Rare Rows, Made in Between

In When One Class Is Rare, SMOTE gave the rare class more rows by interpolating between real ones: each new row is a plausible point placed between a real rare row and one of its rare neighbours, not a copy. Here you build that step yourself.

To make one new row, SMOTE:

1. starts from a rare row $a$;
2. lists the other rare rows by straight-line (Euclidean) distance from $a$, nearest first. Rows of the common class are never neighbours;
3. picks one of them, $c$;
4. picks a gap $g$ between 0 and 1, and puts the new row at

feature by feature. So $g = 0$ lands exactly on $a$, $g = 1$ lands exactly on $c$, and $g = 0.5$ lands halfway between them.

The library makes the choices in steps 3 and 4 at random. To make your output checkable, every new row here comes with its choices written down.

Task: write smote_rows(X, y, minority, recipes).

• X is a list of rows, each a list of numbers, and y holds one label per row. minority is the rare class's label.
• recipes is a list of (row, rank, gap) tuples, one per new row. row is the index in X of the starting rare row $a$. rank picks the neighbour $c$: 1 is the nearest other rare row, 2 the second nearest, and so on. gap is $g$.
• If two rare rows are exactly the same distance from $a$, the one with the smaller index in X counts as nearer.
• A row is never its own neighbour. A different rare row that happens to hold identical values is a genuine neighbour, at distance 0.

Return the new rows, one per recipe and in the same order, with every value rounded to 4 decimal places.

In every test, each recipe's row is a rare row, and its rank is never more than the number of other rare rows.