For example, I have two groups of data:
group 1:
| x | y |
|---|---|
| 1 | 1 |
| 22 | 23 |
| 38 | 42 |
| 100 | 200 |
group 2:
| x | y |
|---|---|
| 2 | 1 |
| 4 | 0 |
| 37 | 13 |
| 108 | 5 |
I want to find a linear formula with integer coefficients to distinguish these two groups, for example: group 1 satisfies $y - x + 1 > 0$, group 2 satisfies $y - x + 1 \le 0$
So how to find this formula? The number of variables could be greater than 2, maybe $\{x_1, x_2, \dots, x_n\}$, and output is the linear formula with integer coefficients like $$ a_0 + \sum_{i=1}^n a_i x_i > 0, \quad a_0, a_1, \dots, a_n \in \mathbb Z $$
The given data make sure the existence of this formula, and I just want to find one of all satisfying formulas.