To write a program to implement the the Logistic Regression Using Gradient Descent.
- Hardware โ PCs
- Anaconda โ Python 3.7 Installation / Jupyter notebook
- Import the data file and import numpy, matplotlib and scipy.
- Visulaize the data and define the sigmoid function, cost function and gradient descent.
- Plot the decision boundary .
- Calculate the y-prediction.
/*
Program to implement the the Logistic Regression Using Gradient Descent.
Developed by:
RegisterNumber:
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize #to remove unwanted data and memory storage
data=np.loadtxt("/content/ex2data1 (1).txt",delimiter=',')
X=data[:,[0,1]]
y=data[:,2]
X[:5]
y[:5]
Visualizing the data
plt.figure()
plt.scatter(X[y==1][:,0],X[y==1][:,1],label="Admitted")
plt.scatter(X[y==0][:,0],X[y==0][:,1],label="Not admitted")
plt.xlabel("Exam 1 score")
plt.ylabel("Exam 2 score")
plt.legend()
plt.show()
Sigmoid fuction
def sigmoid(z):
return 1/(1+np.exp(-z))
plt.plot()
X_plot=np.linspace(-10,10,100)
plt.plot(X_plot, sigmoid(X_plot))
plt.show()
def costFuction(theta,X,y):
h=sigmoid(np.dot(X,theta))
J= -(np.dot(y, np.log(h)) + np.dot(1-y,np.log(1-h))) / X.shape[0]
grad = np.dot(X.T, h-y) / X.shape[0]
return J,grad
X_train=np.hstack((np.ones((X.shape[0],1)),X))
theta=np.array([0,0,0])
J, grad=costFuction(theta, X_train, y)
print(J)
print(grad)
X_train=np.hstack((np.ones((X.shape[0],1)),X))
theta=np.array([-24,0.2,0.2])
J, grad=costFuction(theta, X_train, y)
print(J)
print(grad)
def cost(theta,X,y):
h = sigmoid(np.dot(X,theta))
J= -(np.dot(y, np.log(h)) + np.dot(1-y, np.log(1-h))) / X.shape[0]
return J
def gradient(theta,X,y):
h=sigmoid(np.dot(X,theta))
grad= np.dot(X.T, h-y) / X.shape[0]
return grad
X_train = np.hstack((np.ones((X.shape[0],1)),X))
theta= np.array([0,0,0])
res = optimize.minimize(fun=cost, x0=theta, args=(X_train,y),method="Newton-CG",jac=gradient)
print(res.fun)
print(res.x)
def plotDecisionBoundary(theta,X,y):
x_min, x_max = X[:,0].min() - 1, X[:,0].max()+1
y_min, y_max = X[:,1].min() - 1, X[:,1].max()+1
xx, yy = np.meshgrid(np.arange(x_min,x_max,0.1),
np.arange(y_min,y_max,0.1))
X_plot = np.c_[xx.ravel(), yy.ravel()]
X_plot = np.hstack((np.ones((X_plot.shape[0],1)),X_plot))
y_plot = np.dot(X_plot, theta).reshape(xx.shape)
plt.figure()
plt.scatter(X[y==1][:,0],X[y==1][:,1],label="Admitted")
plt.scatter(X[y==0][:,0],X[y==0][:,1],label="Not admitted")
plt.contour(xx,yy,y_plot, levels=[0])
plt.xlabel("Exam 1 score")
plt.ylabel("Exam 2 score")
plt.legend()
plt.show()
plotDecisionBoundary(res.x,X,y)
prob = sigmoid(np.dot(np.array([1,45,85]),res.x))
print(prob)
def predict(theta,X):
X_train = np.hstack((np.ones((X.shape[0],1)),X))
prob = sigmoid(np.dot(X_train,theta))
return(prob >= 0.5).astype(int)
np.mean(predict(res.x,X)==y)
*/
Thus the program to implement the the Logistic Regression Using Gradient Descent is written and verified using python programming.