# Create linearly separable data in 2d
import numpy as np
import matplotlib.pyplot as plt
%config InlineBackend.figure_format = 'retina'
from sklearn.datasets import make_classification
X, y = make_classification(n_samples=100, n_features=2, n_redundant=0, n_informative=2,
n_clusters_per_class=2, class_sep=1.5, random_state=42)
plt.scatter(X[:, 0], X[:, 1], marker='o', c=y, s=25, edgecolor='k')<matplotlib.collections.PathCollection at 0x12b5ed280>
from sklearn.linear_model import LogisticRegression
# Without regularization
clf = LogisticRegression(random_state=0, penalty='none').fit(X, y)
clf.coef_, clf.intercept_(array([[26.23339925, -5.01002931]]), array([1.74951957]))# Create a surface plot of the decision boundary for any theta_0, theta_1, theta_2
def plot_decision_boundary(theta_0, theta_1, theta_2):
x_lin = np.linspace(-4, 4, 100)
y_lin = -(theta_0 + theta_1 * x_lin) / theta_2
plt.plot(x_lin, y_lin, 'k--', label='Decision boundary ($\sigma(z) = 0.5$))', lw=5)
plt.xlim(-4, 4)
plt.ylim(-4, 4)
plt.xlabel(r'$x_1$')
plt.ylabel(r'$x_2$')
plt.title(r'$\theta_0 = {:.2f}, \theta_1 = {:.2f}, \theta_2 = {:.2f}$'.format(theta_0, theta_1, theta_2))
# Plot the probability of class 1 contour
x1, x2 = np.meshgrid(np.linspace(-4, 4, 100), np.linspace(-4, 4, 100))
z = 1 / (1 + np.exp(-(theta_0 + theta_1 * x1 + theta_2 * x2)))
plt.contourf(x1, x2, z, linestyles='dashed')
plt.colorbar()
# Plot the data
plt.scatter(X[:, 0], X[:, 1], marker='o', c=y, s=25, edgecolor='k')
plt.legend(loc='best')# Create a slider widget to explore the decision boundary
from ipywidgets import interact, FloatSlider
interact(plot_decision_boundary,
theta_0=FloatSlider(min=-2, max=3, step=0.1, value=0.1),
theta_1=FloatSlider(min=-5, max=40, step=0.5, value=0.1),
theta_2=FloatSlider(min=-10, max=5, step=0.1, value=0.1))
<function __main__.plot_decision_boundary(theta_0, theta_1, theta_2)># Create a 3d plot of the decision boundary for any theta_0, theta_1, theta_2
from mpl_toolkits.mplot3d import Axes3D
def plot_decision_boundary_3d(theta_0, theta_1, theta_2, azim=30, elev=30):
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
x_lin = np.linspace(-4, 4, 100)
y_lin = np.linspace(-4, 4, 100)
X_g, Y_g = np.meshgrid(x_lin, y_lin)
Z_g = -(theta_0 + theta_1 * X_g + theta_2 * Y_g)
#ax.plot_surface(X_g, Y_g, Z_g, alpha=0.2)
ax.set_xlabel(r'$x_1$')
ax.set_ylabel(r'$x_2$')
ax.set_zlabel(r'$x_3$')
ax.set_title(r'$\theta_0 = {:.2f}, \theta_1 = {:.2f}, \theta_2 = {:.2f}$'.format(theta_0, theta_1, theta_2))
# Scatter plot of data (class 1 is Z = 1, class 0 is Z = 0)
ax.scatter(X[y == 1, 0], X[y == 1, 1], 1, marker='o', c='b', s=25, edgecolor='k')
ax.scatter(X[y == 0, 0], X[y == 0, 1], 0, marker='o', c='y', s=25, edgecolor='k')
# Plot the 3d sigmoid function
x1, x2 = np.meshgrid(np.linspace(-4, 4, 100), np.linspace(-4, 4, 100))
z = 1 / (1 + np.exp(-(theta_0 + theta_1 * x1 + theta_2 * x2)))
ax.plot_surface(x1, x2, z, alpha=0.2, color='green')
# Rotate the plot so that the sigmoid function is visible
ax.view_init(azim, elev)
# Plot the decision plane
ax.plot_surface(X_g, Y_g, Z_g, alpha=0.2, color='k')
# Create a slider widget to explore the decision boundary
from ipywidgets import interact, FloatSlider
interact(plot_decision_boundary_3d,
theta_0=FloatSlider(min=-2, max=3, step=0.1, value=0.1),
theta_1=FloatSlider(min=-5, max=40, step=0.5, value=0.1),
theta_2=FloatSlider(min=-10, max=5, step=0.1, value=0.1),
azim=FloatSlider(min=-180, max=180, step=1, value=30),
elev=FloatSlider(min=-180, max=180, step=1, value=30))
<function __main__.plot_decision_boundary_3d(theta_0, theta_1, theta_2, azim=30, elev=30)># Create two 3d plot any theta_0, theta_1, theta_2
# First showing the decision boundary
# Second showing the probability of class 1
from mpl_toolkits.mplot3d import Axes3D
def plot_decision_boundary_3d(theta_0, theta_1, theta_2, azim=30, elev=30):
fig = plt.figure(figsize=(10, 8))
ax1 = fig.add_subplot(121, projection='3d')
ax2 = fig.add_subplot(122, projection='3d')
x_lin = np.linspace(-4, 4, 100)
y_lin = np.linspace(-4, 4, 100)
X_g, Y_g = np.meshgrid(x_lin, y_lin)
Z_g = -(theta_0 + theta_1 * X_g + theta_2 * Y_g)
#ax.plot_surface(X_g, Y_g, Z_g, alpha=0.2)
ax1.set_xlabel(r'$x_1$')
ax1.set_ylabel(r'$x_2$')
ax1.set_zlabel(r'$x_3$')
ax1.set_title(r'$\theta_0 = {:.2f}, \theta_1 = {:.2f}, \theta_2 = {:.2f}$'.format(theta_0, theta_1, theta_2))
# Scatter plot of data (class 1 is Z = 1, class 0 is Z = 0)
ax1.scatter(X[y == 1, 0], X[y == 1, 1], 1, marker='o', c='b', s=25, edgecolor='k')
ax1.scatter(X[y == 0, 0], X[y == 0, 1], 0, marker='o', c='y', s=25, edgecolor='k')
# Plot the 3d sigmoid function
x1, x2 = np.meshgrid(np.linspace(-4, 4, 100), np.linspace(-4, 4, 100))
z = 1 / (1 + np.exp(-(theta_0 + theta_1 * x1 + theta_2 * x2)))
# Plot the decision plane
ax1.plot_surface(X_g, Y_g, Z_g, alpha=0.2, color='k')
# Plot the probability of class 1
ax2.plot_surface(x1, x2, z, alpha=0.2, color='black')
ax2.scatter(X[y == 1, 0], X[y == 1, 1], 1, marker='o', c='b', s=25, edgecolor='k')
ax2.scatter(X[y == 0, 0], X[y == 0, 1], 0, marker='o', c='y', s=25, edgecolor='k')
# Rotate the plot so that the sigmoid function is visible
ax1.view_init(azim, elev)
ax2.view_init(azim, elev)# Create a slider widget to explore the decision boundary
from ipywidgets import interact, FloatSlider
interact(plot_decision_boundary_3d,
theta_0=FloatSlider(min=-2, max=3, step=0.1, value=0.1),
theta_1=FloatSlider(min=-5, max=40, step=0.5, value=0.1),
theta_2=FloatSlider(min=-10, max=5, step=0.1, value=0.1),
azim=FloatSlider(min=-180, max=180, step=1, value=30),
elev=FloatSlider(min=-180, max=180, step=1, value=30))
<function __main__.plot_decision_boundary_3d(theta_0, theta_1, theta_2, azim=30, elev=30)>