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SOJNMF: Identifying Multidimensional Molecular Regulatory Modules by Sparse Orthogonality-Regularized Joint Non-Negative Matrix Factorization Algorithm

Cancer is not only a very aggressive but also a very diverse disease. Recent advances in high-throughput omics technologies of cancer have enabled biomedical researchers to have more opportunities for studying its multi-level biological regulatory mechanism. However, there are few methods to explore the underlying mechanism of cancer by identifying its multidimensional molecular regulatory modules from the multidimensional omics data of cancer. In this paper, we propose a sparse orthogonality-regularized joint non-negative matrix factorization (SOJNMF) algorithm which can integratively analyze multidimensional omics data. This method can not only identify multidimensional molecular regulatory modules, but reduce the overlap rate of features among the multidimensional modules while ensuring the sparsity of the coefficient matrix after decomposition. Gene expression data, miRNA expression data and gene methylation data of liver cancer are integratively analyzed based on SOJNMF algorithm. Then, we obtain 238 multidimensional molecular regulatory modules. The results of permutation test indicate that different omics features within these modules are significantly correlated in statistics. Meanwhile, the results of functional enrichment analysis show that these multidimensional modules are significantly related to the underlying mechanism of the occurrence and development of liver cancer.