  Recently, label consistent k-svd (LC-KSVD) algorithm has been successfully
applied in image classification. The objective function of LC-KSVD is consisted
of reconstruction error, classification error and discriminative sparse codes
error with L0-norm sparse regularization term. The L0-norm, however, leads to
NP-hard problem. Despite some methods such as orthogonal matching pursuit can
help solve this problem to some extent, it is quite difficult to find the
optimum sparse solution. To overcome this limitation, we propose a label
embedded dictionary learning (LEDL) method to utilise the L1-norm as the sparse
regularization term so that we can avoid the hard-to-optimize problem by
solving the convex optimization problem. Alternating direction method of
multipliers and blockwise coordinate descent algorithm are then exploited to
optimize the corresponding objective function. Extensive experimental results
on six benchmark datasets illustrate that the proposed algorithm has achieved
superior performance compared to some conventional classification algorithms.
