Semi-supervised dimensionality reduction for image retrieval

This paper proposes a novel semi-supervised dimensionality reduction learning algorithm for the ranking problem. Generally, we do not make the assumption of existence of classes and do not want to find the classification boundaries. Instead, we only assume that the data point cloud can construct a graph which describes the manifold structure, and there are multiple concepts on different parts of the manifold. By maximizing the distance between different concepts and simultaneously preserving the local structure on the manifold, the learned metric can indeed give good ranking results. Moreover, based on the theoretical analysis of the relationship between graph Laplacian and manifold Laplace-Beltrami operator, we develop an online learning algorithm that can incrementally learn the unlabeled data.