  Unsupervised hashing is important for indexing huge image or video
collections without having expensive annotations available. Hashing aims to
learn short binary codes for compact storage and efficient semantic retrieval.
We propose an unsupervised deep hashing layer called Bi-half Net that maximizes
entropy of the binary codes. Entropy is maximal when both possible values of
the bit are uniformly (half-half) distributed. To maximize bit entropy, we do
not add a term to the loss function as this is difficult to optimize and tune.
Instead, we design a new parameter-free network layer to explicitly force
continuous image features to approximate the optimal half-half bit
distribution. This layer is shown to minimize a penalized term of the
Wasserstein distance between the learned continuous image features and the
optimal half-half bit distribution. Experimental results on the image datasets
Flickr25k, Nus-wide, Cifar-10, Mscoco, Mnist and the video datasets Ucf-101 and
Hmdb-51 show that our approach leads to compact codes and compares favorably to
the current state-of-the-art.
