii) = 1;
%disp('o')
end
end

dataset = [X' Y' star'];


save('dataset')

LabTask1
clf
% Line Plot
x1 = 0:0.1:5;
x2 = 2*x1 + 3;
plot(x1,x2)
grid on
hold on

liner = @(x1,x2) x2 - 2*x1 -3;

% Shorter Code
mydata = 5*rand(1,100);
b = max(x2)*rand(1,100);

% Loop check
for ii = 1:size(mydata,2)
if liner(mydata(ii),b(ii)) > liner(x1,x2)
scatter(mydata(ii),b(ii),'o')
%disp('*')
else
scatter(mydata(ii),b(ii),'*')
%disp('o')
end
end

% % Random Data points


% data1 = [];
% data2 = [];
% for ii = 1:200
% if rand > 0.5
% sign1 = -1;
% else
% sign1 = 1;
% end
% tempdata1 = sign1*5*rand;
%
% if rand < 0.5
% sign2 = -1;
% else
% sign2 = 1;
% end
% tempdata2 = sign2*5*rand;
%
% vert = [tempdata1; tempdata2];
% data1 = [data1 vert];
% end
% plot(x1,x2)
% grid on
% hold on
% scatter(data1(1,:),data1(2,:))
Load data set
load('dataset')
X = dataset(:,1);
Y = dataset(:,2);
star = dataset(:,3);

% Plot DataSet
figure(2)
hold on
for ii = 1:size(dataset,1)
if star(ii) == 0
scatter(X(ii),Y(ii),'o')
else
scatter(X(ii),Y(ii),'*')
end
end
PerceptronAlgorithmExample
clc,clear,close
mydata = rand(500,2);
% Separate the data into two classes
% acceptindex = abs(mydata(:,1)-mydata(:,2))>0.012;
acceptindex = abs(mydata(:,1)-mydata(:,2))>0.012;
mydata = mydata(acceptindex,:); % data
myclasses = mydata(:,1)>mydata(:,2); % labels
[m n]=size(mydata);
%training data
x=mydata(1:400,:); y=myclasses(1:400);
% test data
xt=mydata(401:m,:); yt=myclasses(401:m);
%=====================================
% Train the perceptron
%=====================================
[w,b,pass] = PerecptronTrn(x,y)
Iterations=pass
%=====================================
% Test
%=====================================
e=PerecptronTst(xt,yt,w,b)

disp(['Test_Errors=' num2str(e) ' Test Data Size= ' num2str(m-


400)])

%=====================================
% Draw the result (sparating hyperplane)
%=====================================
l=y==0;
hold on
plot(x(l,1),x(l,2),'ko' );
plot(x(~l,1),x(~l,2),'m*');
% [l,p]=size(x);
plot([0,1],[0,1],'r-')
axis([0 1 0 1]), axis square, grid on
drawnow

PerecptronTrn
function [w,b,pass]=PerecptronTrn(x,y);
% %Rosenblatt's Perecptron
tic
[l,p]=size(x);
w=zeros(p,1); % initialize weights
b=0; % initialize bias
ier=1; % initialize a misclassification indicator
pass=0; % number of iterations
n=0.5; % learning rate
r=max(sqrt(sum(x))); % max norm
while ier==1, %repeat until no error
ier=0;
e=0; % number of training errors
for i=1:l % a pass through x
w=w'+(n*y(i))*(x(i,:));
b=b+n*y(i)*(r^2);
e=e+1 ; % number of training errors
w=w';
end;
ee=e; % number of training errors
if ee>0 % cuntinue if there is still errors
ier=1;
end
pass=pass+1; % stop after 10000 iterations
if pass==10000
ier=0;
pass=0;
end;
end;
disp(['Training_Errors=' num2str(e) ' Training data Size='
num2str(l)])
toc

PerecptronTst
function e=PerecptronTst(x,y,w,b);
%==========================================
% Testing phase
%==========================================
tic
[l,p]=size(x);
e=0; % number of test errors
for i=1:l
xx=x(i,:); % take one row
ey=xx*w+b % apply the perceptron classification rule
if ey>=0.5
ey=1;
else
ey=0;
end
if y(i)~=ey
e=e+1
end;
end
toc
Training
load('dataset')
X = dataset(:,1);
Y = dataset(:,2);
star = dataset(:,3);
w1 = 0; w0 = 1; w2 = 1;
Model = @(x1,x2) w2*x2 - w1*x1 - w0;
% Plot DataSet
figure(2)
clf
hold on
for ii = 1:size(dataset,1)
if star(ii) == 0
scatter(X(ii),Y(ii),'ro')
else
scatter(X(ii),Y(ii),'b*')
end
end

for ii = 1:size(dataset,1)
alpha = 0.1;
predict = Model(X(ii),Y(ii));
if predict > 0
predict = 0;
else
predict = 1;
end

w0 = w0 + alpha*(star(ii)-predict);
w1 = w1 + alpha*(star(ii)-predict)*X(ii);
w2 = w2 + alpha*(star(ii)-predict)*Y(ii);
end

x = -1.5:1.5;
Line = @(x) (w1/w2)*x + w0/w2;
plot(Line(x))

% w0 = 4.3471
% w1 = 13.0375

Training_v2
load('dataset')
X = dataset(:,1);
Y = dataset(:,2);
star = dataset(:,3);
w1 = 0; w0 = 3;
Model = @(x1,x2) x2 - w1*x1 - w0;
% Plot DataSet
figure(2)
clf
hold on
for ii = 1:size(dataset,1)
if star(ii) == 0
scatter(X(ii),Y(ii),'o')
else
scatter(X(ii),Y(ii),'*')
end
end
title('Data Points')
xlabel('x1'), ylabel('x2')
axis([min(X) max(X) min(Y) max(Y)]);
iterT = 100;
for iter = 1:iterT
loss = []; count = 1;
alpha = 100/(100+i);
for ii = (count-1)*size(dataset,1)/iterT+1 :
count*size(dataset,1)/iterT+1
predict = Model(X(ii),Y(ii));
if predict > 0
predict = 0;
else
predict = 1;
end
loss = [loss star(ii)-predict];
end
avgLoss = sum(loss)/length(loss);
w0 = w0 + alpha*(avgLoss);
w1 = w1 + alpha*(avgLoss)*X(ii);
end
w0
w1
x = 0:5;
Line = @(x) w1*x + w0;
plot(x,Line(x))

% w0 = 4.3471
% w1 = 13.0375

Lab11 (neualnetwork)
GenerateDataSet
figure(1)
clf
% Equation for Comparison
liner = @(x1,x2) x2 - 2*x1 -3;
plotter = @(x) 2*x1 + 3;
% Line Plot
x1 = 0:0.1:5;
x2 = plotter(x1);
plot(x1,x2, 'LineWidth', 3)
grid on
hold on

% Shorter Code
X = 5*rand(1,500);
Y = 10*rand(1,500);
star = [];

% Loop check
for ii = 1:size(Y,2)
if liner(X(ii),Y(ii)) < 0
scatter(X(ii),Y(ii),'ro')
star(ii) = 0;
%disp('*')
else
scatter(X(ii),Y(ii),'b*')
star(ii) = 1;
%disp('o')
end
end
title('DataSet Generation')
xlabel('x1'), ylabel('x2')
axis([min(X) max(X) min(Y) max(Y)])

dataset = [X' Y' star'];


save('dataset')

NN1
% XOR Function
clear all
dataset = [0,0,0; 0,1,1; 1,0,1; 1,1,0];
sigmoid = @(y) 1/(1+exp(-y));

w13 = 0.5; w14 = 0.9; w23 = 0.4; w24 = 1;


w35 = -1.2; w45 = 1.1;
w03 = 0.8; w04 = -0.1; w05 = 0.3;

for i = 1:1000
%if i < 100
% alpha = 1000/(1000+i);
%else
alpha = 1000/(1000+i);
%end
%i = 4;
%alpha = 0.1;
rower = randi([1,4]);
%mod(i,3);
x1 = dataset(rower,1);
x2 = dataset(rower,2);
y = dataset(rower,3);

% Compute y3, y4
L3 = w23*x2 + w13*x1 - w03;
y3 = 1/(1+exp(-L3)); %sigmoid(L3);
L4 = w24*x2 + w14*x1 - w04;
y4 = 1/(1+exp(-L4)); %sigmoid(L4);

% Compute y5
L5 = w45*y4 + w35*y3 - w05;
y5 = 1/(1+exp(-L5)); %sigmoid(L5);

% Error in Last Layer


E = y - y5;
d5 = y5*(1-y5)*E;

% Desired Changes in weight of Last Layer


deltaw35 = d5*alpha*y3;
deltaw45 = d5*alpha*y4;
deltaw05 = d5*alpha*(-1);

% Error in Hidden Layer


d3 = y3*(1-y3)*d5*w35;
d4 = y4*(1-y4)*d5*w45;

% Desired Changes in weight of Hidden Layer


deltaw03 = d3*alpha*(-1);
deltaw13 = d3*alpha*x1;
deltaw23 = d3*alpha*x2;
deltaw04 = d4*alpha*(-1);
deltaw14 = d4*alpha*x1;
deltaw24 = d4*alpha*x2;

% Weight Updates
w03 = w03 + deltaw03;
w13 = w13 + deltaw13;
w23 = w23 + deltaw23;
w04 = w04 + deltaw04;
w14 = w14 + deltaw14;
w24 = w24 + deltaw24;
w05 = w05 + deltaw05;
w35 = w35 + deltaw35;
w45 = w45 + deltaw45;
end
w = [w03 w13 w23 w04 w14 w24 w05 w35 w45]'
liner = -2:2;
L3 = (-w13*liner + w03)/w23;
L4 = (-w14*liner + w04)/w24;
L5 = (-w35*liner + w05)/w45;
figure(12)
subplot(121), plot(liner, L3, liner, L4)
title('L3,L4'), xlabel('x1'), ylabel('x2')
legend('L3','L4'), grid on, hold on
for ii = 1:size(dataset,1)
if dataset(ii,3) == 0
scatter(dataset(ii,1),dataset(ii,2),'ro')
else
scatter(dataset(ii,1),dataset(ii,2),'b*')
end
end

subplot(122), plot(liner, L5)


title('L5'), xlabel('y3'), ylabel('y4')
legend('L5'), grid on

lab12
GenerateDataSet
figure(1)
clf
% Equation for Comparison
liner = @(x1,x2) x2 - 2*x1 -3;
plotter = @(x) 2*x1 + 3;

% Line Plot
x1 = 0:0.1:5;
x2 = plotter(x1);
plot(x1,x2, 'LineWidth', 3)
grid on
hold on

% Shorter Code
X = 5*rand(1,500);
Y = 10*rand(1,500);
star = [];

% Loop check
for ii = 1:size(Y,2)
if liner(X(ii),Y(ii)) < 0
scatter(X(ii),Y(ii),'ro')
star(ii) = 0;
%disp('*')
else
scatter(X(ii),Y(ii),'b*')
star(ii) = 1;
%disp('o')
end
end
title('DataSet Generation')
xlabel('x1'), ylabel('x2')
axis([min(X) max(X) min(Y) max(Y)])

dataset = [X' Y' star'];


save('dataset')

NN1
% XOR Function
%clear all
dataset = [0,0,0; 0,1,1; 1,0,1; 1,1,0];
sigmoid = @(y) 1/(1+exp(-y));

w13 = 0.5; w14 = 0.9; w23 = 0.4; w24 = 1;


w35 = -1.2; w45 = 1.1;
w03 = 0.8; w04 = -0.1; w05 = 0.3;
SE = 0; MSE4 = [];

for i = 1:1000
%if i < 100
% alpha = 1000/(1000+i);
%else
alpha = 10/(10+i);
%end
%i = 4;
%alpha = 0.1;
rower = randi([1,4]);
%mod(i,3);
x1 = dataset(rower,1);
x2 = dataset(rower,2);
y = dataset(rower,3);

% Compute y3, y4
L3 = w23*x2 + w13*x1 - w03;
y3 = 1/(1+exp(-L3)); %sigmoid(L3);
L4 = w24*x2 + w14*x1 - w04;
y4 = 1/(1+exp(-L4)); %sigmoid(L4);

% Compute y5
L5 = w45*y4 + w35*y3 - w05;
y5 = 1/(1+exp(-L5)); %sigmoid(L5);

% Error in Last Layer


E = y - y5;
d5 = y5*(1-y5)*E;

% Desired Changes in weight of Last Layer


deltaw35 = d5*alpha*y3;
deltaw45 = d5*alpha*y4;
deltaw05 = d5*alpha*(-1);

% Error in Hidden Layer


d3 = y3*(1-y3)*d5*w35;
d4 = y4*(1-y4)*d5*w45;

% Desired Changes in weight of Hidden Layer


deltaw03 = d3*alpha*(-1);
deltaw13 = d3*alpha*x1;
deltaw23 = d3*alpha*x2;
deltaw04 = d4*alpha*(-1);
deltaw14 = d4*alpha*x1;
deltaw24 = d4*alpha*x2;

% Weight Updates
w03 = w03 + deltaw03;
w13 = w13 + deltaw13;
w23 = w23 + deltaw23;
w04 = w04 + deltaw04;
w14 = w14 + deltaw14;
w24 = w24 + deltaw24;
w05 = w05 + deltaw05;
w35 = w35 + deltaw35;
w45 = w45 + deltaw45;

% Difference check
SE = SE + (y-y5)^2;
MSE4 = [MSE4 SE/i];
end
w = [w03 w13 w23 w04 w14 w24 w05 w35 w45]'
liner = -2:2;
L3 = (-w13*liner + w03)/w23;
L4 = (-w14*liner + w04)/w24;
L5 = (-w35*liner + w05)/w45;
figure(12)
subplot(121), plot(liner, L3, liner, L4)
title('L3,L4'), xlabel('x1'), ylabel('x2')
legend('L3','L4'), grid on, hold on
for ii = 1:size(dataset,1)
if dataset(ii,3) == 0
scatter(dataset(ii,1),dataset(ii,2),'ro')
else
scatter(dataset(ii,1),dataset(ii,2),'b*')
end
end

subplot(122), plot(liner, L5)


title('L5'), xlabel('y3'), ylabel('y4')
legend('L5'), grid on

% MSE Plot
%figure(1000), plot(MSE), grid on
%xlabel('Iterations', ylabel('MSE')
%plot(1:1000,MSE,'r',1:1000,MSE2,'b',1:1000,MSE3,'g',1:1000,MSE4,'y')
%legend('100/100+i','1000/1000+i','3000/3000+i','10/10+')
%legend('100/100+i','1000/1000+i','3000/3000+i','10/10+i')

NN1Test
load('w')
w = [w03 w13 w23 w04 w14 w24 w05 w35 w45]
w03 = w(1); w13 = w(2); w23 = w(3);
w04 = w(4); w14 = w(5); w24 = w(6);
w05 = w(7); w35 = w(8); w45 = w(9);

% xaxis = -2:2;
% myline5 = (-w35*xaxis + w05)/w45;
% figure(22)
% plot(xaxis, myline5)
% equator = 1*w35 + 1*w45
disp('----------------------')
x1 = 1, x2 = 1, y = 1

% Compute y3, y4
L3 = w23*x2 + w13*x1 - w03;
y3 = 1/(1+exp(-L3)); %sigmoid(L3);
L4 = w24*x2 + w14*x1 - w04;
y4 = 1/(1+exp(-L4)); %sigmoid(L4);

% Compute y5
L5 = w45*y4 + w35*y3 - w05;
y5 = 1/(1+exp(-L5)) %sigmoid(L5);
if y5 > 0.5
out = 1;
else
out = 0;
end

% Error in Last Layer


disp('Output')
disp(out)

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