A blind sparse approach for estimating constraint matrices in Paralind data models

In this paper we address the problem of estimating the interaction matrices of PARALIND decomposition. In general, this is an ill-posed problem admitting an infinite number of solutions. First we study the gain of imposing sparsity constraints on the interaction matrices, in terms of model identifiability. Then, we propose a new algorithm (S-PARALIND) for fitting the PARALIND model, using a ℓ₂-ℓ₁ optimization step for estimating the interaction matrix. This new approach provides more accurate and robust estimates of the constraint matrices than ALS-PARALIND, thus improving the interpretability of the PARALIND decomposition.