Collaborative filtering (CF) is one of the most popular and important recommendation methodologies in the heart of numerous recommender systems today. Although widely adopted, existing CF-based methods, ranging from matrix factorization to the emerging graph-based methods, suffer inferior performance especially when the data for training are very limited. In this paper, we first pinpoint the root causes of such deficiency and observe two main disadvantages that stem from the inherent designs of existing CF-based methods, i.e., 1) inflexible modeling of users and items and 2) insufficient modeling of high-order correlations among the subjects. Under such circumstances, we propose a dual channel hypergraph collaborative filtering (DHCF) framework to tackle the above issues. First, a dual channel learning strategy, which holistically leverages the divide-and-conquer strategy, is introduced to learn the representation of users and items so that these two types of data can be elegantly interconnected while still maintaining their specific properties. Second, the hypergraph structure is employed for modeling users and items with explicit hybrid high-order correlations. The jump hypergraph convolution (JHConv) method is proposed to support the explicit and efficient embedding propagation of high-order correlations. Comprehensive experiments on two public benchmarks and two new real-world datasets demonstrate that DHCF can achieve significant and consistent improvements against other state-of-the-art methods.

BACKGROUND: The key roles of epistatic interactions between multiple genetic variants in the pathogenesis of complex diseases notwithstanding, the detection of such interactions remains a great challenge in genome-wide association studies. Although some existing multi-locus approaches have shown their successes in small-scale case-control data, the "combination explosion" course prohibits their applications to genome-wide analysis. It is therefore indispensable to develop new methods that are able to reduce the search space for epistatic interactions from an astronomic number of all possible combinations of genetic variants to a manageable set of candidates. RESULTS: We studied case-control data from the viewpoint of binary classification. More precisely, we treated single nucleotide polymorphism (SNP) markers as categorical features and adopted the random forest to discriminate cases against controls. On the basis of the gini importance given by the random forest, we designed a sliding window sequential forward feature selection (SWSFS) algorithm to select a small set of candidate SNPs that could minimize the classification error and then statistically tested up to three-way interactions of the candidates. We compared this approach with three existing methods on three simulated disease models and showed that our approach is comparable to, sometimes more powerful than, the other methods. We applied our approach to a genome-wide case-control dataset for Age-related Macular Degeneration (AMD) and successfully identified two SNPs that were reported to be associated with this disease. CONCLUSION: Besides existing pure statistical approaches, we demonstrated the feasibility of incorporating machine learning methods into genome-wide case-control studies. The gini importance offers yet another measure for the associations between SNPs and complex diseases, thereby complementing existing statistical measures to facilitate the identification of epistatic interactions and the understanding of epistasis in the pathogenesis of complex diseases.