Merge branch 'master' of git://github.com/epicalyx/Python into epicalyx-master

machine_learning/logistic_regression.py

@@ -0,0 +1,98 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# # Logistic Regression from scratch
+
+# In[62]:
+
+
+''' Implementing logistic regression for classification problem 
+     Helpful resources : 1.Coursera ML course    2.https://medium.com/@martinpella/logistic-regression-from-scratch-in-python-124c5636b8ac'''
+
+
+# In[63]:
+
+
+#importing all the required libraries
+import numpy as np
+import matplotlib.pyplot as plt
+get_ipython().run_line_magic('matplotlib', 'inline')
+from sklearn import datasets
+
+
+# In[67]:
+
+
+#sigmoid function or logistic function is used as a hypothesis function in classification problems
+def sigmoid_function(z):
+    return 1/(1+np.exp(-z))
+
+
+def cost_function(h,y):
+    return (-y*np.log(h)-(1-y)*np.log(1-h)).mean()
+
+# here alpha is the learning rate, X is the feature matrix,y is the target matrix
+def logistic_reg(alpha,X,y,max_iterations=70000):
+    converged=False
+    iterations=0
+    theta=np.zeros(X.shape[1])
+    
+    
+    while not converged:
+        z=np.dot(X,theta)
+        h=sigmoid_function(z)
+        gradient = np.dot(X.T,(h-y))/y.size
+        theta=theta-(alpha)*gradient
+        
+        z=np.dot(X,theta)
+        h=sigmoid_function(z)
+        J=cost_function(h,y)
+       
+     
+        
+        iterations+=1   #update iterations
+        
+        
+        if iterations== max_iterations:
+            print("Maximum iterations exceeded!")
+            print("Minimal cost function J=",J)
+            converged=True
+            
+    return theta
+
+
+
+        
+    
+    
+
+
+# In[68]:
+
+
+if __name__=='__main__':
+    iris=datasets.load_iris()
+    X = iris.data[:, :2]
+    y = (iris.target != 0) * 1
+    
+    alpha=0.1
+    theta=logistic_reg(alpha,X,y,max_iterations=70000)
+    print(theta)
+    def predict_prob(X):
+        return sigmoid_function(np.dot(X,theta))              # predicting the value of probability from the logistic regression algorithm
+        
+    
+    plt.figure(figsize=(10, 6))
+    plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], color='b', label='0')
+    plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], color='r', label='1')
+    x1_min, x1_max = X[:,0].min(), X[:,0].max(),
+    x2_min, x2_max = X[:,1].min(), X[:,1].max(),
+    xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))
+    grid = np.c_[xx1.ravel(), xx2.ravel()]
+    probs = predict_prob(grid).reshape(xx1.shape)
+    plt.contour(xx1, xx2, probs, [0.5], linewidths=1, colors='black');
+
+    plt.legend();
+    
+    
+