Minimal Basis Facility Location for Subspace Segmentation

In contrast to the current motion segmentation paradigm that assumes independence between the motion subspaces, we approach the motion segmentation problem by seeking the parsimonious basis set that can represent the data. Our formulation explicitly looks for the overlap between subspaces in order to achieve a minimal basis representation. This parsimonious basis set is important for the performance of our model selection scheme because the sharing of basis results in savings of model complexity cost. We propose the use of affinity propagation based method to determine the number of motion. The key lies in the incorporation of a global cost model into the factor graph, serving the role of model complexity. The introduction of this global cost model requires additional message update in the factor graph. We derive an efficient update for the new messages associated with this global cost model. An important step in the use of affinity propagation is the subspace hypotheses generation. We use the row-sparse convex proxy solution as an initialization strategy. We further encourage the selection of subspace hypotheses with shared basis by integrating a discount scheme that lowers the factor graph facility cost based on shared basis. We verified the model selection and classification performance of our proposed method on both the original Hopkins 155 dataset and the more balanced Hopkins 380 dataset.