ADMM Pursuit for Manifold Regularized Sparse Coding

In this paper, we propose an efficient ADMM-based algorithm for graph regularized sparse coding that explicitly takes into account the local manifold structure of the data. Specifically, the graph Laplacian representing the manifold structure is used as a regularizer, encouraging the resulting sparse codes to vary smoothly along the geodesics of the data manifold. By preserving locality, the obtained representations have more discriminating power compared with traditional sparse coding algorithms and thus can better facilitate machine learning tasks such as classification and clustering. The experimental results demonstrate the effectiveness of our proposed algorithm over other previously suggested approaches, in terms of both lower representation errors and faster, more stable runtimes.