Algorithm 2.

Sidification

1: procedure Sidification(${\left({\mathbf{X}}_i\right)}_{i=1}^n$, δ = 1

2:  Translate each continuous feature so that they are positive and all have the same maximum value (note that the minimum value can differ over variables)

3:  Order the variables in terms of their range with variables with largest range appearing first. This applies only to continuous variables (factors are placed randomly at the end)

4:  Convert any categorical variable with more than two categories to a set of zero-one dummy variables with one for each category

5:  Add δ to the first variable

6:  for number of input variables, excluding the first do

7:   Add δ plus the maximum of the previous input variable to the current variable

8:  end for

9:  ${\left({\mathbf{X}}_i\right)}_{i=1}^n$ have now been staggered to ${\left({\mathbf{Y}}_i\right)}_{i=1}^n={\left({\varphi }_n\right({\mathbf{X}}_i\left)\right)}_{i=1}^n$ the main SID features

10:  for all pairs of main SID features (from Line 9) do

11:   if a pair consists of two dummy variables then

12:    Interaction is a four level factor for each dummy variable combination

13:   else

14:    Create interaction variable by multiplying them

15:   end if

16:  end for

17:  This yields ${\left({\mathbf{Z}}_i\right)}_{i=1}^n={\left({\psi }_n\right({\varphi }_n\left({\mathbf{X}}_i\right))}_{i=1}^n$ the SID interaction features

18: end procedure

19: return ${\mathcal{L}}_n^S={({\mathbf{Y}}_i,{\mathbf{Z}}_i)}_{i=1}^n={\left({\varphi }_n\right({\mathbf{X}}_i),{\psi }_n({\varphi }_n\left({\mathbf{X}}_i\right)\left)\right)}_{i=1}^n$ the sidified data