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About Part 2.4 in the FSQN paper

Hello,

I have read your paper about feature specific quantile normalization in part 2.4, and did not understand it very clearly. According to your source code, the right hand side of projection formula in (3) is a product and thus a real number, but the left hand side of (3) seems to be a vector, instead of formula. Therefore, I am wondering if it is a mistake in the paper?

Besides, would you like to tell me what the function normalize.quantiles.use.target exactly does in your code? Do you know how to present the calculation the function does in the form of mathematical formula?

Thank you very much!

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