A scaling-free minimum enclosing ball method to detect differentially expressed genes for RNA-seq data

Background Identifying differentially expressed genes between the same or different species is an urgent demand for biological and medical research. For RNA-seq data, systematic technical effects and different sequencing depths are usually encountered when conducting experiments. Normalization is regarded as an essential step in the discovery of biologically important changes in expression. The present methods usually involve normalization of the data with a scaling factor, followed by detection of significant genes. However, more than one scaling factor may exist because of the complexity of real data. Consequently, methods that normalize data by a single scaling factor may deliver suboptimal performance or may not even work.The development of modern machine learning techniques has provided a new perspective regarding discrimination between differentially expressed (DE) and non-DE genes. However, in reality, the non-DE genes comprise only a small set and may contain housekeeping genes (in same species) or conserved orthologous genes (in different species). Therefore, the process of detecting DE genes can be formulated as a one-class classification problem, where only non-DE genes are observed, while DE genes are completely absent from the training data. Results In this study, we transform the problem to an outlier detection problem by treating DE genes as outliers, and we propose a scaling-free minimum enclosing ball (SFMEB) method to construct a smallest possible ball to contain the known non-DE genes in a feature space. The genes outside the minimum enclosing ball can then be naturally considered to be DE genes. Compared with the existing methods, the proposed SFMEB method does not require data normalization, which is particularly attractive when the RNA-seq data include more than one scaling factor. Furthermore, the SFMEB method could be easily extended to different species without normalization. Conclusions Simulation studies demonstrate that the SFMEB method works well in a wide range of settings, especially when the data are heterogeneous or biological replicates. Analysis of the real data also supports the conclusion that the SFMEB method outperforms other existing competitors. The R package of the proposed method is available at https://bioconductor.org/packages/MEB.

Twenty-Four-Hour Ahead Probabilistic Global Horizontal Irradiance Forecasting Using Gaussian Process Regression

Probabilistic solar power forecasting has been critical in Southern Africa because of major shortages of power due to climatic changes and other factors over the past decade. This paper discusses Gaussian process regression (GPR) coupled with core vector regression for short-term hourly global horizontal irradiance (GHI) forecasting. GPR is a powerful Bayesian non-parametric regression method that works well for small data sets and quantifies the uncertainty in the predictions. The choice of a kernel that characterises the covariance function is a crucial issue in Gaussian process regression. In this study, we adopt the minimum enclosing ball (MEB) technique. The MEB improves the forecasting power of GPR because the smaller the ball is, the shorter the training time, hence performance is robust. Forecasting of real-time data was done on two South African radiometric stations, Stellenbosch University (SUN) in a coastal area of the Western Cape Province, and the University of Venda (UNV) station in the Limpopo Province. Variables were selected using the least absolute shrinkage and selection operator via hierarchical interactions. The Bayesian approach using informative priors was used for parameter estimation. Based on the root mean square error, mean absolute error and percentage bias the results showed that the GPR model gives the most accurate predictions compared to those from gradient boosting and support vector regression models, making this study a useful tool for decision-makers and system operators in power utility companies. The main contribution of this paper is in the use of a GPR model coupled with the core vector methodology which is used in forecasting GHI using South African data. This is the first application of GPR coupled with core vector regression in which the minimum enclosing ball is applied on GHI data, to the best of our knowledge.

WR-SVM Model Based on the Margin Radius Approach for Solving the Minimum Enclosing Ball Problem in Support Vector Machine Classification

The generalization error of conventional support vector machine (SVM) depends on the ratio of two factors; radius and margin. The traditional SVM aims to maximize margin but ignore minimization of radius, which decreases the overall performance of the SVM classifier. However, different approaches are developed to achieve a trade-off between the margin and radius. Still, the computational cost of all these approaches is high due to the requirements of matrix transformation. Furthermore, a conventional SVM tries to set the best hyperplane between classes, and due to some robust kernel tricks, an SVM is used in many non-linear and complex problems. The configuration of the best hyperplane between classes is not effective; therefore, it is required to bind a class within its limited area to enhance the performance of the SVM classifier. The area enclosed by a class is called its Minimum Enclosing Ball (MEB), and it is one of the emerging problems of SVM. Therefore, a robust solution is needed to improve the performance of the conventional SVM to overcome the highlighted issues. In this research study, a novel weighted radius SVM (WR-SVM) is proposed to determine the tighter bounds of MEB. The proposed solution uses a weighted mean to find tighter bounds of radius, due to which the size of MEB decreases. Experiments are conducted on nine different benchmark datasets and one synthetic dataset to demonstrate the effectiveness of our proposed model. The experimental results reveal that the proposed WR-SVM significantly performed well compared to the conventional SVM classifier. Furthermore, experimental results are compared with F-SVM and traditional SVM in terms of classification accuracy to demonstrate the significance of the proposed WR-SVM.

Improving Localized Multiple Kernel Learning via Radius-Margin Bound

Localized multiple kernel learning (LMKL) is an effective method of multiple kernel learning (MKL). It tries to learn the optimal kernel from a set of predefined basic kernels by directly using the maximum margin principle, which is embodied in support vector machine (SVM). However, LMKL does not consider the radius of minimum enclosing ball (MEB) which actually impacts the error bound of SVM as well as the separating margin. In the paper, we propose an improved version of LMKL, which is named ILMKL. The proposed method explicitly takes into consideration both the margin and the radius and so achieves better performance over its counterpart. Moreover, the proposed method can automatically tune the regularization parameter when learning the optimal kernel. Consequently, it avoids using the time-consuming cross-validation process to choose the parameter. Comprehensive experiments are conducted and the results well demonstrate the effectiveness and efficiency of the proposed method.