# Logic behind SMOTE-NC?

In the SMOTE paper here, the authors present the logic for creating synthetic examples when some of the features are nominal and some are continuous (section 6.1, SMOTE-NC).

This example is provided:

$$F_1$$ = 1 2 3 A B C [Let this be the sample for which we are computing nearest neighbors] $$F_2$$ = 4 6 5 A D E $$F_3$$ = 3 5 6 A B K So, Euclidean Distance between $$F_2$$ and $$F_1$$ would be:

$$Eucl$$ = $$\sqrt{(4-1)^2 + (6-2)^2 + (5-3)^2 + Med^2 + Med^2}$$

Med is the median of the standard deviations of continuous features of the minority class. The median term is included twice for feature numbers $$5: B→D$$ and $$6: C→E$$, which differ for the two feature vectors: $$F_1$$ and $$F_2$$.

The paper lacks explanation about why the nominal features should be affected by the continuous ones.

Can anyone provide such explanation? Did I miss it in the paper?