Binary vector embeddings enable fast nearest neighbor retrieval in large databases of high-dimensional objects, and play an important role in many practical applications, such as image and video retrieval. We study the problem of learning binary vector embeddings under a supervised setting, also known as hashing. We propose a novel supervised hashing method based on optimizing an information-theoretic quantity, mutual information. We show that optimizing mutual information can reduce ambiguity in the induced neighborhood structure in learned Hamming space, which is essential in obtaining high retrieval performance. To this end, we optimize mutual information in deep neural networks with minibatch stochastic gradient descent, with a formulation that maximally and efficiently utilizes available supervision. Experiments on four image retrieval benchmarks, including ImageNet, confirm the effectiveness of our method in learning high-quality binary embeddings for nearest neighbor retrieval.
Learning-based binary hashing has become a powerful paradigm for fast search and retrieval in massive databases. However, due to the requirement of discrete outputs for the hash functions, learning such functions is known to be very challenging. In addition, the objective functions adopted by existing hashing techniques are mostly chosen heuristically. In this paper, we propose a novel generative approach to learn hash functions through Minimum Description Length principle such that the learned hash codes maximally compress the dataset and can also be used to regenerate the inputs. We also develop an efficient learning algorithm based on the stochastic distributional gradient, which avoids the notorious difficulty caused by binary output constraints, to jointly optimize the parameters of the hash function and the associated generative model. Extensive experiments on a variety of large-scale datasets show that the proposed method achieves better retrieval results than the existing state-of-the-art methods.  An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal hash function is difficult because it involves binary constraints, and most approaches approximate the optimization by relaxing the constraints and then binarizing the result. Here, we focus on the binary autoencoder model, which seeks to reconstruct an image from the binary code produced by the hash function. We show that the optimization can be simplified with the method of auxiliary coordinates. This reformulates the optimization as alternating two easier steps: one that learns the encoder and decoder separately, and one that optimizes the code for each image. Image retrieval experiments, using precision recall and a measure of code utilization, show the resulting hash function outperforms or is competitive with state-of-the-art methods for binary hashing.