  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.
