Learning a LowRank Tensor of Pharmacogenomic Multirelations from Biomedical Networks Learning pharmacogenomic multirelations among diseases, genes and chemicals from contentrich biomedical and biological networks can provide important guidance for drug discovery, drug repositioning and disease treatment. Most of the existing methods focus on imputing missing values in the diseasegene, disease chemical and genechemical pairwise relations from the observed relations instead of being designed for learning highorder diseasegenechemical multirelations. To achieve the goal, we propose a general tensorbased optimization framework and a scalable GraphRegularized Tensor Completion from Observed Pairwise Relations (GTCOPR) algorithm to infer the multirelations among the entities across multiple networks in a lowrank tensor, based on manifold regularization with the graph Laplacian of a Cartesian, tensor or strong product of the networks, and consistencies between the collapsed tensors and the observed bipartite relations. Our theoretical analyses also prove the convergence and efficiency of GTCOPR. In the experiments, the tensor fiberwise and slicewise evaluations demonstrate the accuracy of GTCOPR for predicting the diseasegenechemical associations across the largescale proteinprotein interactions network, chemical structural similarity network and phenotypebased human disease network; and the validation on Genomics of Drug Sensitivity in Cancer cell line dataset shows a potential clinical application of GTCOPR for learning diseasespecific chemicalgene interactions. Statistical enrichment analysis demonstrates that GTCOPR is also capable of producing both topologically and biologically relevant disease, gene and chemical components with high significance.

Predicting DrugDisease Treatment Associations Based on Topological Similarity and Singular Value Decomposition To assist drug development, many computational methods have been proposed to identify potential drugdisease treatment associations before wet experiments. Based on the assumption that similar drugs may treat similar diseases, most methods need the similarities of drugs and diseases, and they will not work if the biological or chemical features for computing similarities are missing. Besides, being lack of validated negative samples in the drugdisease associations data, most methods simply select some unlabeled samples as negative ones, which may introduce noises. Herein, we propose a new method (TSSVD) which only uses those known drugprotein, diseaseprotein and drugdisease interactions to predict the potential drugdisease associations. In a constructed drugproteindisease heterogeneous network, we consider the common neighbors of drugs and diseases to obtain the topological similarity. Then the topological similarity matrix of drugs (diseases) will be used to get the low dimensional embedding representations of drugdisease pairs. Finally, a Random Forest classifier is trained to do the prediction. To train a more reasonable model, we select out some reliable negative samples based on the kstep neighbors relationships between drugs and diseases. Compared with some stateoftheart methods, we use less information but achieve better or comparable performance. Meanwhile, our strategy for selecting reliable negative samples can improve the performances of these methods.