Algorithm 1.

Joint Harmonization and Classification.

1:	Set ϱ = 0.1, $\sigma =\sqrt{10},{\epsilon }_B={\epsilon }_P={10}^{-3}$ (according to [4]) and U′ = 0, w′ = 0, q′ = 0, v′ = 1
2:	Repeat
3:	Repeat (Block Coordinate Descent)
4:	U″ ← U′, w″ ← w′, q″ ← q′, v″ v′
5:	U′ ←argminU (1 − λ)lD (U, v′, q′) + λhC (U) (via Gradient Descent)
6:	$(v^{\prime },q^{\prime })\leftarrow \text{arg}{min}_{v,q}(1-\mathrm{\lambda })l_D(U^{\prime },v,q)+\mathit{\varrho }\Vert w^{\prime }-q{\Vert }_2^2$ (via Gradient Descent)
7:	Update w′ by
	Sort groups gj(q′) so that $\Vert g_{j_1}(q^{\prime }){\Vert }_2\ge \Vert g_{j_2}(q^{\prime }){\Vert }_2\ge \dots \ge \Vert g_{j_{n_G}}(q^{\prime }){\Vert }_2$
	Define $𝕀$ to be the set of indices of q′ associated with groups $g_{j_1},\dots ,g_{j_k}{w}_i^{\prime }\leftarrow q_i^{\prime }$ if $q_i^{\prime }$ ∈ $𝕀$ and 0 otherwise.
8:	Until $max\{\frac{\Vert U\prime -U″{\Vert }_{max}}{max\{\Vert U\prime {\Vert }_{max},1\}},\frac{|v\prime -v″|}{max\left\{\right|v\prime |,1\}},\frac{\Vert w\prime -w″{\Vert }_{max}}{max\{\Vert w\prime {\Vert }_{max},1\}},\frac{\Vert q\prime -q″{\Vert }_{max}}{max\{\Vert q\prime {\Vert }_{max},1\}}\}<{\epsilon }_B,$
9:	ϱ ← σ · ϱ
10:	Until ‖w′ − q′ ‖max <εP.