  Dictionary learning and sparse representation (DLSR) is a recent and
successful mathematical model for data representation that achieves
state-of-the-art performance in various fields such as pattern recognition,
machine learning, computer vision, and medical imaging. The original
formulation for DLSR is based on the minimization of the reconstruction error
between the original signal and its sparse representation in the space of the
learned dictionary. Although this formulation is optimal for solving problems
such as denoising, inpainting, and coding, it may not lead to optimal solution
in classification tasks, where the ultimate goal is to make the learned
dictionary and corresponding sparse representation as discriminative as
possible. This motivated the emergence of a new category of techniques, which
is appropriately called supervised dictionary learning and sparse
representation (S-DLSR), leading to more optimal dictionary and sparse
representation in classification tasks. Despite many research efforts for
S-DLSR, the literature lacks a comprehensive view of these techniques, their
connections, advantages and shortcomings. In this paper, we address this gap
and provide a review of the recently proposed algorithms for S-DLSR. We first
present a taxonomy of these algorithms into six categories based on the
approach taken to include label information into the learning of the dictionary
and/or sparse representation. For each category, we draw connections between
the algorithms in this category and present a unified framework for them. We
then provide guidelines for applied researchers on how to represent and learn
the building blocks of an S-DLSR solution based on the problem at hand. This
review provides a broad, yet deep, view of the state-of-the-art methods for
S-DLSR and allows for the advancement of research and development in this
emerging area of research.
