Algorithm 1 .

IVC over all clusterings

Input: π1, …, πG, with corresponding number of clusters κ1, …, κG, respectively.

1: loop ℓ ∈ {1, 2, …, G}

2: π* = πℓ with clusters $V_1^{\left(\ell \right)}$, …, $V_{{\kappa }_{\ell }}^{\left(\ell \right)}$

3: repeat

4:  Let πj($V_k^{\left(\ell \right)}$) := arg maxs |{x ∈ $V_k^{\left(\ell \right)}$ : πj(x) = s}| for j = 1, …, G and k = 1, … κℓ

5:  Let $C_k^{\left(\ell \right)}$ := (π1($V_k^{\left(\ell \right)}$), …, πG($V_k^{\left(\ell \right)}$)) for k = 1, …, κℓ.

6:  loop i ∈ {1, 2, … n}

7:   Let yi := 〈π1(xi), π2(xi), …, πG(xi)〉.

8:   Calculate distance d(yi, $C_k^{\left(\ell \right)}$) := ${\sum }_{j=1}^C$ 𝓘(πj(xi) ≠ πj($V_k^{\left(\ell \right)}$)).

9:   Re-assign label π*(xi) to the value k that minimizes the distance d(yi, $C_k^{\left(\ell \right)}$).

10:  end loop

11: until π* converges.

12: ${\pi }_{\ell }^{\prime }$ := π*

13: end loop

Output: ${\pi }_1^{\prime }$, …, ${\pi }_G^{\prime }$.