Robust Subspace Discovery by Block-diagonal Adaptive Locality-constrained Representation

We propose a novel and unsupervised representation learning model, i.e., Robust Block-Diagonal Adaptive Locality-constrained Latent Representation (rBDLR). rBDLR is able to recover multi-subspace structures and extract the adaptive locality-preserving salient features jointly. Leveraging on the Frobenius-norm based latent low-rank representation model, rBDLR jointly learns the coding coefficients and salient features, and improves the results by enhancing the robustness to outliers and errors in given data, preserving local information of salient features adaptively and ensuring the block-diagonal structures of the coefficients. To improve the robustness, we perform the latent representation and adaptive weighting in a recovered clean data space. To force the coefficients to be block-diagonal, we perform auto-weighting by minimizing the reconstruction error based on salient features, constrained using a block-diagonal regularizer. This ensures that a strict block-diagonal weight matrix can be obtained and salient features will possess the adaptive locality preserving ability. By minimizing the difference between the coefficient and weights matrices, we can obtain a block-diagonal coefficients matrix and it can also propagate and exchange useful information between salient features and coefficients. Extensive results demonstrate the superiority of rBDLR over other state-of-the-art methods.