Efficient Sparse Coding Using Hierarchical Riemannian Pursuit

Sparse coding is a class of unsupervised methods for learning sparse representation the input data in form linear combination dictionary and code. This framework has led to state-of-the-art results various signal processing tasks. However, classical learn code based on alternating optimizations, usually without theoretical guarantees either optimality or convergence due non-convexity problem. Recent works with complete provide strong thanks development non-convex optimization. initial approaches learned problem sequentially an atom-by-atom manner, which long execution time. More recent have sought directly entire at once, substantially reduces associated recovery performance degraded finite number samples. In this paper, we propose efficient scheme two-stage The proposed leverages global local Riemannian geometry optimization facilitates fast implementation superb by We further prove that, high probability, can exactly recover any atom target Experiments both synthetic real-world verify efficiency robustness scheme. 1