  The rapid development of computer hardware and Internet technology makes
large scale data dependent models computationally tractable, and opens a bright
avenue for annotating images through innovative machine learning algorithms.
Semi-supervised learning (SSL) has consequently received intensive attention in
recent years and has been successfully deployed in image annotation. One
representative work in SSL is Laplacian regularization (LR), which smoothes the
conditional distribution for classification along the manifold encoded in the
graph Laplacian, however, it has been observed that LR biases the
classification function towards a constant function which possibly results in
poor generalization. In addition, LR is developed to handle uniformly
distributed data (or single view data), although instances or objects, such as
images and videos, are usually represented by multiview features, such as
color, shape and texture. In this paper, we present multiview Hessian
regularization (mHR) to address the above two problems in LR-based image
annotation. In particular, mHR optimally combines multiple Hessian
regularizations, each of which is obtained from a particular view of instances,
and steers the classification function which varies linearly along the data
manifold. We apply mHR to kernel least squares and support vector machines as
two examples for image annotation. Extensive experiments on the PASCAL VOC'07
dataset validate the effectiveness of mHR by comparing it with baseline
algorithms, including LR and HR.
