In many information processing tasks, labels are usually expensive and the unlabeled data points are abundant. To reduce the cost on collecting labels, it is crucial to predict which unlabeled examples are the most informative, i.e., improve the classifier the most if they were labeled. Many active learning techniques have been proposed for text categorization, such as SVMActive and Transductive Experimental Design. However, most of previous approaches try to discover the discriminant structure of the data space, whereas the geometrical structure is not well respected. In this paper, we propose a novel active learning algorithm which is performed in the data manifold adaptive kernel space. The manifold structure is incorporated into the kernel space by using graph Laplacian. This way, the manifold adaptive kernel space reflects the underlying geometry of the data. By minimizing the expected error with respect to the optimal classifier, we can select the most representative and discriminative data points for labeling. Experimental results on text categorization have demonstrated the effectiveness of our proposed approach.
