  Sparse coding represents a signal sparsely by using an overcomplete
dictionary, and obtains promising performance in practical computer vision
applications, especially for signal restoration tasks such as image denoising
and image inpainting. In recent years, many discriminative sparse coding
algorithms have been developed for classification problems, but they cannot
naturally handle visual data represented by multiview features. In addition,
existing sparse coding algorithms use graph Laplacian to model the local
geometry of the data distribution. It has been identified that Laplacian
regularization biases the solution towards a constant function which possibly
leads to poor extrapolating power. In this paper, we present multiview Hessian
discriminative sparse coding (mHDSC) which seamlessly integrates Hessian
regularization with discriminative sparse coding for multiview learning
problems. In particular, mHDSC exploits Hessian regularization to steer the
solution which varies smoothly along geodesics in the manifold, and treats the
label information as an additional view of feature for incorporating the
discriminative power for image annotation. We conduct extensive experiments on
PASCAL VOC'07 dataset and demonstrate the effectiveness of mHDSC for image
annotation.
