  Existing block-diagonal representation researches mainly focuses on casting
block-diagonal regularization on training data, while only little attention is
dedicated to concurrently learning both block-diagonal representations of
training and test data. In this paper, we propose a discriminative
block-diagonal low-rank representation (BDLRR) method for recognition. In
particular, the elaborate BDLRR is formulated as a joint optimization problem
of shrinking the unfavorable representation from off-block-diagonal elements
and strengthening the compact block-diagonal representation under the
semi-supervised framework of low-rank representation. To this end, we first
impose penalty constraints on the negative representation to eliminate the
correlation between different classes such that the incoherence criterion of
the extra-class representation is boosted. Moreover, a constructed subspace
model is developed to enhance the self-expressive power of training samples and
further build the representation bridge between the training and test samples,
such that the coherence of the learned intra-class representation is
consistently heightened. Finally, the resulting optimization problem is solved
elegantly by employing an alternative optimization strategy, and a simple
recognition algorithm on the learned representation is utilized for final
prediction. Extensive experimental results demonstrate that the proposed method
achieves superb recognition results on four face image datasets, three
character datasets, and the fifteen scene multi-categories dataset. It not only
shows superior potential on image recognition but also outperforms
state-of-the-art methods.
