Content Based Image Retrieval (CBIR) has become one of the most active research areas in computer science. Relevance feedback is often used in CBIR systems to bridge the semantic gap. Typically, users are asked to make relevance judgements on some query results, and the feedback information is then used to re-rank the images in the database. An effective relevance feedback algorithm must provide the users with the most informative images with respect to the ranking function. In this paper, we propose a novel active learning algorithm, called Convex Laplacian Regularized Ioptimal Design (CLapRID), for relevance feedback image retrieval. Our algorithm is based on a regression model which minimizes the least square error on the labeled images and simultaneously preserves the intrinsic geometrical structure of the image space. It selects the most informative images which minimize the average predictive variance. The optimization problem of CLapRID can be cast as a semidefinite programmin...