  We propose a joint subspace recovery and enhanced locality based robust
flexible label consistent dictionary learning method called Robust Flexible
Discriminative Dictionary Learning (RFDDL). RFDDL mainly improves the data
representation and classification abilities by enhancing the robust property to
sparse errors and encoding the locality, reconstruction error and label
consistency more accurately. First, for the robustness to noise and sparse
errors in data and atoms, RFDDL aims at recovering the underlying clean data
and clean atom subspaces jointly, and then performs DL and encodes the locality
in the recovered subspaces. Second, to enable the data sampled from a nonlinear
manifold to be handled potentially and obtain the accurate reconstruction by
avoiding the overfitting, RFDDL minimizes the reconstruction error in a
flexible manner. Third, to encode the label consistency accurately, RFDDL
involves a discriminative flexible sparse code error to encourage the
coefficients to be soft. Fourth, to encode the locality well, RFDDL defines the
Laplacian matrix over recovered atoms, includes label information of atoms in
terms of intra-class compactness and inter-class separation, and associates
with group sparse codes and classifier to obtain the accurate discriminative
locality-constrained coefficients and classifier. Extensive results on public
databases show the effectiveness of our RFDDL.
