SUBSPACE CLUSTERINGWITH 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 al-gorithm for learning unions of subspaces directly from a collection of data; our approach is based upon forming mini-mum `2-norm (least-squares) representations of a signal with respect to other signals in the collection. The resulting repre-sentations 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 represen-tations of collections of data provide significant advantages over current methods that rely upon sparse representations. Index Terms — Subspace clustering, unions of subspaces, least-squares methods, sparsity, sparse recovery methods 1