A central challenge in protein modeling research and protein structure prediction in particular is known as decoy selection. The problem refers to selecting biologically-active/native tertiary structures among a multitude of physically-realistic structures generated by template-free protein structure prediction methods. Research on decoy selection is active. Clustering-based methods are popular, but they fail to identify good/near-native decoys on datasets where near-native decoys are severely under-sampled by a protein structure prediction method. Reasonable progress is reported by methods that additionally take into account the internal energy of a structure and employ it to identify basins in the energy landscape organizing the multitude of decoys. These methods, however, incur significant time costs for extracting basins from the landscape. In this paper, we propose a novel decoy selection method based on non-negative matrix factorization. We demonstrate that our method outperforms energy landscape-based methods. In particular, the proposed method addresses both the time cost issue and the challenge of identifying good decoys in a sparse dataset, successfully recognizing near-native decoys for both easy and hard protein targets.