  Low-rank Multi-view Subspace Learning (LMvSL) has shown great potential in
cross-view classification in recent years. Despite their empirical success,
existing LMvSL based methods are incapable of well handling view discrepancy
and discriminancy simultaneously, which thus leads to the performance
degradation when there is a large discrepancy among multi-view data. To
circumvent this drawback, motivated by the block-diagonal representation
learning, we propose Structured Low-rank Matrix Recovery (SLMR), a unique
method of effectively removing view discrepancy and improving discriminancy
through the recovery of structured low-rank matrix. Furthermore, recent
low-rank modeling provides a satisfactory solution to address data contaminated
by predefined assumptions of noise distribution, such as Gaussian or Laplacian
distribution. However, these models are not practical since complicated noise
in practice may violate those assumptions and the distribution is generally
unknown in advance. To alleviate such limitation, modal regression is elegantly
incorporated into the framework of SLMR (term it MR-SLMR). Different from
previous LMvSL based methods, our MR-SLMR can handle any zero-mode noise
variable that contains a wide range of noise, such as Gaussian noise, random
noise and outliers. The alternating direction method of multipliers (ADMM)
framework and half-quadratic theory are used to efficiently optimize MR-SLMR.
Experimental results on four public databases demonstrate the superiority of
MR-SLMR and its robustness to complicated noise.
