logistic_visualize.py

# visualizes the Bayes solution
#
# the notes for this class can be found at: 
# https://www.udemy.com/data-science-logistic-regression-in-python

import numpy as np
import matplotlib.pyplot as plt

N = 100
D = 2


X = np.random.randn(N,D)

# center the first 50 points at (-2,-2)
X[:50,:] = X[:50,:] - 2*np.ones((50,D))

# center the last 50 points at (2, 2)
X[50:,:] = X[50:,:] + 2*np.ones((50,D))

# labels: first 50 are 0, last 50 are 1
T = np.array([0]*50 + [1]*50)

# add a column of ones
# ones = np.array([[1]*N]).T
ones = np.ones((N, 1))
Xb = np.concatenate((ones, X), axis=1)

def sigmoid(z):
    return 1/(1 + np.exp(-z))

# get the closed-form solution
w = np.array([0, 4, 4])

# calculate the model output
z = Xb.dot(w)
Y = sigmoid(z)

plt.scatter(X[:,0], X[:,1], c=T, s=100, alpha=0.5)

x_axis = np.linspace(-6, 6, 100)
y_axis = -x_axis
plt.plot(x_axis, y_axis)
plt.show()