ml_hw2.py

# -*- coding: utf-8 -*-
"""ML-HW2.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/1Xs6z2FGDz3glvuD0XBmqLboFPEBx6bO_

Anshika Gupta [ag8800]

Q1. Perceptron with stochastic gradient descent
"""

import scipy.io
import numpy as np
import matplotlib.pyplot as plt

Dataset_MATLAB = scipy.io.loadmat('data3.mat')
Dataset_MATLAB["data"]
X = Dataset_MATLAB["data"][:,:2]
Y= Dataset_MATLAB["data"][:,-1:]

X

Y

#classifying y as per given constraints
def y_func(y):
  y[y<0]= -1
  y[y>=0]= 1
  return y

# y_func(Y)
# Y

def get_risk(y, y_pred, N):
  risk = np.sum(y_func(np.multiply(y_pred, -y)))
  avg_risk = float(risk/N)
  return (avg_risk)

def get_error(y, y_pred, N):
  error = np.count_nonzero(y_func(y_pred)!=y)
  avg_error = float(error/N)
  return avg_error

def perceptron(x, y):
  num_sample, num_feature = x.shape
  lr         = 1
  weights    = np.random.random_sample((num_feature, 1))
  error_list = []
  risk_list  = []
  iters      = 0

  while iters < max_iters:
      i = np.random.randint(num_sample)
      output = x[i].reshape((1,3)).dot(weights)
      if y_func(np.multiply(y[i],output))[0]==-1:
          weights += lr * x[i].reshape((3, 1)).dot(y[i].reshape((1,1)))
          y_pred = x.dot(weights)
          error_list.append(get_error(y, y_pred, num_sample))
          risk_list.append(get_risk(y, y_pred, num_sample))
          iters += 1
          if error_list[-1]==0:
              break

  return weights, iters, error_list, risk_list

X_new  = np.concatenate((X, np.ones((X.shape[0],1))), axis=1)
max_iters = 1000
weights, iters, error_list, risk_list= perceptron(X_new, Y)

num_sample = X_new.shape[0]
for i in range(num_sample):
    plt.plot(X_new[i,0], X_new[i,1], 'r.')

max_x = max(X_new[:,0])
min_x = min(X_new[:,0])

y_max_x = float(-weights[2] - weights[0] * max_x) / weights[1]
y_min_x = float(-weights[2] - weights[0] * min_x) / weights[1]

plt.plot([min_x, max_x], [y_min_x, y_max_x], '-b')
plt.xlabel('x1')
plt.ylabel('x2')
plt.title("Decision Boundary")
plt.show()

#plotting the error and risk graph 

plt.plot(range(iters), error_list,'r-',label='Error')
plt.plot(range(iters), risk_list, 'b-',label='Risk')
plt.xlabel('Number of iterations')
plt.legend()
plt.show()

iters

"""Hence, the given function takes the above number of iterations to converge."""