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High-throughput sequencing of single-cell gene expression reveals a complex mechanism of individual cell's heterogeneity in a population. An important purpose for analyzing single-cell RNA sequencing (scRNA-seq) data is to identify cell subtypes and functions by cell clustering. To deal with high levels of noise and cellular heterogeneity, we introduced a new single cell data analysis model called Adaptive Total-Variation Regularized Low-Rank Representation (ATV-LRR). In scRNA-seq data, ATV-LRR can reconstruct the low-rank subspace structure to learn the similarity of cells. The low-rank representation can not only segment multiple linear subspaces, but also extract important information. Moreover, adaptive total variation also can remove cell noise and preserve cell feature details by learning the gradient information of the data. At the same time, to analyze scRNA-seq data with unknown prior information, we introduced the maximum eigenvalue method into the ATV-LRR model to automatically identify cell populations. The final clustering results show that the ATV-LRR model can detect cell types more effectively and stably.

There is much evidence that long non-coding RNA (lncRNA) is associated with many diseases. However, it is time-consuming and expensive to identify meaningful lncRNA-disease associations (LDAs) through medical or biological experiments. Therefore, investigating how to identify more meaningful LDAs is necessary, and at the same time it is conducive to the prevention, diagnosis and treatment of complex diseases. Considering the limitations of some current prediction models, a novel model based on bipartite local model with nearest profile-based association inferring, BLM-NPAI, is developed for predicting LDAs. This model predicts novel LDAs from the lncRNA side and the disease side, respectively. More importantly, for some lncRNAs and diseases without any association, the model can also be predicted by their nearest neighbors. Leave-one-out cross validation (LOOCV) and 5-fold cross validation are implemented for BLM-NPAI to evaluate the performance of this model. Our model is superior to current advanced methods in most cases. In addition, to verify the validity and reliability of BLM-NPAI, three disease cases and three lncRNA cases are analyzed to further evaluate BLM-NPAI. Finally, these predicted novel LDAs are confirmed by using the LncRNA-disease database.

Background: As a method to identify Differentially Expressed Genes (DEGs), Non- Negative Matrix Factorization (NMF) has been widely praised in bioinformatics. Although NMF can make DEGs to be easily identified, it cannot provide more associated information for these DEGs. Objective: The methods of network analysis can be used to analyze the correlation of genes, but they caused more data redundancy and great complexity in gene association analysis of high dimensions. Dimensionality reduction is worth considering in this condition. Methods: In this paper, we provide a new framework by combining the merits of two: NMF is applied to select DEGs for dimensionality reduction, and then Weighted Gene Co-Expression Network Analysis (WGCNA) is introduced to cluster on DEGs into similar function modules. The combination of NMF and WGCNA as a novel model accomplishes the analysis of DEGs for cholangiocarcinoma (CHOL). Results: Some hub genes from DEGs are highlighted in the co-expression network. Candidate pathways and genes are also discovered in the most relevant module of CHOL. Conclusion: The experiments indicate that our framework is effective and the works also provide some useful clues to the reaches of CHOL.

Background Predicting drug-target interactions is time-consuming and expensive. It is important to present the accuracy of the calculation method. There are many algorithms to predict global interactions, some of which use drug-target networks for prediction (ie, a bipartite graph of bound drug pairs and targets known to interact). Although these algorithms can predict some drug-target interactions to some extent, there is little effect for some new drugs or targets that have no known interaction. Results Since the datasets are usually located at or near low-dimensional nonlinear manifolds, we propose an improved GRMF (graph regularized matrix factorization) method to learn these flow patterns in combination with the previous matrix-decomposition method. In addition, we use one of the pre-processing steps previously proposed to improve the accuracy of the prediction. Conclusions Cross-validation is used to evaluate our method, and simulation experiments are used to predict new interactions. In most cases, our method is superior to other methods. Finally, some examples of new drugs and new targets are predicted by performing simulation experiments. And the improved GRMF method can better predict the remaining drug-target interactions.

The rapid development of single cell RNA sequencing (scRNA-seq) has made it possible to study the association between cells and genes at molecular resolution. When the follow-up analysis is carried out, it is often difficult to extract the cell information in high-dimensional space because of the high gene dimension in single-cell sequencing, which leads to inaccurate results in the follow-up analysis. To solve the problem, we propose a method called locally manifold non-negative matrix factorization based on centroid for scRNA-seq data analysis (MNMFC). MNMFC is a similarity modeling scheme based on locally manifold, which can map cell association in high dimensional space. Through similarity learning based on locally manifold and non-negative matrix decomposition (NMF) algorithm, the data in high-dimensional space can be mapped to low-dimensional space, which provides help for downstream clustering analysis. The performance of the model was validated experimentally on 10 scRNA-seq datasets. Compared with other nine advanced single-cell clustering methods, whether it is a comprehensive analysis or an individual analysis of the dataset, MNMFC has achieved encouraging results.

Background In the development of science and technology, there are increasing evidences that there are some associations between lncRNAs and human diseases. Therefore, finding these associations between them will have a huge impact on our treatment and prevention of some diseases. However, the process of finding the associations between them is very difficult and requires a lot of time and effort. Therefore, it is particularly important to find some good methods for predicting lncRNA-disease associations (LDAs). Results In this paper, we propose a method based on dual sparse collaborative matrix factorization (DSCMF) to predict LDAs. The DSCMF method is improved on the traditional collaborative matrix factorization method. To increase the sparsity, the L2,1-norm is added in our method. At the same time, Gaussian interaction profile kernel is added to our method, which increase the network similarity between lncRNA and disease. Finally, the AUC value obtained by the experiment is used to evaluate the quality of our method, and the AUC value is obtained by the ten-fold cross-validation method. Conclusions The AUC value obtained by the DSCMF method is 0.8523. At the end of the paper, simulation experiment is carried out, and the experimental results of prostate cancer, breast cancer, ovarian cancer and colorectal cancer are analyzed in detail. The DSCMF method is expected to bring some help to lncRNA-disease associations research. The code can access the https://github.com/Ming-0113/DSCMF website.

Background MicroRNAs (miRNAs) are non-coding RNAs with regulatory functions. Many studies have shown that miRNAs are closely associated with human diseases. Among the methods to explore the relationship between the miRNA and the disease, traditional methods are time-consuming and the accuracy needs to be improved. In view of the shortcoming of previous models, a method, collaborative matrix factorization based on matrix completion (MCCMF) is proposed to predict the unknown miRNA-disease associations. Results The complete matrix of the miRNA and the disease is obtained by matrix completion. Moreover, Gaussian Interaction Profile kernel is added to the miRNA functional similarity matrix and the disease semantic similarity matrix. Then the Weight K Nearest Known Neighbors method is used to pretreat the association matrix, so the model is close to the reality. Finally, collaborative matrix factorization method is applied to obtain the prediction results. Therefore, the MCCMF obtains a satisfactory result in the fivefold cross-validation, with an AUC of 0.9569 (0.0005). Conclusions The AUC value of MCCMF is higher than other advanced methods in the fivefold cross validation experiment. In order to comprehensively evaluate the performance of MCCMF, accuracy, precision, recall and f-measure are also added. The final experimental results demonstrate that MCCMF outperforms other methods in predicting miRNA-disease associations. In the end, the effectiveness and practicability of MCCMF are further verified by researching three specific diseases.

The noise problem of cancer sequencing data has been a problem that can't be ignored. Utilizing considerable way to reduce noise of these cancer data is an important issue in the analysis of gene co-expression network. In this paper, we apply a sparse and low-rank method which is Robust Principal Component Analysis (RPCA) to solve the noise problem for integrated data of multi-cancers from The Cancer Genome Atlas (TCGA). And then we build the gene co-expression network based on the integrated data after noise reduction. Finally, we perform nodes and pathways mining on the denoising networks. Experiments in this paper show that after denoising by RPCA, the gene expression data tend to be orderly and neat than before, and the constructed networks contain more pathway enrichment information than unprocessed data. Moreover, learning from the betweenness centrality of the nodes in the network, we find some abnormally expressed genes and pathways proven that are associated with many cancers from the denoised network. The experimental results indicate that our method is reasonable and effective, and we also find some candidate suspicious genes that may be linked to multi-cancers.

Studies of cancers have become diversified in recent years, especially with the availability of multi-omics data. Establishing an effective integrative model to process more types of data has become a new research hotspot. In order to conduct deeper mining in cancer, building a gene co-expression network based on multi-omics data for more valuable clues is the useful means in this research. Based on the data-driven problems of cancer networks, this paper proposes an integrated Graph Regularized Non-negative Matrix Factorization model that can be used for network analysis called iGMFNA. We apply iGMFNA to two cancer datasets from The Cancer Genome Atlas (TCGA) for analysis. We demonstrate that our method is indeed more effective than other integrated methods. In terms of network analysis and mining, we also define a multi-measure for nodes in the network to identify cancer-related genes. Through text mining, we verify some genes discovered by iGMFNA.

As we all know, science and technology are developing faster and faster. Many experts and scholars have demonstrated that human diseases are related to lncRNA, but only a few associations have been confirmed, and many unknown associations need to be found. In the process of finding associations, it takes a lot of time, so finding an efficient way to predict the associations between lncRNAs and diseases is particularly important. In this paper, we propose a multi-label fusion collaborative matrix factorization (MLFCMF) approach for predicting lncRNA-disease associations (LDAs). Firstly, the lncRNA space and disease space are optimized by multi-label to enhance the intrinsic link between lncRNA and disease and to tap potential information. Multi-label learning can encode a variety of data information from the sample space. Secondly, to learn multi-label information in the data space, the fusion method is used to handle the relationship between multiple labels. More comprehensive information will be obtained by weighing the effects of different labels. The addition of Gaussian interaction profile (GIP) kernel can increase the network similarity. Finally, the lncRNA-disease associations are predicted by the method of collaborative matrix factorization. The ten-fold cross-validation method is used to evaluate the MLFCMF method, and our method finally obtains an AUC value of 0.8612. Detailed analysis of ovarian cancer, colorectal cancer, and lung cancer in the simulation experiment results. So it can be seen that our method MLFCMF is an effective model for predicting lncRNA-disease associations.

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 mainly focuses 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.

In modern molecular biology, the hotspots and difficulties of this field are identifying characteristic genes from gene expression data. Traditional reconstruction-error-minimization model principal component analysis (PCA) as a matrix decomposition method uses quadratic error function, which is known sensitive to outliers and noise. Hence, it is necessary to learn a good PCA method when outliers and noise exist. In this paper, we develop a novel PCA method enforcing P-norm on error function and graph-Laplacian regularization term for matrix decomposition problem, which is called as PgLPCA. The heart of the method designing for reducing outliers and noise is a new error function based on non-convex proximal P-norm. Besides, Laplacian regularization term is used to find the internal geometric structure in the data representation. To solve the minimization problem, we develop an efficient optimization algorithm based on the augmented Lagrange multiplier method. This method is used to select characteristic genes and cluster the samples from explosive biological data, which has higher accuracy than compared methods.

// Dong-Qin Wang 1 , Ying-Lian Gao 2 , Jin-Xing Liu 1 , Chun-Hou Zheng 1 and Xiang-Zhen Kong 1 1 School of Information Science and Engineering, Qufu Normal University, Rizhao, China 2 Library of Qufu Normal University, Qufu Normal University, Rizhao, China Correspondence to: Jin-Xing Liu, email: sdcavell@126.com Chun-Hou Zheng, email: zhengch99@126.com Keywords: L 2,1 -norm, L 1 -norm, integrative penalized matrix decomposition, paired drug-pathway associations, drug discovery Received: January 23, 2017 Accepted: May 01, 2017 Published: May 29, 2017 ABSTRACT The traditional methods of drug discovery follow the “one drug-one target” approach, which ignores the cellular and physiological environment of the action mechanism of drugs. However, pathway-based drug discovery methods can overcome this limitation. This kind of method, such as the Integrative Penalized Matrix Decomposition (iPaD) method, identifies the drug-pathway associations by taking the lasso-type penalty on the regularization term. Moreover, instead of imposing the L 1 -norm regularization, the L 2,1 -Integrative Penalized Matrix Decomposition (L 2,1 -iPaD) method imposes the L 2,1 -norm penalty on the regularization term. In this paper, based on the iPaD and L 2,1 -iPaD methods, we propose a novel method named L 1 L 2,1 -iPaD (L 1 L 2,1 -Integrative Penalized Matrix Decomposition), which takes the sum of the L 1 -norm and L 2,1 -norm penalties on the regularization term. Besides, we perform permutation test to assess the significance of the identified drug-pathway association pairs and compute the P-values. Compared with the existing methods, our method can identify more drug-pathway association pairs which have been validated in the CancerResource database. In order to identify drug-pathway associations which are not validated in the CancerResource database, we retrieve published papers to prove these associations. The results on two real datasets prove that our method can achieve better enrichment for identified association pairs than the iPaD and L 2,1 -iPaD methods.

It is of urgency to effectively identify differentially expressed genes from RNA-Seq data. In this paper, we proposed a novel method, joint-L2,1-norm-constraint-based semi-supervised feature extraction (L21SFE), to analyze RNA-Seq data. Our scheme was shown as follows. Firstly, we constructed a graph Laplacian matrix and refined it by using the labeled samples. Our graph construction method can make full use of a large number of unlabelled samples. Secondly, we found semi-supervised optimal maps by solving a generalized eigenvalue problem. Thirdly, we solved an optimal problem via the joint L2,1-norm constraint to obtain a projection matrix. It can diminish the impact of noises and outliers by using the L2,1-norm constraint and produce more precise results. Finally, we identified differentially expressed genes based on the projection matrix. The results on simulation and real RNA-Seq data sets demonstrated the feasibility and effectiveness of our method.

Non-negative Matrix Factorization (NMF) is a dimensionality reduction approach for learning a parts-based and linear representation of non-negative data. It has attracted more attention because of that. In practice, NMF not only neglects the manifold structure of data samples, but also overlooks the priori label information of different classes. In this paper, a novel matrix decomposition method called Hyper-graph regularized Constrained Non-negative Matrix Factorization (HCNMF) is proposed for selecting differentially expressed genes and tumor sample classification. The advantage of hyper-graph learning is to capture local spatial information in high dimensional data. This method incorporates a hyper-graph regularization constraint to consider the higher order data sample relationships. The application of hyper-graph theory can effectively find pathogenic genes in cancer datasets. Besides, the label information is further incorporated in the objective function to improve the discriminative ability of the decomposition matrix. Supervised learning with label information greatly improves the classification effect. We also provide the iterative update rules and convergence proofs for the optimization problems of HCNMF. Experiments under The Cancer Genome Atlas (TCGA) datasets confirm the superiority of HCNMF algorithm compared with other representative algorithms through a set of evaluations.

Lately, on account of being associated with many human diseases, more and more attentions are paid to microRNAs (miRNAs). Accumulating experimental studies of predicting novel miRNA-disease associations (MDAs) are costly and time-consuming. And there are also many unknown associations between miRNAs and diseases. Therefore, it is a momentous topic to predict possible associations between miRNAs and diseases. Also, it is urgent to increase the accuracy of predictive performance. In this paper, we put forward a computation method of Predicting MiRNA-Disease Associations with Collaborative Matrix Factorization based on Double Sparse and Nearest Profile (DSNPCMF) to estimate underlying miRNA-disease associations. In this model, we integrate Nearest Profile (NP) and Gaussian Interaction Profile (GIP) kernels of miRNAs and diseases to augment information of their neighbors and kernel similarities to improve the predictive ability. In addition, L2,1-norm and L1-norm are introduced into this method to increase the sparseness. Then five-fold cross validation is used for assessing our developed method. At the same time, simulation experiment is used to detect the result of prediction, including both known MDAs and new MDAs that are in descending order. In the end, the results prove that the accuracy of our prediction is better than other previous perfect methods. And our method has the ability to predict latent associations of miRNAs and diseases.

In recent years, with the diversity and variability of cancer information, the multi-omics data have been applied in various fields. Many existing models of principal component analysis can only process single data, which makes limitations on cancer research. Therefore, in this paper, a new model called integrative principal component analysis (IPCA) is proposed to achieve the unification of multi-omics data. In addition, in order to preserve the high-order manifold structure between the data, an integrative hypergraph regularization principal component analysis (IHPCA) is further proposed by applying the hypergraph regularization constraint. The effectiveness of IHPCA method is tested on four multi-omics datasets. Experimental results show that the proposed method has better performance than other representative methods on sample clustering and common expression genes (co-expression genes) network analysis.

BackgroundAs one of the most popular data representation methods, non-negative matrix decomposition (NMF) has been widely concerned in the tasks of clustering and feature selection. However, most of the previously proposed NMF-based methods do not adequately explore the hidden geometrical structure in the data. At the same time, noise and outliers are inevitably present in the data.ResultsTo alleviate these problems, we present a novel NMF framework named robust hypergraph regularized non-negative matrix factorization (RHNMF). In particular, the hypergraph Laplacian regularization is imposed to capture the geometric information of original data. Unlike graph Laplacian regularization which captures the relationship between pairwise sample points, it captures the high-order relationship among more sample points. Moreover, the robustness of the RHNMF is enhanced by using the L2,1-norm constraint when estimating the residual. This is because the L2,1-norm is insensitive to noise and outliers.ConclusionsClustering and common abnormal expression gene (com-abnormal expression gene) selection are conducted to test the validity of the RHNMF model. Extensive experimental results on multi-view datasets reveal that our proposed model outperforms other state-of-the-art methods.

Background Predicting meaningful miRNA-disease associations (MDAs) is costly. Therefore, an increasing number of researchers are beginning to focus on methods to predict potential MDAs. Thus, prediction methods with improved accuracy are under development. An efficient computational method is proposed to be crucial for predicting novel MDAs. For improved experimental productivity, large biological datasets are used by researchers. Although there are many effective and feasible methods to predict potential MDAs, the possibility remains that these methods are flawed. Results A simple and effective method, known as Nearest Profile-based Collaborative Matrix Factorization (NPCMF), is proposed to identify novel MDAs. The nearest profile is introduced to our method to achieve the highest AUC value compared with other advanced methods. For some miRNAs and diseases without any association, we use the nearest neighbour information to complete the prediction. Conclusions To evaluate the performance of our method, five-fold cross-validation is used to calculate the AUC value. At the same time, three disease cases, gastric neoplasms, rectal neoplasms and colonic neoplasms, are used to predict novel MDAs on a gold-standard dataset. We predict the vast majority of known MDAs and some novel MDAs. Finally, the prediction accuracy of our method is determined to be better than that of other existing methods. Thus, the proposed prediction model can obtain reliable experimental results.

Principal Component Analysis (PCA) as a tool for dimensionality reduction is widely used in many areas. In the area of bioinformatics, each involved variable corresponds to a specific gene. In order to improve the robustness of PCA-based method, this paper proposes a novel graph-Laplacian PCA algorithm by adoptingL1/2constraint (L1/2gLPCA) on error function for feature (gene) extraction. The error function based onL1/2-norm helps to reduce the influence of outliers and noise. Augmented Lagrange Multipliers (ALM) method is applied to solve the subproblem. This method gets better results in feature extraction than other state-of-the-art PCA-based methods. Extensive experimental results on simulation data and gene expression data sets demonstrate that our method can get higher identification accuracies than others.

With the development of deep sequencing technologies, many RNA-Seq data have been generated. Researchers have proposed many methods based on the sparse theory to identify the differentially expressed genes from these data. In order to improve the performance of sparse principal component analysis, in this paper, we propose a novel class-information-based sparse component analysis (CISCA) method which introduces the class information via a total scatter matrix. First, CISCA normalizes the RNA-Seq data by using a Poisson model to obtain their differential sections. Second, the total scatter matrix is gotten by combining the between-class and within-class scatter matrices. Third, we decompose the total scatter matrix by using singular value decomposition and construct a new data matrix by using singular values and left singular vectors. Then, aiming at obtaining sparse components, CISCA decomposes the constructed data matrix by solving an optimization problem with sparse constraints on loading vectors. Finally, the differentially expressed genes are identified by using the sparse loading vectors. The results on simulation and real RNA-Seq data demonstrate that our method is effective and suitable for analyzing these data.

Non-negative Matrix Factorization (NMF) is a popular data dimension reduction method in recent years. The traditional NMF method has high sensitivity to data noise. In the paper, we propose a model called Sparse Robust Graph-regularized Non-negative Matrix Factorization based on Correntropy (SGNMFC). The maximized correntropy replaces the traditional minimized Euclidean distance to improve the robustness of the algorithm. Through the kernel function, correntropy can give less weight to outliers and noise in data but give greater weight to meaningful data. Meanwhile, the geometry structure of the high-dimensional data is completely preserved in the low-dimensional manifold through the graph regularization. Feature selection and sample clustering are commonly used methods for analyzing genes. Sparse constraints are applied to the loss function to reduce matrix complexity and analysis difficulty. Comparing the other five similar methods, the effectiveness of the SGNMFC model is proved by selection of differentially expressed genes and sample clustering experiments in three The Cancer Genome Atlas (TCGA) datasets.

With the development of cancer research, various gene expression datasets containing cancer information show an explosive growth trend. In addition, due to the continuous maturity of single-cell RNA sequencing (scRNA-seq) technology, the protein information and pedigree information of a single cell are also continuously mined. It is a technical problem of how to classify these high-dimensional data correctly. In recent years, Extreme Learning Machine (ELM) has been widely used in the field of supervised learning and unsupervised learning. However, the traditional ELM does not consider the robustness of the method. To improve the robustness of ELM, in this paper, a novel ELM method based on L 2 , 1 -norm named L 2 , 1 -Extreme Learning Machine ( L 2 , 1 -ELM) has been proposed. The method introduces L 2 , 1 -norm on loss function to improve the robustness, and minimizes the influence of noise and outliers. Firstly, we evaluate the new method on five UCI datasets. The experiment results prove that our method can achieve competitive results. Next, the novel method is applied to the problem of classification of cancer samples and single-cell RNA sequencing datasets. The experimental results on The Cancer Genome Atlas (TCGA) datasets and scRNA-seq datasets prove that ELM and its variants has great potential in the classification of cancer samples.

Background Predicting drug-disease interactions (DDIs) is time-consuming and expensive. Improving the accuracy of prediction results is necessary, and it is crucial to develop a novel computing technology to predict new DDIs. The existing methods mostly use the construction of heterogeneous networks to predict new DDIs. However, the number of known interacting drug-disease pairs is small, so there will be many errors in this heterogeneous network that will interfere with the final results. Results A novel method, known as the dual-network L2,1-collaborative matrix factorization, is proposed to predict novel DDIs. The Gaussian interaction profile kernels and L2,1-norm are introduced in our method to achieve better results than other advanced methods. The network similarities of drugs and diseases with their chemical and semantic similarities are combined in this method. Conclusions Cross validation is used to evaluate our method, and simulation experiments are used to predict new interactions using two different datasets. Finally, our prediction accuracy is better than other existing methods. This proves that our method is feasible and effective.

With the development of science and technology, there are increasing evidences that lncRNAs are associated with diseases, so it is particularly important to find some novel lncRNA-disease associations (LDAs). Finding some novel lncRNA-disease associations is benefit to us in the treatment and prevention of diseases, but this process requires a lot of energy and time, so there is an urgent need to discover some new methods. In this paper, a dual sparse collaborative matrix factorization method based on gaussian kernel function (DSCMF) is proposed to predict novel LDAs. DSCMF is based on the traditional collaborative matrix factorization method. The lncRNA network similarity matrix is combined with the lncRNA expression similarity matrix, and the disease network similarity matrix is combined with the disease expression similarity matrix. Therefore, the Gaussian interaction profile kernel is added. To increase the sparsity, the L2,1-norm is also added. Finally, the AUC value is obtained by ten-fold cross-validation method as the evaluation indicator of the performance of this method. The simulation experiment is used to predict some novel associations. The experimental results prove that this method will be of great help to future research.

In the big data era, sequencing technology has produced a large number of biological sequencing data. Different views of the cancer genome data provide sufficient complementary information to explore genetic activity. The identification of differentially expressed genes from multiview cancer gene data is of great importance in cancer diagnosis and treatment. In this paper, we propose a novel method for identifying differentially expressed genes based on tensor robust principal component analysis (TRPCA), which extends the matrix method to the processing of multiway data. To identify differentially expressed genes, the plan is carried out as follows. First, multiview data containing cancer gene expression data from different sources are prepared. Second, the original tensor is decomposed into a sum of a low-rank tensor and a sparse tensor using TRPCA. Third, the differentially expressed genes are considered to be sparse perturbed signals and then identified based on the sparse tensor. Fourth, the differentially expressed genes are evaluated using Gene Ontology and Gene Cards tools. The validity of the TRPCA method was tested using two sets of multiview data. The experimental results showed that our method is superior to the representative methods in efficiency and accuracy aspects.

Nonnegative Matrix Factorization (NMF) is a significant big data analysis technique. However, standard NMF regularized by simple graph does not have discriminative function, and traditional graph models cannot accurately reflect the problem of multigeometry information between data. To solve the above problem, this paper proposed a new method called Hypergraph Regularized Discriminative Nonnegative Matrix Factorization (HDNMF), which captures intrinsic geometry by constructing hypergraphs rather than simple graphs. The introduction of the hypergraph method allows high-order relationships between samples to be considered, and the introduction of label information enables the method to have discriminative effect. Both the hypergraph Laplace and the discriminative label information are utilized together to learn the projection matrix in the standard method. In addition, we offered a corresponding multiplication update solution for the optimization. Experiments indicate that the method proposed is more effective by comparing with the earlier methods.

Non-negative matrix decomposition (NMF) has been widely used for sample clustering and feature selection in the field of bioinformatics. However, the existing methods based on NMF cannot effectively deal with the problem of intrinsic geometrical structure, noise, and outliers in gene expression data. In this paper, a novel method called Robust Hypergraph regularized Non-negative Matrix Factorization (RHNMF) is proposed to solve the above problem. Firstly, the hypergraph Laplacian regularization is introduced to consider the intrinsic geometrical structure of the high dimension data. Secondly, the L 2,1 -norm is applied in the error function to reduce effects of the noise and outliers, which may improve the robustness of the algorithm. Finally, we perform clustering and common abnormal expression genes (com-abnormal expression genes) selection on multi-view gene expression data to verify the rationality and validity of the RHNMF method. Extensive experimental results demonstrate that our proposed RHNMF method has better performance than other state-of-the-art methods.

Non-negative Matrix Factorization (NMF) is recognized as one of fundamentally important and highly popular methods for clustering and feature selection, and many related methods have been proposed so far. Nevertheless, their performances, especially on real data, are still unclear due to few studies focusing on their comparison. This study aims at a assessment study of several representative methods from clustering and feature selection, including NMF, GNMF, MD-NMF, L2,1NMF, LNMF, Convex-NMF and Semi-NMF, on the data of the Cancer Genome Atlas (TCGA), which is one of current research hotspot of bioinformatics. Specifically, three data types of four cancers are either separately or integratedly decomposed as the coefficient matrices and the basis matrices by these NMF methods. The coefficient matrices are evaluated by accuracies of clustered samples and the basis matrices are assessed by p-values of selected genes. Experiment results not only show merits and limitations of compared NMF methods, which may provide guidelines for applying them and proposing novel NMF methods, but also reveal several clues for the exploration of related cancers.

Background Traditional drug identification methods follow the “one drug-one target” thought. But those methods ignore the natural characters of human diseases. To overcome this limitation, many identification methods of drug-pathway association pairs have been developed, such as the integrative penalized matrix decomposition (iPaD) method. The iPaD method imposes the L1-norm penalty on the regularization term. However, lasso-type penalties have an obvious disadvantage, that is, the sparsity produced by them is too dispersive. Results Therefore, to improve the performance of the iPaD method, we propose a novel method named L2,1-iPaD to identify paired drug-pathway associations. In the L2,1-iPaD model, we use the L2,1-norm penalty to replace the L1-norm penalty since the L2,1-norm penalty can produce row sparsity. Conclusions By applying the L2,1-iPaD method to the CCLE and NCI-60 datasets, we demonstrate that the performance of L2,1-iPaD method is superior to existing methods. And the proposed method can achieve better enrichment in terms of discovering validated drug-pathway association pairs than the iPaD method by performing permutation test. The results on the two real datasets prove that our method is effective.

Low-rank representation (LRR) via rank minimization is a high efficiency method for capturing low-dimensional structure embedded in high-dimensional data. However, minimizing the rank of a matrix is NP-hard. In this paper, robust truncated nuclear norm low-rank representation regularized by L 2,1 -norm method (RTLRR) is proposed. The truncated nuclear norm is introduced to replace the nuclear norm to approximate the rank function. At the same time, L 2,1 -norm is used to regularize the sparse matrix to achieve better sparse effect of the algorithm. The proposed method is divided into two steps. Firstly, we do singular value decomposition (SVD) to the original data matrix. Then we apply the truncated nuclear norm and L 2,1 -norm constraints to subproblems and use inexact augmented Lagrange multiplier method to solve subproblems. Finally, the genes with high scores will be identified as differentially expressed genes according to the sparse matrix. The results on The Cancer Genome Atlas (TCGA) data illustrate that the effectiveness of RTLRR method outperforms many methods.

Identifying differentially expressed genes from the thousands of genes is a challenging task. Robust principal component analysis (RPCA) is an efficient method in the identification of differentially expressed genes. RPCA method uses nuclear norm to approximate the rank function. However, theoretical studies showed that the nuclear norm minimizes all singular values, so it may not be the best solution to approximate the rank function. The truncated nuclear norm is defined as the sum of some smaller singular values, which may achieve a better approximation of the rank function than nuclear norm. In this paper, a novel method is proposed by replacing nuclear norm of RPCA with the truncated nuclear norm, which is named robust principal component analysis regularized by truncated nuclear norm (TRPCA). The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Thus, the differentially expressed genes can be identified according to the sparse matrix. The experimental results on The Cancer Genome Atlas data illustrate that the TRPCA method outperforms other state-of-the-art methods in the identification of differentially expressed genes.

Robust Principal Component Analysis (RPCA) is an efficient method in the selection of differentially expressed genes. However, nuclear norm minimizes all singular values simultaneously, so it may not be the best solution to replace the low-rank function. In this paper, the truncated nuclear norm is introduced. And a new method named Truncated nuclear norm regularized Robust Principal Component Analysis (TRPCA) is proposed. The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. The differentially expressed genes can be selected according to the sparse matrix. The experimental results on the The Cancer Genome Atlas (TCGA) data illustrate that the TRPCA method outperforms other state-of-the-art methods in the selection of differentially expressed genes.

Sparse Principal Component Analysis (SPCA) is a method that can get the sparse loadings of the principal components (PCs), and it may formulate PCA as a regression-type optimization problem by using the elastic net. But the selected features are different with each PC and generally independent. A new method named SPCA has been proposed for removing these detect, which replaces the elastic net with L 2,1 -norm penalty. The results of the method on gene expression data are still unknown. Therefore, we will take a test to prove this point in this paper. Firstly, this method is applied to the simulated data for obtaining an optimal parameter. Secondly, the L 2,1 SPCA method is applied to the gene expression data, that is the head and neck squamous carcinoma data (HNSC). Thirdly, the characteristic genes are selected according the PCs. The results consist of very lower P-value and very higher hit count, which shows the method of L 2,1 SPCA can obtain higher recognition accuracy and higher relevancy to the genes. Finally, the experimental results demonstrate that the L 2,1 SPCA works well and has good performances in the gene expression data.

Pathway-based drug discovery overcomes the disadvantages of the “one drug-one target” method, which aims to find the effective drugs to act on single targets. The current method “iPaD” identities the drug-pathway association pairs by taking the lasso-type penalty on the drug-pathway association matrix. In order to enhance the robustness of the methods and be more effective to find the novel drug-pathway association pairs, we introduce a new method named “L 2,1 -iPaD”. Compared with the iPaD method, we impose the L 2,1 -norm constraint on the drug-pathway association coefficient matrix. By applying our method to a real widely datasets (CCLE dataset), we demonstrate that our method is superior to the iPaD method. And our method can obtain the smaller P-values than the iPaD method by performing permutation test to assess the significance of the identified drug-pathway association pairs. More importantly, compared with the iPaD method, our method can identify larger numbers of validated drug-pathway association pairs. The experimental results on the real dataset demonstrate the effectiveness of our method.

The LLRR method decomposes the original data matrix into one low-rank matrix and one sparse matrix. And the low-rank matrix is represented by dictionary learning. The differentially expressed genes can be discovered from the sparse matrix.Display Omitted The Laplacian regularized low-rank representation method is introduced.The LLRR method is applied on genomic data to discover differentially expressed genes.The experiments are conducted on The Cancer Genome Atlas data. With the rapid development of DNA microarray technology and next-generation technology, a large number of genomic data were generated. So how to extract more differentially expressed genes from genomic data has become a matter of urgency. Because Low-Rank Representation (LRR) has the high performance in studying low-dimensional subspace structures, it has attracted a chunk of attention in recent years. However, it does not take into consideration the intrinsic geometric structures in data.In this paper, a new method named Laplacian regularized Low-Rank Representation (LLRR) has been proposed and applied on genomic data, which introduces graph regularization into LRR. By taking full advantages of the graph regularization, LLRR method can capture the intrinsic non-linear geometric information among the data. The LLRR method can decomposes the observation matrix of genomic data into a low rank matrix and a sparse matrix through solving an optimization problem. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Therefore, the differentially expressed genes can be selected according to the sparse matrix. Finally, we use the GO tool to analyze the selected genes and compare the P-values with other methods.The results on the simulation data and two real genomic data illustrate that this method outperforms some other methods: in differentially expressed gene selection.

The Cancer Genome Atlas (TCGA) dataset provides us more opportunities to systematically and comprehensively learn some biological mechanism of cancers formation, growth and metastasis. Since TCGA dataset includes heterogeneous data, it is one of the bioinformatics bottlenecks to mine some meaningful information from them. In this paper, to improve the performance of Robust Principal Component Analysis (RPCA) analyzing these heterogeneous data, a modified RPCA-based method, Block-Constraint Robust Principal Component Analysis (BCRPCA), is proposed. Since different categories data have different peculiarities, BCRPCA enforces different constraint intensities on different categories to improve the performance of RPCA. Firstly, the observation matrix of TCGA data is decomposed into two adding matrices A and S by using BCRPCA. Secondly, we use a ranking scheme to evaluate every feature and project these features to the genes. Then, the genes with high scores will be identified as differentially expressed ones. The main contributions of this paper are as following: firstly, it proposes, for the first time, the idea and method of BCRPCA to model TCGA data; secondly, it provides a BCRPCA-based framework for integrated analysis of TCGA data. The results show that our method is effective and suitable to analyze these data.

Recent research has demonstrated that characteristic gene selection based on gene expression data remains faced with considerable challenges. This is primarily because gene expression data are typically high dimensional, negative, non-sparse and noisy. However, existing methods for data analysis are able to cope with only some of these challenges. In this paper, we address all of these challenges with a unified method: nonnegative matrix factorization via the L2,1-norm (NMF-L2,1). While L2,1-norm minimization is applied to both the error function and the regularization term, our method is robust to outliers and noise in the data and generates sparse results. The application of our method to plant and tumor gene expression data demonstrates that NMF-L2,1 can extract more characteristic genes than other existing state-of-the-art methods.