Linear Separability

Question 1

What is a linear classifier

Answer 1

A simple classifier that can only generate linear decision boundaries

Question 2

Rewrite the decision boundary formula to have one side = 0

Answer 2

When priors are equal, using bayes rule

Question 3

What is the discriminant function gi(x) used for

Answer 3

We can define a discriminant function gi(x) for each class i that is used to classify every point in out features space (x)

x belongs to ωi if gi(x) > gj(x) else x belongs to ωj

The decision boundary is defined by

gi(x) - gj(x)

Question 4

What do we define the discriminant function as

Answer 4

For our bayesian classifiers, define the natural log as our discriminant function

gi(x) = ln(P(ωi|x)

Then applying bayes rule we can get this (image)

Question 5

Why use the discriminant function

Answer 5

When using distributions like guassian, the ln cancels out all the exponentials making the maths easier

Also, to get the product you have to sum them rather than multiply them