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102 lines
2.4 KiB
Python
102 lines
2.4 KiB
Python
#!/usr/bin/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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# In[63]:
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# importing all the required libraries
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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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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(
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alpha,
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X,
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y,
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max_iterations=70000,
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):
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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),
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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(
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xx1,
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xx2,
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probs,
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[0.5],
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linewidths=1,
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colors='black',
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)
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plt.legend()
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