Fig. 1

Scheme depicting the role of compressed sensing in NGG and computational complexity with big O notation. In both cases, we compare our method to EMMA with Kinship matrix computation, but we take into account only the matrix inversion part in terms of computational complexity. A is the classic 1D GWAS with at the top the EMMA path, with a final complexity of at least O(p^3), and at the bottom, our 2D GWAS solution, with a final complexity of O(p log(p) n). B is the case of interactions modeling using the proposed model, the computational complexity is shown in terms of the basic p size of input, before the interactions. In this case, the naïve standard approach becomes O(p^6) in computational complexity, whereas our method is now O(p^2 log(p) n), and presents a clear gain in terms of computational time. It is noticeable that, because the compression is in log(p^q), for q whatever the number of interactive SNPs we are interested in, our method will result in a O(p^q log(p) n) algorithm, hence the fact that we say we linearize the computational complexity in term of q