One of the central tasks of genome research is to predict phenotypes and discover some important gene biomarkers. However, there are three main problems in analyzing genomics data to predict phenotypes and gene marker selection. Such as large p and small n, low reproducibility of the selected biomarkers, and high noise. To provide a unified solution to alleviate the problems as mentioned above, we propose a self-paced learning L 1 / 2 ${{\rm{L}}}_{1/2}$ absolute network-based logistic regression model, called SLNL. Through the L 1 / 2 ${L}_{1/2}$ regularization, the model can get a more sparse result, which provides better interpretability. The absolute network-based penalty enables the model to integrate the feature network knowledge and helps select higher reproducibility genes. Moreover, this proposed penalty overcomes the drawback of a traditional network penalty without considering the sign of the coefficient. By the self-paced learning strategy, the model can now consider the noise level in gene expression data, lower the impact of high noise samples in data to model training, and provide better prediction accuracy. We compare the proposed method with six alternative approaches in various experimental scenarios, including a comprehensive simulation, four benchmark gene expression datasets, one lung cancer data set, and three lung cancer validation sets. Results show that SLNL can identify fewer meaningful biomarkers and obtain the best or equivalent prediction performance. Moreover, biological analysis shows that the genes selected by the SLNL might be helpful to tumor diagnosis and treatment.

In genome research, it is a fundamental issue to identify few but important survival-related biomarkers. The Cox model is a widely used survival analysis technique, which is used to study the relationship between characteristics and survival response. However, limitations of the existing Cox methods for genomic data are as follows: (1) a typical gene expression data set consists of tens of thousands of genes, and the result of current methods may not be sparse enough; (2) a wealth of structural information about many biological processes, such as regulatory networks and pathways, has often been ignored; (3) genomic data is usually considered as high noise, which is usually ignored in current methods. To alleviate the above problems, in this paper, we study a novel sparse Cox regression model, called SPLSN, which combines self-paced learning (SPL) and a log-sum absolute network-based penalty (Logsum-Net), especially for biomarker selection in survival analysis. SPL is embedded in curriculum design, and the model is trained by gradually increasing samples from low noise to high noise during the training process. The Logsum-Net encourages smoothness among the coefficients of adjacent genes on a specific biological network. We compare the proposed method with five alternative approaches in various experimental scenarios, including a comprehensive simulation, seven benchmark gene expression data sets, and one large validation data set. Results show that the SPLSN can identify fewer meaningful biomarkers and obtain the best or equivalent prediction performance. Moreover, the biological analysis shows that the genes selected by the SPLSN might be helpful to tumor treatment.

Mobile edge caching scheme (MECS) can determine where, how, and what to cache on user equipment by employing its own storage. When considering the performance of MECS, it is often full of uncertainty. The q-rung orthopair fuzzy set (q-ROFS), characterized by membership and nonmembership degrees with adjustable parameter q, is quite a high-efficiency way to capture uncertainty. In this paper, first, information measure (entropy, distance measure, and similarity measure)-based area difference under the q-rung orthopair fuzzy (q-ROF) circumstance is studied along with their detailed proofs. Then, we present a comprehensive weight-determination method by combining objective weights (determining by entropy) and subjective weights (given by experts) as combined weights, which can effectually alleviate the unconscionable influence of extreme data on evaluation results and simultaneously reflect objective data and subjective emotion. Moreover, q-ROF score function-based distance measure is presented for dealing with a value comparison problem. Later, q-ROF multicriteria decision-making (MCDM) method called total area based on orthogonal vector (TAOV) is introduced. Moreover, its feasibility is illustrated by MECS selection problem. Finally, a comparison of some existing MCDM methods and the proposed method is constructed for displaying their effectiveness. This proposed method can effectively avoid counterintuitive phenomena, eliminate antilogarithm by negative and zero issue, and has no division by zero issue.