Robust hypergraph regularized non-negative matrix factorization for sample clustering and feature selection in multi-view gene expression data

Preprocessing of Single Cell RNA Sequencing Data Using Correlated Clustering and Projection

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing the downstream analysis. We present Correlated Clustering and Projection (CCP), a new data-domain dimensionality reduction method, for the first time. CCP projects each cluster of similar genes into a supergene defined as the accumulated pairwise nonlinear gene-gene correlations among all cells. Using 14 benchmark data sets, we demonstrate that CCP has significant advantages over classical principal component analysis (PCA) for clustering and/or classification problems with intrinsically high dimensionality. In addition, we introduce the Residue-Similarity index (RSI) as a novel metric for clustering and classification and the R-S plot as a new visualization tool. We show that the RSI correlates with accuracy without requiring the knowledge of the true labels. The R-S plot provides a unique alternative to the uniform manifold approximation and projection (UMAP) and t-distributed stochastic neighbor embedding (t-SNE) for data with a large number of cell types.

Multi-View Enhanced Tensor Nuclear Norm and Local Constraint Model for Cancer Clustering and Feature Gene Selection

The analysis of cancer data from multi-omics can effectively promote cancer research. The main focus of this article is to cluster cancer samples and identify feature genes to reveal the correlation between cancers and genes, with the primary approach being the analysis of multi-view cancer omics data. Our proposed solution, the Multi-View Enhanced Tensor Nuclear Norm and Local Constraint (MVET-LC) model, aims to utilize the consistency and complementarity of omics data to support biological research. The model is designed to maximize the utilization of multi-view data and incorporates a nuclear norm and local constraint to achieve this goal. The first step involves introducing the concept of enhanced partial sum of tensor nuclear norm, which significantly enhances the flexibility of the tensor nuclear norm. After that, we incorporate total variation regularization into the MVET-LC model to further augment its performance. It enables MVET-LC to make use of the relationship between tensor data structures and sparse data while paying attention to the feature details of the tensor data. To tackle the iterative optimization problem of MVET-LC, the alternating direction method of multipliers is utilized. Through experimental validation, it is demonstrated that our proposed model outperforms other comparison models.

Robust Graph Regularized NMF with Dissimilarity and Similarity Constraints for ScRNA-seq Data Clustering

The notable progress in single-cell RNA sequencing (ScRNA-seq) technology is beneficial to accurately discover the heterogeneity and diversity of cells. Clustering is an extremely important step during the ScRNA-seq data analysis. However, it cannot achieve satisfactory performances by directly clustering ScRNA-seq data due to its high dimensionality and noise. To address these issues, we propose a novel ScRNA-seq data representation model, termed Robust Graph regularized Non-Negative Matrix Factorization with Dissimilarity and Similarity constraints (RGNMF-DS), for ScRNA-seq data clustering. To accurately characterize the structure information of the labeled samples and the unlabeled samples, respectively, the proposed RGNMF-DS model adopts a couple of complementary regularizers (i.e., similarity and dissimilar regularizers) to guide matrix decomposition. In addition, we construct a graph regularizer to discover the local geometric structure hidden in ScRNA-seq data. Moreover, we adopt the l_2,1-norm to measure the reconstruction error and thereby effectively improve the robustness of the proposed RGNMF-DS model to the noises. Experimental results on several ScRNA-seq datasets have demonstrated that our proposed RGNMF-DS model outperforms other state-of-the-art competitors in clustering.

Gene Expression Analysis through Parallel Non-Negative Matrix Factorization

Genetic expression analysis is a principal tool to explain the behavior of genes in an organism when exposed to different experimental conditions. In the state of art, many clustering algorithms have been proposed. It is overwhelming the amount of biological data whose high-dimensional structure exceeds mostly current computational architectures. The computational time and memory consumption optimization actually become decisive factors in choosing clustering algorithms. We propose a clustering algorithm based on Non-negative Matrix Factorization and K-means to reduce data dimensionality but whilst preserving the biological context and prioritizing gene selection, and it is implemented within parallel GPU-based environments through the CUDA library. A well-known dataset is used in our tests and the quality of the results is measured through the Rand and Accuracy Index. The results show an increase in the acceleration of 6.22× compared to the sequential version. The algorithm is competitive in the biological datasets analysis and it is invariant with respect to the classes number and the size of the gene expression matrix.

HTRPCA: Hypergraph Regularized Tensor Robust Principal Component Analysis for Sample Clustering in Tumor Omics Data

In recent years, clustering analysis of cancer genomics data has gained widespread attention. However, limited by the dimensions of the matrix, the traditional methods cannot fully mine the underlying geometric structure information in the data. Besides, noise and outliers inevitably exist in the data. To solve the above two problems, we come up with a new method which uses tensor to represent cancer omics data and applies hypergraph to save the geometric structure information in original data. This model is called hypergraph regularized tensor robust principal component analysis (HTRPCA). The data processed by HTRPCA becomes two parts, one of which is a low-rank component that contains pure underlying structure information between samples, and the other is some sparse interference points. So we can use the low-rank component for clustering. This model can retain complex geometric information between more sample points due to the addition of the hypergraph regularization. Through clustering, we can demonstrate the effectiveness of HTRPCA, and the experimental results on TCGA datasets demonstrate that HTRPCA precedes other advanced methods. This paper proposes a new method of using tensors to represent cancer omics data and introduces hypergraph items to save the geometric structure information of the original data. At the same time, the model decomposes the original tensor into low-order tensors and sparse tensors. The low-rank tensor was used to cluster cancer samples to verify the effectiveness of the method.

L2,1-Extreme Learning Machine: An Efficient Robust Classifier for Tumor Classification

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.