Non-negative matrix factorization (NMF) has become one of the most powerful methods for clustering and feature selection. However, the performance of the traditional NMF method severely degrades when the data contain noises and outliers or the manifold structure of the data is not taken into account. In this article, a novel method called correntropy-based hypergraph regularized NMF (CHNMF) is proposed to solve the above problem. Specifically, we use the correntropy instead of the Euclidean norm in the loss term of CHNMF, which will improve the robustness of the algorithm. And the hypergraph regularization term is also applied to the objective function, which can explore the high-order geometric information in more sample points. Then, the half-quadratic (HQ) optimization technique is adopted to solve the complex optimization problem of CHNMF. Finally, extensive experimental results on multi-cancer integrated data indicate that the proposed CHNMF method is superior to other state-of-the-art methods for clustering and feature selection.

Microarray techniques have been used to delineate cancer groups or to identify candidate genes for cancer prognosis. As such problems can be viewed as classification ones, various classification methods have been applied to analyze or interpret gene expression data. In this paper, we propose a novel method based on robust principal component analysis (RPCA) to classify tumor samples of gene expression data. Firstly, RPCA is utilized to highlight the characteristic genes associated with a special biological process. Then, RPCA and RPCA+LDA (robust principal component analysis and linear discriminant analysis) are used to identify the features. Finally, support vector machine (SVM) is applied to classify the tumor samples of gene expression data based on the identified features. Experiments on seven data sets demonstrate that our methods are effective and feasible for tumor classification.

Identifying epistasis or epistatic interactions, which refer to nonlinear interaction effects of single nucleotide polymorphisms (SNPs), is essential to understand disease susceptibility and to detect genetic architectures underlying complex diseases. Though many works have been done for identifying epistatic interactions, due to their methodological and computational challenges, the algorithmic development is still ongoing. In this study, a method epiACO is proposed to identify epistatic interactions, which based on ant colony optimization algorithm. Highlights of epiACO are the introduced fitness function Svalue, path selection strategies, and a memory based strategy. The Svalue leverages the advantages of both mutual information and Bayesian network to effectively and efficiently measure associations between SNP combinations and the phenotype. Two path selection strategies, i.e., probabilistic path selection strategy and stochastic path selection strategy, are provided to adaptively guide ant behaviors of exploration and exploitation. The memory based strategy is designed to retain candidate solutions found in the previous iterations, and compare them to solutions of the current iteration to generate new candidate solutions, yielding a more accurate way for identifying epistasis. Experiments of epiACO and its comparison with other recent methods epiMODE, TEAM, BOOST, SNPRuler, AntEpiSeeker, AntMiner, MACOED, and IACO are performed on both simulation data sets and a real data set of age-related macular degeneration. Results show that epiACO is promising in identifying epistasis and might be an alternative to existing methods.

SNP-SNP interactions have been receiving increasing attention in understanding the mechanism underlying susceptibility to complex diseases. Though many works have been done for the detection of SNP-SNP interactions, the algorithmic development is still ongoing. In this study, an improved opposition-based learning particle swarm optimization (IOBLPSO) is proposed for the detection of SNP-SNP interactions. Highlights of IOBLPSO are the introduction of three strategies, namely, opposition-based learning, dynamic inertia weight, and a postprocedure. Opposition-based learning not only enhances the global explorative ability, but also avoids premature convergence. Dynamic inertia weight allows particles to cover a wider search space when the considered SNP is likely to be a random one and converges on promising regions of the search space while capturing a highly suspected SNP. The postprocedure is used to carry out a deep search in highly suspected SNP sets. Experiments of IOBLPSO are performed on both simulation data sets and a real data set of age-related macular degeneration, results of which demonstrate that IOBLPSO is promising in detecting SNP-SNP interactions. IOBLPSO might be an alternative to existing methods for detecting SNP-SNP interactions.

Principal component analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the so-called sparse PCA, which focuses on seeking sparse loadings. However, the performance of these methods is still far from satisfactory due to their limitation of using unsupervised learning methods; moreover, the class ambiguity within the sample is high. To overcome this problem, this paper developed a new PCA method, which is named the supervised discriminative sparse PCA (SDSPCA). The main innovation of this method is the incorporation of discriminative information and sparsity into the PCA model. Specifically, in contrast to the traditional sparse PCA, which imposes sparsity on the loadings, here, sparse components are obtained to represent the data. Furthermore, via the linear transformation, the sparse components approximate the given label information. On the one hand, sparse components improve interpretability over the traditional PCA, while on the other hand, they are have discriminative abilities suitable for classification purposes. A simple algorithm is developed, and its convergence proof is provided. SDSPCA has been applied to the common-characteristic gene selection and tumor classification on multiview biological data. The sparsity and classification performance of SDSPCA are empirically verified via abundant, reasonable, and effective experiments, and the obtained results demonstrate that SDSPCA outperforms other state-of-the-art methods.

Non-negative Matrix Factorization (NMF), a classical method for dimensionality reduction, has been applied in many fields. It is based on the idea that negative numbers are physically meaningless in various data-processing tasks. Apart from its contribution to conventional data analysis, the recent overwhelming interest in NMF is due to its newly discovered ability to solve challenging data mining and machine learning problems, especially in relation to gene expression data. This survey paper mainlyfocuses on research examining the application of NMF to identify differentially expressed genes and to cluster samples, and the main NMF models, properties, principles, and algorithms with its various generalizations, extensions, and modifications are summarized. The experimental results demonstrate the performance of the various NMF algorithms in identifying differentially expressed genes and clustering samples.