ML-Logistic regression
Sigmoid function & Hypothesis representation
Before this post, our goal was to “somehow” curve our hypothesis function. Well, now’s the time for that “somehow”.
Sigmoid function
The sigmoid function allows us to curve our hypothesis function.
Sigmoid converges to 1 when x → ∞, and converges to 0 when x → -∞.
Hypothesis Representation
So we have the tools to manipulate the values to fit into the range of 0 and 1.
We want to change the values of our original linear regression hypothesis, so we apply the sigmoid function g(z).
About the sigmoid function
Why does the sigmoid function look like that? Let’s look at the detailed math.
First, we start from the graph y = exp(x).
The exp(-x) will look like this.
So we can derive these facts:
Now we get the sigmoid function.
So how do we divide the examples and put it into separate classes?
Simple. If the hypothesis function exceeds 0.5, we put it into Class 1, and if the hypothesis function is less than 0.5, we put it into Class 0.
