  In this paper, we aim at learning simultaneously a discriminative dictionary
and a robust projection matrix from noisy data. The joint learning, makes the
learned projection and dictionary a better fit for each other, so a more
accurate classification can be obtained. However, current prevailing joint
dimensionality reduction and dictionary learning methods, would fail when the
training samples are noisy or heavily corrupted. To address this issue, we
propose a joint projection and dictionary learning using low-rank
regularization and graph constraints (JPDL-LR). Specifically, the
discrimination of the dictionary is achieved by imposing Fisher criterion on
the coding coefficients. In addition, our method explicitly encodes the local
structure of data by incorporating a graph regularization term, that further
improves the discriminative ability of the projection matrix. Inspired by
recent advances of low-rank representation for removing outliers and noise, we
enforce a low-rank constraint on sub-dictionaries of all classes to make them
more compact and robust to noise. Experimental results on several benchmark
datasets verify the effectiveness and robustness of our method for both
dimensionality reduction and image classification, especially when the data
contains considerable noise or variations.
