Subspace clustering with dense representations

Unions of subspaces have recently been shown to provide a compact nonlinear signal model for collections of high-dimensional data, such as large collections of images or videos. In this paper, we introduce a novel data-driven algorithm for learning unions of subspaces directly from a collection of data; our approach is based upon forming minimum ℓ₂-norm (least-squares) representations of a signal with respect to other signals in the collection. The resulting representations are then used as feature vectors to cluster the data in accordance with each signal's subspace membership. We demonstrate that the proposed least-squares approach leads to improved classification performance when compared to state-of-the-art subspace clustering methods on both synthetic and real-world experiments. This study provides evidence that using least-squares methods to form data-driven representations of collections of data provide significant advantages over current methods that rely upon sparse representations.