Question

The value of a weight vector is given as (w1=3, w2=-2, w0=1) for a linear model with soft threshold (sigmoid) function f(x). Define a decision boundary, where the values of the feature vector x result in f(x)=0.5. Plot the decision boundary in two dimensions.

Answer 1

SOLUTION:

1.

We consider a linear sample between -5 to 5 consisting of 100 hunderd sample sample to plot the sigmoid function and its decision boundary.

In python, a sigmoid function can be written as

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

we plot the sigmoid function and decision boundary with the following code:

import matplotlib.pyplot as plt

import numpy as np

x_sample = np.linspace(-5,5,100)

plt.plot(x_sample, sigmoid(x_sample))
plt.plot([-5,5],[.5,.5])

plt.xlabel("z")
plt.ylabel("sigmoid(z)")

plt.show()

The 2D graph of sigmoid function and decision boundary look like:

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