Towards robust subspace recovery via sparsity-constrained latent low-rank representation

• We present a Sparse Latent Low-rank representation approach for robust visual recovery.
• This approach constructs the dictionary using both observed and hidden data.
• A low-rank representation with enhanced sparsity can be derived.
• Extensive experiments have confirmed the superiority of the proposed method.

Robust recovery of subspace structures from noisy data has received much attention in visual analysis recently. To achieve this goal, previous works have developed a number of low-rank based methods, among of which Low-Rank Representation (LRR) is a typical one. As a refined variant, Latent LRR constructs the dictionary using both observed and hidden data to relieve the insufficient sampling problem. However, they fail to consider the observation that each data point can be represented by only a small subset of atoms in a dictionary. Motivated by this, we present the Sparse Latent Low-rank representation (SLL) method, which explicitly imposes the sparsity constraint on Latent LRR to encourage a sparse representation. In this way, each data point can be represented by only selecting a few points from the same subspace. Its objective function is solved by the linearized Augmented Lagrangian Multiplier method. Favorable experimental results on subspace clustering, salient feature extraction and outlier detection have verified promising performances of our method.