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99 lines
2.4 KiB
Python
99 lines
2.4 KiB
Python
#!/usr/bin/env python
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# coding: utf-8
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# # Logistic Regression from scratch
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# In[62]:
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''' Implementing logistic regression for classification problem
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Helpful resources : 1.Coursera ML course 2.https://medium.com/@martinpella/logistic-regression-from-scratch-in-python-124c5636b8ac'''
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# In[63]:
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#importing all the required libraries
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import numpy as np
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import matplotlib.pyplot as plt
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get_ipython().run_line_magic('matplotlib', 'inline')
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from sklearn import datasets
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# In[67]:
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#sigmoid function or logistic function is used as a hypothesis function in classification problems
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def sigmoid_function(z):
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return 1/(1+np.exp(-z))
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def cost_function(h,y):
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return (-y*np.log(h)-(1-y)*np.log(1-h)).mean()
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# here alpha is the learning rate, X is the feature matrix,y is the target matrix
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def logistic_reg(alpha,X,y,max_iterations=70000):
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converged=False
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iterations=0
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theta=np.zeros(X.shape[1])
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while not converged:
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z=np.dot(X,theta)
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h=sigmoid_function(z)
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gradient = np.dot(X.T,(h-y))/y.size
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theta=theta-(alpha)*gradient
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z=np.dot(X,theta)
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h=sigmoid_function(z)
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J=cost_function(h,y)
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iterations+=1 #update iterations
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if iterations== max_iterations:
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print("Maximum iterations exceeded!")
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print("Minimal cost function J=",J)
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converged=True
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return theta
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# In[68]:
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if __name__=='__main__':
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iris=datasets.load_iris()
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X = iris.data[:, :2]
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y = (iris.target != 0) * 1
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alpha=0.1
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theta=logistic_reg(alpha,X,y,max_iterations=70000)
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print(theta)
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def predict_prob(X):
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return sigmoid_function(np.dot(X,theta)) # predicting the value of probability from the logistic regression algorithm
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plt.figure(figsize=(10, 6))
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plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], color='b', label='0')
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plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], color='r', label='1')
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x1_min, x1_max = X[:,0].min(), X[:,0].max(),
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x2_min, x2_max = X[:,1].min(), X[:,1].max(),
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xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))
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grid = np.c_[xx1.ravel(), xx2.ravel()]
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probs = predict_prob(grid).reshape(xx1.shape)
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plt.contour(xx1, xx2, probs, [0.5], linewidths=1, colors='black');
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plt.legend();
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