A novel double-layer sparse representation approach for unsupervised dictionary learning

• We propose a DLSR approach for dictionary learning.
• The DLSR formulation enhances reconstructive and discriminative abilities of dictionary.
• A DLSR-OMP algorithm is developed to solve the DLSR formulation.

This paper presents a novel double-layer sparse representation (DLSR) approach, for improving both reconstructive and discriminative capabilities of unsupervised dictionary learning. In supervised/unsupervised discriminative dictionary learning, classical approaches usually develop a discriminative term for learning multiple sub-dictionaries, each of which corresponds to one-class training image patches. As such, the image patches for different classes can be discriminated by coefficients of sparse representation, with respect to different sub-dictionaries. However, in the unsupervised scenario, some of the training patches for learning the sub-dictionaries of different clusters are related to more than one cluster. Thus, we propose a DLSR formulation in this paper to impose the first-layer sparsity on the coefficients and the second-layer sparsity on the clusters for each training patch, embedding both the reconstructive (via the first-layer) and discriminative (via the second-layer) capabilities in the learned dictionary. To address the proposed DLSR formulation, a simple yet effective algorithm, called DLSR-OMP, is developed on the basis of the conventional OMP algorithm. Finally, the experiments verify that our approach can improve reconstruction and clustering performance of the learned dictionaries of the conventional approaches. More importantly, the experimental results on texture segmentation show that our approach outperforms other state-of-the-art discriminative dictionary learning approaches in the clustering task.