Can we realize nonnegative blind source separation with incomplete matrix?

In this paper, we propose an algorithm for nonnegative blind source separation (N-BSS) using incomplete matrix and, moreover, find and prove the theorem on which this algorithm depends. We select the intersection of binary edge features of source estimation to evaluate the effect of N-BSS, rather than the traditional Minimum Volume Simplex (MVS) criterion. We verify the feasibility of the algorithm through an example. Our method does not need the independence hypothesis and local dominance hypothesis of the source, nor does it require the particularity of the shape of the mixtures’ scatterplot. As long as the source is nonnegative and bounded, our method has stronger applicability. Compared with the algorithm of MVS based, the computational complexity of our algorithm does not increase significantly with the increase of the order of the mixing system, so it is suitable for high-order mixing systems.