Biclustering aims to identify coherent submatrices by jointly selecting subsets of rows and columns. Sparse low-rank factorization is scalable and interpretable, yet in rank- \(K\) settings it often suffers from cross-component co-activation: when true biclusters overlap, different components may repeatedly select the same variables, yielding redundant and unstable supports. We propose a global rank- \(K\) sparse factorization framework with a mixed product-based penalty that couples within-component sparsity and explicit cross-component de-redundancy, allowing limited, interpretable overlap while avoiding unnecessary repetition. We develop an efficient coordinate-wise updating algorithm and use a support-constrained refit-BIC for robust hyperparameter selection. Simulations are organized into three parts to isolate architectural effects, evaluate the penalty under randomized overlaps and complex signals, and benchmark rectangular (asymmetric) settings against representative baselines. An application to the NKI breast cancer microarray dataset further demonstrates clearer, less redundant biclusters.
