Grassmannian sparse representations

Abstract. We present Grassmannian sparse representations (GSR), a sparse representation Grassmann learning framework for efficient classification. Sparse representation classification offers a powerful approach for recognition in a variety of contexts. However, a major drawback of sparse representation methods is their computational performance and memory utilization for high-dimensional data. A Grassmann manifold is a space that promotes smooth surfaces where points represent subspaces and the relationship between points is defined by the mapping of an orthogonal matrix. Grassmann manifolds are well suited for computer vision problems because they promote high between-class discrimination and within-class clustering, while offering computational advantages by mapping each subspace onto a single point. The GSR framework combines Grassmannian kernels and sparse representations, including regularized least squares and least angle regression, to improve high accuracy recognition while overcoming the drawbacks of performance and dependencies on high dimensional data distributions. The effectiveness of GSR is demonstrated on computationally intensive multiview action sequences, three-dimensional action sequences, and face recognition datasets.