  In this paper, we extend the popular dictionary pair learning (DPL) into the
scenario of twin-projective latent flexible DPL under a structured
twin-incoherence. Technically, a novel framework called Twin-Projective Latent
Flexible DPL (TP-DPL) is proposed, which minimizes the twin-incoherence
constrained flexibly-relaxed reconstruction error to avoid the possible
over-fitting issue and produce accurate reconstruction. In this setting, our
TP-DPL integrates the twin-incoherence based latent flexible DPL and the joint
embedding of codes as well as salient features by twin-projection into a
unified model in an adaptive neighborhood-preserving manner. As a result,
TP-DPL unifies the salient feature extraction, representation and
classification. The twin-incoherence constraint on codes and features can
explicitly ensure high intra-class compactness and inter-class separation over
them. TP-DPL also integrates the adaptive weighting to preserve the local
neighborhood of the coefficients and salient features within each class
explicitly. For efficiency, TP-DPL uses Frobenius-norm and abandons the costly
l0/l1-norm for group sparse representation. Another byproduct is that TP-DPL
can directly apply the class-specific twin-projective reconstruction residual
to compute the label of data. Extensive results on public databases show that
TP-DPL can deliver the state-of-the-art performance.
