perception.py

import numpy as np
import matplotlib.pyplot as plt 

def draw(x1,x2):
  ln=plt.plot(x1,x2)
 
def sigmoid(score):
  return 1/(1+np.exp(-score))

def calculate_error(line_parameters, points, y):
    n= points.shape[0]
    p= sigmoid(points * line_parameters)
    cross_entropy = -(1/n)*(np.log(p).T * y + np.log(1-p).T *(1-y))
    return cross_entropy

def gradient_descent(line_parameters, points, y, alpha):
    n= points.shape[0]
    for i in range(20000):
        p= sigmoid(points * line_parameters)
        gradient = points.T*(p-y)*(alpha / n)
        line_parameters = line_parameters - gradient

        w1 = line_parameters.item(0)
        w2 = line_parameters.item(1)
        b = line_parameters.item(2)

        x1=np.array([points[:,0].min(), points[:,0].max()])
        x2= -b/w2 + (x1*(-w1/w2))
        print(calculate_error(line_parameters, points, y))
    draw(x1, x2)


n_pts=100
np.random.seed(0)
bias= np.ones(n_pts)
top_region=np.array([np.random.normal(10,2,n_pts), np.random.normal(12,2,n_pts), bias]).T
bottom_region= np.array([np.random.normal(5,2, n_pts), np.random.normal(6,2, n_pts), bias]).T
all_points=np.vstack((top_region, bottom_region))
line_parameters = np.matrix([np.zeros(3)]).T
#x1=np.array([bottom_region[:,0].min(), top_region[:,0].max()])
#x2= -b/w2 + (x1*(-w1/w2))
linear_combination= all_points*line_parameters 
y = np.array([np.zeros(n_pts), np.ones(n_pts)]).reshape(n_pts*2, 1)
#print(y)  

_, ax= plt.subplots(figsize=(4,4))
ax.scatter(top_region[:,0], top_region[:,1], color='r')
ax.scatter(bottom_region[:,0], bottom_region[:,1], color='b')
#draw(x1,x2)
gradient_descent(line_parameters, all_points, y, 0.06)
plt.show()


print(calculate_error(line_parameters, all_points, y))