I am studying t-distributed stochastic neighbor embedding, and I am trying to figure out the mathematical expression of the stochastic neighbor embedding. https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding elucidate the t-distributed Stochastic Neighbor Embedding and https://wikimedia.org/api/rest_v1/media/math/render/svg/104366ddd486f8bacde07597eadb24733839baa7 is the URL of the mathematical expression. I have three questions about the formula.
1- What is the symbol that exists at the end of the numerator and denominator and its multiplier is two?
2- What is the double vertical bar? Is it "norm"? https://en.wikipedia.org/wiki/Vertical_bar
3- What does the sum symbol tell us at the denominator?
Thanks in advance.