  Learning based hashing methods have attracted considerable attention due to
their ability to greatly increase the scale at which existing algorithms may
operate. Most of these methods are designed to generate binary codes preserving
the Euclidean similarity in the original space. Manifold learning techniques,
in contrast, are better able to model the intrinsic structure embedded in the
original high-dimensional data. The complexities of these models, and the
problems with out-of-sample data, have previously rendered them unsuitable for
application to large-scale embedding, however. In this work, how to learn
compact binary embeddings on their intrinsic manifolds is considered. In order
to address the above-mentioned difficulties, an efficient, inductive solution
to the out-of-sample data problem, and a process by which non-parametric
manifold learning may be used as the basis of a hashing method is proposed. The
proposed approach thus allows the development of a range of new hashing
techniques exploiting the flexibility of the wide variety of manifold learning
approaches available. It is particularly shown that hashing on the basis of
t-SNE outperforms state-of-the-art hashing methods on large-scale benchmark
datasets, and is very effective for image classification with very short code
lengths. The proposed hashing framework is shown to be easily improved, for
example, by minimizing the quantization error with learned orthogonal
rotations. In addition, a supervised inductive manifold hashing framework is
developed by incorporating the label information, which is shown to greatly
advance the semantic retrieval performance.
