I was doing research work for a paper that I need to write for my master studies and I came across the cosine similarity concept.
After a quick look in wikipedia there's this mathematical formula that I don't fully understand:
In my use-case we're working with sets of words (so called text strings) and the top of the formula is the dot product of the two sets.
What I've never seen is the || symbols for a set. I know that |A| stands for the cardinality of the set A but I've never seen the other symbol. Is it the same?
The Wikipedia article on "Cosine similarity" you mentioned says explicitly that $A$ and $B$ are vectors:
For a vector $A=(A_1,\cdots,A_n)$ in the Euclidean space $\mathbb{R}^n$, its "norm" is given by $$ \|A\|:=\sqrt{A_1^2+\cdots+A_n^2} $$