Supervised Dictionary Learning
  It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of purely reconstructive ones. This paper proposes a new step in that direction, with a novel sparse representation for signals belonging to different classes in terms of a shared dictionary and multiple class-decision functions. The linear variant of the proposed model admits a simple probabilistic interpretation, while its most general variant admits an interpretation in terms of kernels. An optimization framework for learning all the components of the proposed model is presented, along with experimental results on standard handwritten digit and texture classification tasks. 
Julien Mairal (WILLOW), Francis Bach (WILLOW), Jean Ponce (WILLOW,   LIENS), Guillermo Sapiro, Andrew Zisserman (WILLOW, VGG)