In this paper, we present an unsupervised distance learning approach for improving the effectiveness of image retrieval tasks. We propose a Reciprocal kNN Graph algorithm that considers the relationships among ranked lists in the context of a k-reciprocal neighborhood. The similarity is propagated among neighbors considering the geometry of the dataset manifold. The proposed method can be used both for re-ranking and rank aggregation tasks. Unlike traditional diffusion process methods, which require matrix multiplication operations, our algorithm takes only a subset of ranked lists as input, presenting linear complexity in terms of computational and storage requirements. We conducted a large evaluation protocol involving shape, color, and texture descriptors, various datasets, and comparisons with other post-processing approaches. The re-ranking and rank aggregation algorithms yield better results in terms of effectiveness performance than various state-of-the-art algorithms recently proposed in the literature, achieving bull's eye and MAP scores of 100% on the well-known MPEG-7 shape dataset. 
Unsupervised manifold learning using Reciprocal kNN Graphs in image re-ranking and rank aggregation tasks