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The development of single-cell RNA sequencing (scRNA-seq) technology has made it possible to measure gene expression levels at the resolution of a single cell, which further reveals the complex growth processes of cells such as mutation and differentiation. Recognizing cell heterogeneity is one of the most critical tasks in scRNA-seq research. To solve it, we propose a non-negative matrix factorization framework based on multi-subspace cell similarity learning for unsupervised scRNA-seq data analysis (MscNMF). MscNMF includes three parts: data decomposition, similarity learning, and similarity fusion. The three work together to complete the data similarity learning task. MscNMF can learn the gene features and cell features of different subspaces, and the correlation and heterogeneity between cells will be more prominent in multi-subspaces. The redundant information and noise in each low-dimensional feature space are eliminated, and its gene weight information can be further analyzed to calculate the optimal number of subpopulations. The final cell similarity learning will be more satisfactory due to the fusion of cell similarity information in different subspaces. The advantage of MscNMF is that it can calculate the number of cell types and the rank of Non-negative matrix factorization (NMF) reasonably. Experiments on eight real scRNA-seq datasets show that MscNMF can effectively perform clustering tasks and extract useful genetic markers. To verify its clustering performance, the framework is compared with other latest clustering algorithms and satisfactory results are obtained. The code of MscNMF is free available for academic (https://github.com/wangchuanyuan1/project-MscNMF). [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization (NMF) is a dimensionality reduction technique based on high-dimensional mapping. It can learn part-based representations effectively. In this paper, we propose a method called Dual Hyper-graph Regularized Supervised Non-negative Matrix Factorization (HSNMF). To encode the geometric information of the data, the hyper-graph is introduced into the model as a regularization term. The advantage of hyper-graph learning is to find higher order data relationship to enhance data relevance. This method constructs the data hyper-graph and the feature hyper-graph to find the data manifold and the feature manifold simultaneously. The application of hyper-graph theory in cancer datasets can effectively find pathogenic genes. The discrimination information is further introduced into the objective function to obtain more information about the data. Supervised learning with label information greatly improves the classification effect. Furthermore, the real datasets of cancer usually contain sparse noise, so the $L_{2,1}$ L 2 , 1 -norm is applied to enhance the robustness of HSNMF algorithm. Experiments under The Cancer Genome Atlas (TCGA) datasets verify the feasibility of the HSNMF method. [ABSTRACT FROM AUTHOR]

The identification of differentially expressed genes plays an increasingly important role biologically. Therefore, the feature selection approach has attracted much attention in the field of bioinformatics. The most popular method of principal component analysis studies two-dimensional data without considering the spatial geometric structure of the data. The recently proposed tensor robust principal component analysis method performs sparse and low-rank decomposition on three-dimensional tensors and effectively preserves the spatial structure. Based on this approach, the L2,1-norm regularization term is introduced into the DSTPCA (Double-Sparse Constrained Tensor Principal Component Analysis) method. The DSTPCA method removes the redundant noise by double sparse constraints on the objective function to obtain sufficiently sparse results. After the regularization norm is introduced into the model, the ADMM (alternating direction method of multipliers) algorithm is used to solve the optimal problem. In the experiment of feature selection, while the more redundant genes were filtered out, the more genes closely associated with disease were screened. Experimental results using different datasets indicate that our method outperforms other methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In recent years, many human diseases have been determined to be associated with certain lncRNAs. Only a small percentage of all lncRNA-disease associations (LDAs) have been discovered by researchers. Predicting novel LDAs is time-consuming and costly. It is crucial to propose a method that can effectively identify potential LDAs to solve this problem based on the available datasets. Although some current methods can effectively predict potential LDAs, the prediction accuracy needs to be improved, and there are few known associations. Moreover, there are notable errors in the method of constructing the network and the bipartite graph, which interfere with the final results. A weighted graph regularized collaborative matrix factorization (WGRCMF) method is proposed to predict novel LDAs. We introduce the graph regularization terms into the collaborative matrix factorization. Considering that manifold learning can recover low-dimensional manifold structures from high-dimensional sampled data, we can find low-dimensional manifolds in high-dimensional space. In addition, a weight matrix is also introduced into the method, the significance of which is to prevent unknown associations from contributing to the final prediction matrix. Finally, the prediction accuracy of this method is better than those of other methods. In several cancer cases, we implemented the corresponding simulation experiments. According to the experimental results, the proposed method is feasible and effective. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: Predicting miRNA-disease associations (MDAs) is time-consuming and expensive. It is imminent to improve the accuracy of prediction results. So it is crucial to develop a novel computing technology to predict new MDAs. Although some existing methods can effectively predict novel MDAs, there are still some shortcomings. Especially when the disease matrix is processed, its sparsity is an important factor affecting the final results. Results: A robust collaborative matrix factorization (RCMF) is proposed to predict novel MDAs. The L2,1-norm are introduced to our method to achieve the highest AUC value than other advanced methods. Conclusions: 5-fold cross validation is used to evaluate our method, and simulation experiments are used to predict novel associations on Gold Standard Dataset. Finally, our prediction accuracy is better than other existing advanced methods. Therefore, our approach is effective and feasible in predicting novel MDAs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

In terms of making genes expression data more interpretable and comprehensible, there exists a significant superiority on sparse methods. Many sparse methods, such as penalized matrix decomposition (PMD) and sparse principal component analysis (SPCA), have been applied to extract plants core genes. Supervised algorithms, especially the support vector machine-recursive feature elimination (SVM-RFE) method, always have good performance in gene selection. In this paper, we draw into class information via the total scatter matrix and put forward a class-information-based penalized matrix decomposition (CIPMD) method to improve the gene identification performance of PMD-based method. Firstly, the total scatter matrix is obtained based on different samples of the gene expression data. Secondly, a new data matrix is constructed by decomposing the total scatter matrix. Thirdly, the new data matrix is decomposed by PMD to obtain the sparse eigensamples. Finally, the core genes are identified according to the nonzero entries in eigensamples. The results on simulation data show that CIPMD method can reach higher identification accuracies than the conventional gene identification methods. Moreover, the results on real gene expression data demonstrate that CIPMD method can identify more core genes closely related to the abiotic stresses than the other methods. [ABSTRACT FROM AUTHOR]

With the development of deep sequencing, vast amounts of RNA-Seq data have been generated. It is crucial how to extract and interpret the meaningful information contained in deep sequencing data. In this paper, based on penalized matrix decomposition (PMD), a novel method, named PMDSeq, was proposed to analyze RNA-seq count data. Firstly, to obtain the differential expression matrix, the matrix of RNA-seq count data was normalized. Secondly, the differential expression matrix was decomposed into three factor matrices. By imposing appropriate constraint on factor matrices, the PMDSeq method can highlight the differentially expressed genes. Thirdly, the proposed method can identify the differentially expressed genes based on the scaled eigensamples. Finally, we used gene ontology tools to check these differentially expressed genes. The experimental results on simulation and three real RNA-seq count data sets demonstrated the effectiveness of our method. [ABSTRACT FROM PUBLISHER]