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.