# What is the definition of margin for multi-class classification?

I heard the definition was as follows:

Let $y_{best} = arg \max_{c \in Classes} f(x)_c$ be the best class and let the prediction function be an output vector $f(x) \in R^{|Classes|}$. Then define:

$$margin = f(x)_{y_{best}} - \max_{c \neq y_{best}} f(x)_c$$

there seems something fishy becaue for me there should be some sense of dividing by some "normalization" because otherwise it seems like "functional margin". Anyway, is this correct? How does it compare to the binary margin and functional margin definitions?