Given a metric measure space, we evaluate the sign intermixing of a real valued function using the KR-norm (= Kantorovich-Rubinstein-Wasserstein optimal transportation cost). The smaller is the KR-norm, the better is the sign intermixing. For the standard $L^2$ space over a d-dimensional cube, we find sharp smallness intervals where the KR-norms of a Riesz bases/frames "must be" and/or "can be". Possible applications to other compact embeddings of $L^2$ spaces are also discussed. The talk is mostly based on a joint work with Alexander Volberg.