Long non-coding RNAs (lncRNAs) have been shown to be involved in multiple biological processes and play critical roles in tumorigenesis. Numerous lncRNAs have been discovered in diverse species, but the functions of most lncRNAs still remain unclear. Meanwhile, their expression patterns and regulation mechanisms are also far from being fully understood. With the advances of high-throughput technologies, the increasing availability of genomic data creates opportunities for deciphering the molecular mechanism and underlying pathogenesis of human diseases. Here, we develop an integrative framework called JONMF to identify lncRNA-mRNA co-expression modules based on the sample-matched lncRNA and mRNA expression profiles. We formulate the module detection task as an optimization problem with joint orthogonal non-negative matrix factorization that could effectively prevent multicollinearity and produce a good modularity interpretation. The constructed lncRNA-mRNA co-expression network and the gene-gene interaction network are used as the network-regularized constraints to improve the module accuracy, while the sparsity constraints are simultaneously utilized to achieve modular sparse solutions. We applied JONMF to human ovarian cancer dataset and the experiment results demonstrate that the proposed method can effectively discover biologically functional co-expression modules, which may provide insights into the function of lncRNAs and molecular mechanism of human diseases.

High-throughput technology has generated large-scale protein interaction data, which is crucial in our understanding of biological organisms. Many complex identification algorithms have been developed to determine protein complexes. However, these methods are only suitable for dense protein interaction networks, because their capabilities decrease rapidly when applied to sparse protein–protein interaction (PPI) networks. In this study, based on penalized matrix decomposition (PMD), a novel method of penalized matrix decomposition for the identification of protein complexes (i.e., PMD_pc) was developed to detect protein complexes in the human protein interaction network. This method mainly consists of three steps. First, the adjacent matrix of the protein interaction network is normalized. Second, the normalized matrix is decomposed into three factor matrices. The PMD_pc method can detect protein complexes in sparse PPI networks by imposing appropriate constraints on factor matrices. Finally, the results of our method are compared with those of other methods in human PPI network. Experimental results show that our method can not only outperform classical algorithms, such as CFinder, ClusterONE, RRW, HC-PIN, and PCE-FR, but can also achieve an ideal overall performance in terms of a composite score consisting of F-measure, accuracy (ACC), and the maximum matching ratio (MMR).