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 Libraries
- Load and Prepare Data
- Feature Scaling (Optional)
- Define the Logistic Regression Model
- Make Predictions
- Evaluate the Model
- Plot the Learning Curve (Optional)
/*
Program to implement the the Logistic Regression Using Gradient Descent.
Developed by: SYED ADIL BASHA
RegisterNumber: 212221043008
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
data = np.loadtxt("/content/ex2data1 (1).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 signoid(z):
return 1/(1+np.exp(-z))
plt.plot()
x_plot=np.linspace(-10,10,100)
plt.plot(x_plot,signoid(x_plot))
plt.show()
def costFunction(theta,x,y):
h=signoid(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=signoid(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=signoid(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=signoid(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=signoid(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.