Notation

[Make42]

I am looking forward to your code! It an interesting paper.

Is your arxiv paper already your final version or is it possible to still suggest improvements? My main suggestion is to rework some of the notations. Just a short example: You use

{x_i}_{i\in{ 1:N }}

which already considered to be a notation reserved to denote sequences, but you use it to describe a set. Instead, I'd suggest to use the set builder notation: https://en.m.wikipedia.org/wiki/Set-builder_notation

Also the notation of the pairwise cost matrix is difficult.

Is <> denoting an inner product? How is it defined if it is not the standard for product? Logically I think you want to use the element wise hardamard product, which uses a circle with a dot in the middle as a symbol (but should still be mentioned as such), together with a L2 norm: || A⊙ \Delta(...) ||_2

How is A chosen in (2)?