Uncovering block structures in large rectangular matrices

In this article, we proposed a conceptually simple, efficient, and easily implemented approach, named Block-structure Analysis on Rectangular Matrix (BARM), for learning the block structure in a large rectangular data matrix corrupted with random effects and white noise. With the possible unknown order of row or column variables, their group structures can be directly uncovered based on the singular values and singular vectors of the scaled data matrix. We also established the asymptotic properties of the proposed approach under regular conditions. Extensive experimental evaluations also demonstrate the reliability and robustness of the proposed approach.