Have a look at this:
import csv
import numpy as np
import matplotlib.pyplot as plt
def loadCSV(filename):
'''
function to load dataset
'''
with open(filename,"r") as csvfile:
lines = csv.reader(csvfile)
dataset = list(lines)
for i in range(len(dataset)):
dataset[i] = [float(x) for x in dataset[i]]
return np.array(dataset)
def normalize(X):
'''
function to normalize feature matrix, X
'''
mins = np.min(X, axis = 0)
maxs = np.max(X, axis = 0)
rng = maxs - mins
norm_X = 1 - ((maxs - X)/rng)
return norm_X
def logistic_func(beta, X):
'''
logistic(sigmoid) function
'''
return 1.0/(1 + np.exp(-np.dot(X, beta.T)))
def log_gradient(beta, X, y):
'''
logistic gradient function
'''
first_calc = logistic_func(beta, X) - y.reshape(X.shape[0], -1)
final_calc = np.dot(first_calc.T, X)
return final_calc
def cost_func(beta, X, y):
'''
cost function, J
'''
log_func_v = logistic_func(beta, X)
y = np.squeeze(y)
step1 = y * np.log(log_func_v)
step2 = (1 - y) * np.log(1 - log_func_v)
final = -step1 - step2
return np.mean(final)
def grad_desc(X, y, beta, lr=.01, converge_change=.001):
'''
gradient descent function
'''
cost = cost_func(beta, X, y)
change_cost = 1
num_iter = 1
while(change_cost > converge_change):
old_cost = cost
beta = beta - (lr * log_gradient(beta, X, y))
cost = cost_func(beta, X, y)
change_cost = old_cost - cost
num_iter += 1
return beta, num_iter
def pred_values(beta, X):
'''
function to predict labels
'''
pred_prob = logistic_func(beta, X)
pred_value = np.where(pred_prob >= .5, 1, 0)
return np.squeeze(pred_value)
def plot_reg(X, y, beta):
'''
function to plot decision boundary
'''
# labelled observations
x_0 = X[np.where(y == 0.0)]
x_1 = X[np.where(y == 1.0)]
# plotting points with diff color for diff label
plt.scatter([x_0[:, 1]], [x_0[:, 2]], c='b', label='y = 0')
plt.scatter([x_1[:, 1]], [x_1[:, 2]], c='r', label='y = 1')
# plotting decision boundary
x1 = np.arange(0, 1, 0.1)
x2 = -(beta[0,0] + beta[0,1]*x1)/beta[0,2]
plt.plot(x1, x2, c='k', label='reg line')
plt.xlabel('x1')
plt.ylabel('x2')
plt.legend()
plt.show()
if __name__ == "__main__":
# load the dataset
dataset = loadCSV('dataset1.csv')
# normalizing feature matrix
X = normalize(dataset[:, :-1])
# stacking columns wth all ones in feature matrix
X = np.hstack((np.matrix(np.ones(X.shape[0])).T, X))
# response vector
y = dataset[:, -1]
# initial beta values
beta = np.matrix(np.zeros(X.shape[1]))
# beta values after running gradient descent
beta, num_iter = grad_desc(X, y, beta)
# estimated beta values and number of iterations
print("Estimated regression coefficients:", beta)
print("No. of iterations:", num_iter)
# predicted labels
y_pred = pred_values(beta, X)
# number of correctly predicted labels
print("Correctly predicted labels:", np.sum(y == y_pred))
# plotting regression line
plot_reg(X, y, beta)
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