Search

Recommendation efficiency and data sparsity problems have been regarded as two challenges of improving performance for online recommendation. Most of the previous related work focus on improving recommendation accuracy instead of efficiency. In this paper, we propose a Deep Pairwise Hashing (DPH) to map users and items to binary vectors in Hamming space, where a user's preference for an item can be efficiently calculated by Hamming distance, which significantly improves the efficiency of online recommendation. To alleviate data sparsity and cold-start problems, the user-item interactive information and item content information are unified to learn effective representations of items and users. Specifically, we first pre-train robust item representation from item content data by a Denoising Auto-encoder instead of other deterministic deep learning frameworks; then we finetune the entire framework by adding a pairwise loss objective with discrete constraints; moreover, DPH aims to minimize a pairwise ranking loss that is consistent with the ultimate goal of recommendation. Finally, we adopt the alternating optimization method to optimize the proposed model with discrete constraints. Extensive experiments on three different datasets show that DPH can significantly advance the state-of-the-art frameworks regarding data sparsity and item cold-start recommendation. [ABSTRACT FROM AUTHOR]

Diameter perfect codes form a natural generalization for perfect codes. They are based on the code-anticode bound which generalizes the sphere-packing bound. The code-anticode bound was proved by Delsarte for distance-regular graphs and it holds for some other metrics too. In this paper we prove the bound for non-binary constant-weight codes with the Hamming metric and characterize the diameter perfect codes and the maximum size anticodes for these codes. We distinguish between six families of non-binary diameter constant-weight codes and four families of maximum size non-binary constant-weight anticodes. Each one of these families of diameter perfect codes raises some different questions. We consider some of these questions and leave lot of ground for further research. Finally, as a consequence, some $t$ -intersecting families related to the well-known Erdös-Ko-Rado theorem, are constructed. [ABSTRACT FROM AUTHOR]

Hashing methods have been widely used in Approximate Nearest Neighbor (ANN) search for big data due to low storage requirements and high search efficiency. These methods usually map the ANN search for big data into the $k$ -Nearest Neighbor ($k$ NN) search problem in Hamming space. However, Hamming distance calculation ignores the bit-level distinction, leading to confusing ranking. In order to further increase search accuracy, various bit-level weights have been proposed to rank hash codes in weighted Hamming space. Nevertheless, existing ranking methods in weighted Hamming space are almost based on exhaustive linear scan, which is time consuming and not suitable for large datasets. Although Multi-Index hashing that is a sub-linear search method has been proposed, it relies on Hamming distance rather than weighted Hamming distance. To address this issue, we propose an exact $k$ NN search approach with Multiple Tables in Weighted Hamming space named WHMT, in which the distribution of bit-level weights is incorporated into the multi-index building. By WHMT, we can get the optimal candidate set for exact $k$ NN search in weighted Hamming space without exhaustive linear scan. Experimental results show that WHMT can achieve dramatic speedup up to 69.8 times over linear scan baseline without losing accuracy in weighted Hamming space. [ABSTRACT FROM AUTHOR]