Decision Boundary

Decision Boundary

From the graph of Sigmoid function, we can see that

if $z \ge 0$ then $g(z) = g(\theta^{T}x) = h_\theta(x) \ge 0.5$

Decision boundary is a property of the hypothesis and is NOT a property of the dataset, ie. we don't need to have a dataset to establish the decision boundary. Dataset though indirectly affects decision boundary by fitting the parameter $\theta$
Decision boundary separates the area where y = 0 and where y = 1. It is created by hypothesis function.

Resources:
- https://www.coursera.org/learn/machine-learning/lecture/WuL1H/decision-boundary