How it works

1. Calculate the posterior of category 1 (C1) given X:

where the marginal likelihood $P(X)$ is determined by the size of the cluster around $X$ (the gray circle below).

2. Calculate the same for other categories (C2, ...) (by using the same P(X))
4. Compare $P(C1|X)$ with $P(C2|X)$ to classify

thus you can ignore the marginal likelihood P(X) because it is same for all categories.

Why "Naïve"

• Often although it applies and works, the variables are not independent.