Single-Cell RNA Sequencing Data Clustering by Low-Rank Subspace Ensemble Framework

Latent Low-Rank Representation With Weighted Distance Penalty for Clustering

Latent low-rank representation (LatLRR) is a critical self-representation technique that improves low-rank representation (LRR) by using observed and unobserved samples. It can simultaneously learn the low-dimensional structure embedded in the data space and capture the salient features. However, LatLRR ignores the local geometry structure and can be affected by the noise and redundancy in the original data space. To solve the above problems, we propose a latent LRR with weighted distance penalty (LLRRWD) for clustering in this article. First, a weighted distance is proposed to enhance the original Euclidean distance by enlarging the distance among the unconnected samples, which can enhance the discriminitation of the distance among the samples. By leveraging on the weighted distance, a weighted distance penalty is introduced to the LatLRR model to enable the method to preserve both the local geometric information and global information, improving discrimination of the learned affinity matrix. Moreover, a weight matrix is imposed on the sparse error norm to reduce the effect of noise and redundancy. Experimental results based on several benchmark databases show the effectiveness of our method in clustering.

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.

scRAE: Deterministic Regularized Autoencoders With Flexible Priors for Clustering Single-Cell Gene Expression Data

Clustering single-cell RNA sequence (scRNA-seq) data poses statistical and computational challenges due to their high-dimensionality and data-sparsity, also known as 'dropout' events. Recently, Regularized Auto-Encoder (RAE) based deep neural network models have achieved remarkable success in learning robust low-dimensional representations. The basic idea in RAEs is to learn a non-linear mapping from the high-dimensional data space to a low-dimensional latent space and vice-versa, simultaneously imposing a distributional prior on the latent space, which brings in a regularization effect. This paper argues that RAEs suffer from the infamous problem of bias-variance trade-off in their naive formulation. While a simple AE wita latent regularization results in data over-fitting, a very strong prior leads to under-representation and thus bad clustering. To address the above issues, we propose a modified RAE framework (called the scRAE) for effective clustering of the single-cell RNA sequencing data. scRAE consists of deterministic AE with a flexibly learnable prior generator network, which is jointly trained with the AE. This facilitates scRAE to trade-off better between the bias and variance in the latent space. We demonstrate the efficacy of the proposed method through extensive experimentation on several real-world single-cell Gene expression datasets. The code for our work is available at https://github.com/arnabkmondal/scRAE.

Visualization and Analysis of Single cell RNA-seq Data by Maximizing Correntropy based Non-negative Low Rank Representation

The exploration of single cell RNA-sequencing (scRNA-seq) technology generates a new perspective to analyze biological problems. One of the major applications of scRNA-seq data is to discover subtypes of cells by cell clustering. Nevertheless, it is challengeable for traditional methods to handle scRNA-seq data with high level of technical noise and notorious dropouts. To better analyze single cell data, a novel scRNA-seq data analysis model called Maximum correntropy criterion based Non-negative and Low Rank Representation (MccNLRR) is introduced. Specifically, the maximum correntropy criterion, as an effective loss function, is more robust to the high noise and large outliers existed in the data. Moreover, the low rank representation is proven to be a powerful tool for capturing the global and local structures of data. Therefore, some important information, such as the similarity of cells in the subspace, is also extracted by it. Then, an iterative algorithm on the basis of the half-quadratic optimization and alternating direction method is developed to settle the complex optimization problem. Before the experiment, we also analyze the convergence and robustness of MccNLRR. At last, the results of cell clustering, visualization analysis, and gene markers selection on scRNA-seq data reveal that MccNLRR method can distinguish cell subtypes accurately and robustly.

SCDRHA: A scRNA-Seq Data Dimensionality Reduction Algorithm Based on Hierarchical Autoencoder

Dimensionality reduction of high-dimensional data is crucial for single-cell RNA sequencing (scRNA-seq) visualization and clustering. One prominent challenge in scRNA-seq studies comes from the dropout events, which lead to zero-inflated data. To address this issue, in this paper, we propose a scRNA-seq data dimensionality reduction algorithm based on a hierarchical autoencoder, termed SCDRHA. The proposed SCDRHA consists of two core modules, where the first module is a deep count autoencoder (DCA) that is used to denoise data, and the second module is a graph autoencoder that projects the data into a low-dimensional space. Experimental results demonstrate that SCDRHA has better performance than existing state-of-the-art algorithms on dimension reduction and noise reduction in five real scRNA-seq datasets. Besides, SCDRHA can also dramatically improve the performance of data visualization and cell clustering.

Adaptive Total-Variation Regularized Low-Rank Representation for Analyzing Single-Cell RNA-seq Data

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.