Discrete Collaborative Filtering

We address the efficiency problem of Collaborative Filtering (CF) by hashing users and items as latent vectors in the form of binary codes, so that user-item affinity can be efficiently calculated in a Hamming space. However, existing hashing methods for CF employ binary code learning procedures that most suffer from the challenging discrete constraints. Hence, those methods generally adopt a two-stage learning scheme composed of relaxed optimization via discarding the discrete constraints, followed by binary quantization. We argue that such a scheme will result in a large quantization loss, which especially compromises the performance of large-scale CF that resorts to longer binary codes. In this paper, we propose a principled CF hashing framework called Discrete Collaborative Filtering (DCF), which directly tackles the challenging discrete optimization that should have been treated adequately in hashing. The formulation of DCF has two advantages: 1) the Hamming similarity induced loss that preserves the intrinsic user-item similarity, and 2) the balanced and uncorrelated code constraints that yield compact yet informative binary codes. We devise a computationally efficient algorithm with a rigorous convergence proof of DCF. Through extensive experiments on several real-world benchmarks, we show that DCF consistently outperforms state-of-the-art CF hashing techniques, e.g, though using only 8 bits, DCF is even significantly better than other methods using 128 bits.