Problem formulation model

Question

I have to define a problem formulation for a classification supervised task in machine learning. In input I have 15 predictors $$ X= {x1,...x2} $$ and the output Y can take 2 values $$ Y = (Label1 , Label2) = (0,1) $$. Is it correct to say the model f that I am looking for is: $$ f:\mathbb{R}\times\mathbb{R} \rightharpoonup\left\{ Label1,Label2\right\} $$

Or as I have 15 inputs, R should have a shape to reflect input data and the formulation should be: $$ f:\mathbb{R}^{15} \rightharpoonup\left\{ Label1,Label2\right\} $$

Answer 1

Your domain should describe the number of predictor.

Assuming your predictors are real number, it should be $\mathbb{R}^{15}$.