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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]

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]

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]

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. [ABSTRACT FROM AUTHOR]

Cancer genomic data contain views from different sources that provide complementary information about genetic activity. This provides a new way for cancer research. Feature selection and multi-view clustering are hot topics in bioinformatics, and they can make full use of complementary information to improve the effect. In this paper, a novel integrated model called Multi-view Non-negative Matrix Factorization (MvNMF) is proposed for the selection of common differential genes (co-differential genes) and multi-view clustering. In order to encode the geometric information in the multi-view genomic data, graph regularized MvNMF (GMvNMF) is further proposed by applying the graph regularization constraint in the objective function. GMvNMF can not only obtain the potential shared feature structure and shared cluster group structure, but also capture the manifold structure of multi-view data. The validity of the proposed GMvNMF method was tested in four multi-view genomic data. Experimental results showed that the GMvNMF method has better performance than other representative methods. [ABSTRACT FROM AUTHOR]