What does this mean from Andrew’s Lab - Softmax;
{\mathbb 1}\{y == n\} == \Biggl \{ \begin{aligned} 1, \;\;\; \text{if} \; \text{y == n.} \\ 0, \;\;\; \text{otherwise.}\\ \end{aligned}
It’s confusing.
Shouldn’t it just be this;
\text{Indicator} == \Biggl \{ \begin{aligned} 1, \;\;\; \text{if} \; \text{y == n.} \\ 0, \;\;\; \text{otherwise.}\\ \end{aligned}
It would be clearer and more mathematically standard to write:
𝟙 \{y = n\} = \begin{cases} 1, & \text{if } y = n \\ 0, & \text{otherwise} \end{cases}
I still don’t know what that means.
Perhaps you could explain in words only what it means then the correct mathematical description can be written?
For me I think it can be described as follow;
“if the output label y is equal to n, where n is in the range 0 to N-1, then the Indicator Function should be 1, otherwise it should be 0.”
It also can be defined as follows:
“The indicator function 𝟙\{{\rm predicate}\} returns 1 if the predicate is true, and 0 otherwise.” It doesn’t place any constraints on y or n.
Thank you.
I have never seen this notation before. It’s a pity Andrew didn’t make it clearer that that is what he is doing in his video presentation.
What is the significance of the different font used for the number 1 at the extreme left of this expression for the indicator function?