Regularized regression on image manifold for retrieval

Recently, there have been considerable interests in geometric-based methods for image retrieval. These methods consider the image space as a smooth manifold and apply manifold learning techniques to find a Euclidean embedding. Thus, the Euclidean distances in the embedding space can be used as approximations to the geodesic distances on the manifold. A main advantage of these methods is that the relevance feedbacks during retrieval can be naturally incorporated into the system as prior information. In this paper, we consider the retrieval problem as a classification problem on manifold. Instead of learning a distance measure, we aim to learn a classification function on the image manifold. Considering efficiency is a key issue in image retrieval, especially on the Webscale, we propose a novel approach for image retrieval on manifold. This approach is based on a regularized linear regression framework. The local manifold structure and user-provided relevance feedbacks are incorporated into the image retrieval system through a Locality Preserving Regularizer. Extensive experiments are carried out on a large image database which demonstrates the efficiency and effectiveness of the proposed approach.