Hashing is one of the most popular methods for similarity search because of its speed and efficiency. Dense binary hashing is prevalent in the literature. Recently, insect olfaction was shown to be structurally and functionally analogous to sparse hashing [6]. Here, we prove that this biological mechanism is the solution to a well-posed optimization problem. Furthermore, we show that orthogonality increases the accuracy of sparse hashing. Next, we present a novel method, Procrustean Orthogonal Sparse Hashing (POSH), that unifies these findings, learning an orthogonal transform from training data compatible with the sparse hashing mechanism. We provide theoretical evidence of the shortcomings of Optimal Sparse Lifting (OSL) [22] and BioHash [30], two related olfaction-inspired methods, and propose two new methods, Binary OSL and SphericalHash, to address these deficiencies. We compare POSH, Binary OSL, and SphericalHash to several state-of-the-art hashing methods and provide empirical results for the superiority of the proposed methods across a wide range of standard benchmarks and parameter settings.

In recent years, the similarity learning problem has been widely studied. Most of the existing works focus on images and few of these works could be applied to learn similarity between neuroimages, such as fMRI images and DTI images, which are important data sources for human brain analysis. In this paper, we focus on the similarity learning for fMRI brain network analysis. We propose a general framework called Multi-hop Siamese GCN for similarity learning on graphs. This framework provides options for refining the graph representations with high-order structure information, thus can be used for graph similarity learning on various brain network data sets. We apply the proposed Multi-hop Siamese GCN approach on four real fMRI brain network datasets for similarity learning with respect to brain health status and cognitive abilities. Our proposed method achieves an average AUC gain of 82.6 % compared to PCA, and an average AUC gain of 42 % compared to S-GCN across a variety of datasets, indicating its promising learning ability for clinical investigation and brain disease diagnosis.