To write a program to implement the the Logistic Regression Using Gradient Descent.
- Hardware โ PCs
- Anaconda โ Python 3.7 Installation / Jupyter notebook
- Use the standard libraries in python for finding linear regression.
- Set variables for assigning dataset values.
- Import linear regression from sklearn.
- Predict the values of array.
- Calculate the accuracy, confusion and classification report b
- importing the required modules from sklearn. Obtain the graph. .
/*
Program to implement the the Logistic Regression Using Gradient Descent.
Developed by: RAJESH A
RegisterNumber: 212222100042
*/
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
data=np.loadtxt("/content/ex2data1.txt",delimiter=',')
X=data[:, [0, 1]]
y=data[:, 2]
X[:5]
y[:5]
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()
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 costFunction(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=costFunction(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=costFunction(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()
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.