The key issue affecting Cognitive Diagnostic Models (CDMs) is how to specify attributes and the Q-matrix. In this paper, we first attempt to use the Boolean Matrix Factorization (BMF) method to express conjunctive models in CDMs. Because BMF is an NPhard problem [2], we propose a recursive method that updates the attribute matrix (its rank equals to one) in each step. As Boolean algebra is irre...

This problem generalizes the spectral norm of a matrix (p = q = 2) and the Grothendieck problem (p = ∞, q = 1), and has been widely studied in various regimes. When p ≥ q, the problem exhibits a dichotomy: constant factor approximation algorithms are known if 2 ∈ [q, p], and the problem is hard to approximate within almost polynomial factors when 2 / ∈ [q, p]. The regime when p < q, known as hy...