Topology preserving hashing for similarity search

Binary hashing has been widely used for efficient similarity search. Learning efficient codes has become a research focus and it is still a challenge. In many cases, the real-world data often lies on a low-dimensional manifold, which should be taken into account to capture meaningful neighbors with hashing. The importance of a manifold is its topology, which represents the neighborhood relationships between its subregions and the relative proximities between the neighbors of each subregion, e.g. the relative ranking of neighbors of each subregion. Most existing hashing methods try to preserve the neighborhood relationships by mapping similar points to close codes, while ignoring the neighborhood rankings. Moreover, most hashing methods lack in providing a good ranking for query results since they use Hamming distance as the similarity metric, and in practice, there are often a lot of results sharing the same distance to a query. In this paper, we propose a novel hashing method to solve these two issues jointly. The proposed method is referred to as Topology Preserving Hashing (TPH). TPH is distinct from prior works by preserving the neighborhood rankings of data points in Hamming space. The learning stage of TPH is formulated as a generalized eigendecomposition problem with closed form solutions. Experimental comparisons with other state-of-the-art methods on three noted image benchmarks demonstrate the efficacy of the proposed method.