Algorithm 2.

Re-clustering procedure given classifiers

Input: positive samples ${\mathbf{x}}_i^{+}$, classifiers βl, current cluster assignment which assigns sample i to cluster l(i).

for all i ∈ {1, …, N+} do

for all l ∈ {1, …, L} do

calculate the projection $a_i^l$ of positive sample i onto the classifier for cluster l using only elements in a feature set 𝒞: $a_i^l={{\mathbf{x}}_{i,𝒞}^{+}}^{\prime }{\mathit{\beta }}_{𝒞}^l$;

end for

update cluster assignment of sample i from l(i) to $l^{\ast }(i)=\text{arg }\underset{l}{\text{max}}{a}_i^l$, subject to $${{\mathbf{x}}_i^{+}}^{\prime }{\mathit{\beta }}^{l^{\ast }(i)}+{\beta }_0^{l^{\ast }(i)}\ge {{\mathbf{x}}_i^{+}}^{\prime }{\mathit{\beta }}^{l(i)}+{\beta }_0^{l(i)}.$$ (5)

end for