Abstract. Sparse representation of signals has been the focus of much research in the recent years. A vast majority of existing algorithms deal with vectors, and higher-order data like images are dealt with by vectorization. However, the structure of the data may be lost in the process, leading to a poorer representation and overall performance degradation. In this paper we propose a novel approach for sparse representation of positive definite matrices, where vectorization will destroy the inherent structure of the data. The sparse decomposition of a positive definite matrix is formulated as a convex optimization problem, which falls under the category of determinant maximization (MAXDET) problems [1], for which efficient interior point algorithms exist. Experimental results are shown with simulated examples as well as in real-world computer vision applications, demonstrating the suitability of the new model. This forms the first step toward extending the cornucopia of sparsity-based algorithms to positive definite matrices.
The tensor sparse model introduced in REF learns a sparse representation over positive definite matrices.
Tensor Sparse Coding for Region Covariances
ECCV
Computer Science