In this paper, we introduce and formalize a rank-one partitioning learning paradigm that unifies partitioning methods that proceed by summarizing a data set using a single vector that is further used to derive the final clustering partition. Using this unification as a starting point, we propose a novel algorithmic solution for the partitioning problem based on rank-one matrix factorization and denoising of piecewise constant signals. Finally, we propose an empirical demonstration of our findings and demonstrate the robustness of the proposed denoising step. We believe that our work provides a new point of view for several unsupervised learning techniques that helps to gain a deeper understanding about the general mechanisms of data partitioning.