diff --git a/machine learning/assignment 1.R b/machine learning/assignment 1.R
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+exam1 = read.table('C:\\work\\BaiduNetdiskWorkspace\\coursera\\machine learning\\machine-learning-ex1\\ex1\\ex1data1.txt', sep = ",")
+# identity matrix
+diag(5)
+
+# Plotting the Data
+plot(exam1$V1,exam1$V2,pch = 4 ,col='red', xlab='Population of City in 10,000s',ylab='Profit in $10,000s')
+
+# Implementation
+m = length(exam1$V1)
+X = cbind(rep(1,m),exam1$V1)
+theta = matrix(c(0,0),2,1)
+iter = 1500
+alpha = 0.01
+
+# computing the cost
+h=X%*%theta
+J = 1/(2*m)*sum((h-exam1$V2)^2)
+
+i=0
+# Gradient descent
+for (i in seq(0,m)) { 
+  theta=theta-alpha/m*t(X)%*%(h-exam1$V2)
+  h=X%*%theta
+  J = 1/(2*m)*sum((h-exam1$V2)^2)
+  i=i+1
+}
+
+# predict
+h=X%*%theta
+p1 = matrix(c(1,3.5),1,2)
+p2 = matrix(c(1,7),1,2)
+h1 = p1%*%theta
+plot(exam1$V1,exam1$V2,pch = 4 ,col='red', xlab='Population of City in 10,000s',ylab='Profit in $10,000s')
+lines(X[,2],h,col='blue',type='l')
+
+### multivariable
+exam2 = read.table('C:\\work\\BaiduNetdiskWorkspace\\coursera\\machine learning\\machine-learning-ex1\\ex1\\ex1data2.txt', sep = ",")
+
+# Implementation
+m = length(exam2$V1)
+X = cbind(rep(1,m),exam2$V1,exam2$V2)
+theta = matrix(c(0,0,0),3,1)
+iter = 1500
+alpha = 0.01
+
+# standardized
+mean1=mean(X[,2])
+std1 = sd(X[,2])
+X[,2] = (X[,2]-mean1)/std1
+
+mean2=mean(X[,3])
+std2 = sd(X[,3])
+X[,3] = (X[,3]-mean2)/std2
+
+# computing the cost
+h=X%*%theta
+J=rep(0,m)
+
+i=0
+# Gradient descent
+for (i in seq(0,iter)) { 
+  theta=theta-alpha/m*t(X)%*%(h-exam2$V3)
+  h=X%*%theta
+  J[i] = 1/(2*m)*sum((h-exam2$V3)^2)
+  i=i+1
+}
+
+plot(seq(1,iter),J,type = 'l',col='green')
+
+# theta Normal Equations
+library(matlib)
+theta_n = inv(t(X)%*%X)%*%t(X)%*%exam2$V3
diff --git a/machine learning/exam 2.R b/machine learning/exam 2.R
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+# read data
+data1 = read.table('C:\\work\\BaiduNetdiskWorkspace\\coursera\\machine learning\\machine-learning-ex2\\ex2\\ex2data1.txt',sep = ',')
+
+colors = c('yellow','black')
+pch = c(16,3)
+X1 = seq(30,100,1)
+X2 = -theta[1]/theta[3]-theta[2]*X1/theta[3]
+
+plot(data1$V1, data1$V2, col=colors[factor(data1$V3, levels = c("0", "1"))],pch = pch[factor(data1$V3, levels = c("0", "1"))],xlab='Exam 1 score',ylab='exam 2 score')
+lines(X1,X2,col='blue',type='l')
+
+plot(X1,X2)
+
+iter = 400
+alpha = 0.001
+#sigmoid function
+m = length(data1$V1)
+X = cbind(rep(1,m),data1$V1,data1$V2)
+theta = matrix(c(0.1,0.1,0.1),3,1)
+z = X%*%theta
+sig = 1/(1+exp(-z))
+
+
+# Cost function
+J = rep(0,iter)
+i=1
+for (i in 1:iter) {
+  theta = theta-alpha/m*t(X)%*%(sig-data1$V3)
+  z = X%*%theta
+  sig = 1/(1+exp(-z))
+  J[i] = 1/m*sum(-data1$V3*log(sig)-(1-data1$V3)*log(1-sig))
+  i=i+1
+}
+
+plot(seq(1,iter),J,type = 'l')
+
+
+# cost function
+J <- function(theta){
+  z = X%*%theta
+  sig = 1/(1+exp(-z))
+  C=1/m*sum(-data1$V3*log(sig)-(1-data1$V3)*log(1-sig))
+  return(C)
+}
+z <- outer(theta1, theta2, J)
+persp(theta1, theta2, z)
+library(rgl)
+persp3d(theta1, theta3, z,theta=155,phi=30,col="green4", ltheta=-120,shade=.75,border=NA,box=FALSE)
+
+z = matrix(0,101,101)
+
+for (i in 1:101) {
+  for (j in 1:101) {
+    z[i,j] = J(theta1[i],theta3[j])
+  }
+}
+
+theta_optim <- optim(par=theta,fn=J)
+#set theta
+theta <- theta_optim$par
+#cost at optimal value of the theta
+theta_optim$value
+
+
+# Predict 
+p1 = c(1,45,85)
+z = p1%*%theta
+sig = 1/(1+exp(-z))
+
+# multi
+data2 = read.table('C:\\work\\BaiduNetdiskWorkspace\\coursera\\machine learning\\machine-learning-ex2\\ex2\\ex2data2.txt',sep = ',')
+
+#Visualizing the data
+colors = c('yellow','black')
+plot(data2$V1, data2$V2, col=colors[factor(data2$V3, levels = c("0", "1"))],pch = pch[factor(data2$V3, levels = c("0", "1"))],xlab='Exam 1 score',ylab='exam 2 score')
+
+# Cost function
+m = length(data2$V1)
+mapfeature = cbind(rep(1,length(data2$V1)),data2$V1,data2$V2,data2$V1^2,data2$V1*data2$V2,data2$V2^2,data2$V1^3,data2$V1^2*data2$V2,data2$V1*data2$V2^2,data2$V2^3,data2$V1^4,data2$V1^3*data2$V2,data2$V1^2*data2$V2^2,data2$V1*data2$V2^3,data2$V2^4,data2$V1^5,data2$V1^4*data2$V2,data2$V1^3*data2$V2^2,data2$V1^2*data2$V2^3,data2$V1*data2$V2^4,data2$V2^5,data2$V1^6,data2$V1^5*data2$V2,data2$V1^4*data2$V2^2,data2$V1^3*data2$V2^3,data2$V1^2*data2$V2^4,data2$V1*data2$V2^5,data2$V2^6)
+theta2 = matrix(rep(0,28),28,1)
+z = mapfeature%*%theta2
+sig = 1/(1+exp(-z))
+lambda = 1
+J = 1/m*sum(-data2$V3*log(sig)-(1-data2$V3)*log(1-sig))+lambda*sum(theta2[2:28]^2)/(2*m)
+
+# cost function
+J <- function(theta){
+  z = mapfeature%*%theta
+  sig = 1/(1+exp(-z))
+  C=1/m*sum(-data2$V3*log(sig)-(1-data2$V3)*log(1-sig))+lambda*sum(theta2[2:28]^2)/(2*m)
+  return(C)
+}
+theta_optim <- optim(par=theta2,fn=J)
+#set theta
+theta <- theta_optim$par
+#cost at optimal value of the theta
+theta_optim$value
+
+#plot decision rule boundary
+# class labels: simple distance from origin
+classes <- ifelse(z > 0, "black", "orange")
+
+grid <- expand.grid(x=1:100, y=1:100)
+classes.grid <- knn(train.df, grid, classes, k=25, prob=TRUE)  # note last argument
+prob.grid <- attr(classes.grid, "prob")
+prob.grid <- ifelse(classes.grid == "blue", prob.grid, 1 - prob.grid)
+
+# plot the boundary
+contour(x=1:100, y=1:100, z=matrix(prob.grid, nrow=100), levels=0.5,
+        col="grey", drawlabels=FALSE, lwd=2)
+# add points from test dataset
+points(test.df, col=classes.test)
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diff --git a/machine learning/exam 3.R b/machine learning/exam 3.R
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+data1 = readMat('C:\\work\\BaiduNetdiskWorkspace\\coursera\\machine learning\\machine-learning-ex3\\ex3\\ex3data1.mat')
+m = length(data1$y);
+rand_indices = sample(1:m,100,replace = F);
+sel = X(rand_indices, :);
+X = data1$X[rand_indices,]
+y= data1$y[rand_indices,]
+m = 100
+n = 400
+example_width = 20
+example_height = 20
+
+# Compute number of items to display
+display_rows = 10
+display_cols = 10
+
+# Between images padding
+pad = 1
+
+# Setup blank display
+display_array = matrix(rep(1),pad + display_rows * (example_height + pad),pad + display_cols * (example_width + pad))
+
+# Copy each example into a patch on the display array
+curr_ex = 1;
+for (j in 1:display_rows){
+  for (i in 1:display_cols){
+      display_array[pad + (j - 1) * (example_height + pad) + (1:example_height),pad + (j - 1) * (example_width + pad) + (1:example_width)] =  matrix(X[curr_ex, ], example_height, example_width) 
+      curr_ex = curr_ex + 1
+    
+  }
+}
+
+
+# The col argument allows customizing the color palette of the image. You can pass as variable a function such as gray.colors, topo.colors, hcl.colors or a similar function. The default value is hcl.colors(12, "YlOrRd", rev = TRUE).
+# Note that if you increase the number of values the color image will be smoothed.
+
+image(display_array, col = gray.colors(50))
+
+# Part 2a: Vectorize Logistic Regression 
+theta = matrix(c(-2,-1,1,2),4,1)
+X_t = cbind(rep(1,5),matrix(seq(1,15,1)/10,5,3))
+y_t = matrix(c(1,0,1,0,1),5,1)
+m= length(y_t)
+lambda_t = 3
+g = 1/(1+exp(-X_t%*%theta))
+reg = lambda_t/(2*m)*t(theta[2:4])%*%theta[2:4]
+C = 1/m*sum(-y_t*log(g)-(1-y_t)*log(1-g)) + reg
+grad = matrix(rep(0,4),4,1)
+grad[1]=1/m*t(g-y_t)%*%X_t[,1]
+grad[2:4]=1/m*t(g-y_t)%*%X_t[,2:4]+lambda_t/m*theta[2:4]
+
+all_theta_t = matrix(rep(0,40),10,4)
+
+cost_function = function(Y,theta){
+  
+  m = length(Y)
+  n = length(theta)
+  g = 1/(1+exp(-X%*%theta))
+  reg = 0.1/(2*m)*t(theta[2:n])%*%theta[2:n]
+  C = 1/m*sum(-Y*log(g)-(1-Y)*log(1-g)) + reg
+  return(C)
+}
+
+
+a = cost_function(X_t,y_t,theta,lambda_t)
+
+all_theta = matrix(rep(0.05,4010),401,10)
+cost = rep(0,10)
+X = cbind(matrix(rep(1,5000),5000,1), data1$X)
+lambda_t = 0.1
+for (i in 1:10) {
+  Y = ifelse(data1$y==i,1,0)
+  all_theta[,i] <- optim(par=all_theta[,i],fn=cost_function,Y=Y)$par
+  cost[i]= optim(par=all_theta[,i],fn=cost_function)$value
+}
+
+G = 1/(1+exp(-X%*%all_theta))
+G = cbind(G,matrix(rep(0,5000),5000,1))
+
+G[,11] = max(G[,1:10])
+for (i in 1:5000) {
+  G[i,11] = max(G[i,1:10])
+}
+
+colnames(G)[apply(G,1,which.max)]
+theta1 = data2$Theta1
+theta2 = data2$Theta2
+
+# Neural Networks
+data2 = readMat('C:\\work\\BaiduNetdiskWorkspace\\coursera\\machine learning\\machine-learning-ex3\\ex3\\ex3weights.mat')
+cost_function_NN = function(theta1,theta2,X){
+  m=dim(data1$X)[1]
+  num_labels = dim(data2$Theta2)[1]
+  p = matrix(rep(0,m),m,1)
+  g1 = 1/(1+exp(-X%*%t(theta1)))
+  g1 = cbind(matrix(rep(1,5000),5000,1), g1)
+  g2 = 1/(1+exp(-g1%*%t(theta2)))
+  
+}
+
+colnames(g2) = c(1,2,3,4,5,6,7,8,9,10)
+Y_pred = colnames(g2)[apply(g2,1,which.max)]
+count(Y_pred==data1$y)/5000
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