With the development of high-throughput technologies, the accumulation of large amounts of multidimensional genomic data provides an excellent opportunity to study the multilevel biological regulatory relationships in cancer. Based on the hypothesis of competitive endogenous ribonucleic acid (RNA) (ceRNA) network, lncRNAs can eliminate the inhibition of microRNAs (miRNAs) on their target genes by binding to intracellular miRNA sites so as to improve the expression level of these target genes. However, previous studies on cancer expression mechanism are mostly based on individual or two-dimensional data, and lack of integration and analysis of various RNA-seq data, making it difficult to verify the complex biological relationships involved. To explore RNA expression patterns and potential molecular mechanisms of cancer, a network-regularized sparse orthogonal-regularized joint non-negative matrix factorization (NSOJNMF) algorithm is proposed, which combines the interaction relations among RNA-seq data in the way of network regularization and effectively prevents multicollinearity through sparse constraints and orthogonal regularization constraints to generate good modular sparse solutions. NSOJNMF algorithm is performed on the datasets of liver cancer and colon cancer, then ceRNA co-modules of them are recognized. The enrichment analysis of these modules shows that >90% of them are closely related to the occurrence and development of cancer. In addition, the ceRNA networks constructed by the ceRNA co-modules not only accurately mine the known correlations of the three RNA molecules but also further discover their potential biological associations, which may contribute to the exploration of the competitive relationships among multiple RNAs and the molecular mechanisms affecting tumor development.

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Studies have confirmed that the occurrence of many complex diseases in the human body is closely related to the microbial community, and microbes can affect tumorigenesis and metastasis by regulating the tumor microenvironment. However, there are still large gaps in the clinical observation of the microbiota in disease. Although biological experiments are accurate in identifying disease-associated microbes, they are also time-consuming and expensive. The computational models for effective identification of diseases related microbes can shorten this process, and reduce capital and time costs. Based on this, in the paper, a model named DSAE_RF is presented to predict latent microbe–disease associations by combining multi-source features and deep learning. DSAE_RF calculates four similarities between microbes and diseases, which are then used as feature vectors for the disease-microbe pairs. Later, reliable negative samples are screened by k-means clustering, and a deep sparse autoencoder neural network is further used to extract effective features of the disease-microbe pairs. In this foundation, a random forest classifier is presented to predict the associations between microbes and diseases. To assess the performance of the model in this paper, 10-fold cross-validation is implemented on the same dataset. As a result, the AUC and AUPR of the model are 0.9448 and 0.9431, respectively. Furthermore, we also conduct a variety of experiments, including comparison of negative sample selection methods, comparison with different models and classifiers, Kolmogorov–Smirnov test and t-test, ablation experiments, robustness analysis, and case studies on Covid-19 and colorectal cancer. The results fully demonstrate the reliability and availability of our model.

Although many single-cell computational methods proposed use gene expression as input, recent studies show that replacing ‘unstable’ gene expression with ‘stable’ gene–gene associations can greatly improve the performance of downstream analysis. To obtain accurate gene–gene associations, conditional cell-specific network method (c-CSN) filters out the indirect associations of cell-specific network method (CSN) based on the conditional independence of statistics. However, when there are strong connections in networks, the c-CSN suffers from false negative problem in network construction. To overcome this problem, a new partial cell-specific network method (p-CSN) based on the partial independence of statistics is proposed in this paper, which eliminates the singularity of the c-CSN by implicitly including direct associations among estimated variables. Based on the p-CSN, single-cell network entropy (scNEntropy) is further proposed to quantify cell state. The superiorities of our method are verified on several datasets. (i) Compared with traditional gene regulatory network construction methods, the p-CSN constructs partial cell-specific networks, namely, one cell to one network. (ii) When there are strong connections in networks, the p-CSN reduces the false negative probability of the c-CSN. (iii) The input of more accurate gene–gene associations further optimizes the performance of downstream analyses. (iv) The scNEntropy effectively quantifies cell state and reconstructs cell pseudo-time.

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