2014/03/24 by Xuan Vinh Doan, Doan, Xuan Vinh, Stephen A. Vavasis +2
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Remote-Sensing Image Classification #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.1403.5901
openalex publication_date 2014/03/24 · arxiv created 2015/11/30 · arxiv updated 2015/12/01 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We propose a convex optimization formulation with the Ky Fan 2-k-norm and ℓ1-norm to find k largest approximately rank-one submatrix blocks of a given nonnegative matrix that has low-rank block diagonal structure with noise. We analyze low-rank and sparsity structures of the optimal solutions using properties of these two matrix norms. We show that, under certain hypotheses, with high probability, the approach can recover rank-one submatrix blocks even when they are corrupted with random noise and inserted into a much larger matrix with other random noise blocks.