An image search reranking (ISR) technique aims at refining text-based search results by mining images' visual content. Feature extraction and ranking function design are two key steps in ISR. Inspired by the idea of hypersphere in one-class classification, this paper proposes a feature extraction algorithm named hypersphere-based relevance preserving projection (HRPP) and a ranking function called hypersphere-based rank (H-Rank). Specifically, an HRPP is a spectral embedding algorithm to transform an original high-dimensional feature space into an intrinsically low-dimensional hypersphere space by preserving the manifold structure and a relevance relationship among the images. An H-Rank is a simple but effective ranking algorithm to sort the images by their distances to the hypersphere center. Moreover, to capture the user's intent with minimum human interaction, a reversed k-nearest neighbor (KNN) algorithm is proposed, which harvests enough pseudorelevant images by requiring that the user gives only one click on the initially searched images. The HRPP method with reversed KNN is named one-click-based HRPP (OC-HRPP). Finally, an OC-HRPP algorithm and the H-Rank algorithm form a new ISR method, H-reranking. Extensive experimental results on three large real-world data sets show that the proposed algorithms are effective. Moreover, the fact that only one relevant image is required to be labeled makes it has a strong practical significance.