A novel low-rank representation method for identifying differentially expressed genes

Xu, Xiu; Gao, Ying; Liu, Jinxing; Wang, Ya Xuan; Dai, Ling; Kong, Xiang; Yuan, Sha Sha

doi:10.1504/ijdmb.2017.090985

Cited by 4 publications

(4 citation statements)

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“…where ( is the i -th largest singular value of Z ) denotes the nuclear norm of matrix Z , and denotes the L 2,1 -norm of matrix P . To get a self-expression model, the observation data X are generally installed as the dictionary matrix [ 13 , 14 , 22 ]. The final LRR model becomes …”

Section: Methodsmentioning

confidence: 99%

“…Graph-Laplacian regularization is an outstanding manifold learning method, which can uncover the internal geometrical structures among the data points. As a result, naturally, appears a number of LRR models regularized by graph embedding manifold regularization [ 13 , 43 ].…”

Section: Methodsmentioning

confidence: 99%

“…The experimental data X are usually obtained from a union of multiple subspaces rather than a single space, where indicates low-dimensional space hidden in high-dimensional space [ 13 – 15 ]. Since these methods related to PCA prefer to research the data obtained from a single low-dimensional space, Liu et al .…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the nuclear norm maybe not the best way to approximate the rank of the matrix. To better approximate the rank and handle the non-convex optimizing problems, the truncated nuclear norm (TNN) was proposed in [ 24 ] and attracted much attention [ 13 , 23 , 25 , 26 ]. The TNN that is the sum of few smallest singular values of a matrix can dispel the harm of shrinkage of the leading singular values, so it may be a more robust regularization to get the rank of a matrix than the nuclear norm.…”

Section: Introductionmentioning

confidence: 99%

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A truncated nuclear norm and graph-Laplacian regularized low-rank representation method for tumor clustering and gene selection

Liu

2021

BMC Bioinformatics

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Background Clustering and feature selection act major roles in many communities. As a matrix factorization, Low-Rank Representation (LRR) has attracted lots of attentions in clustering and feature selection, but sometimes its performance is frustrated when the data samples are insufficient or contain a lot of noise. Results To address this drawback, a novel LRR model named TGLRR is proposed by integrating the truncated nuclear norm with graph-Laplacian. Different from the nuclear norm minimizing all singular values, the truncated nuclear norm only minimizes some smallest singular values, which can dispel the harm of shrinkage of the leading singular values. Finally, an efficient algorithm based on Linearized Alternating Direction with Adaptive Penalty is applied to resolving the optimization problem. Conclusions The results show that the TGLRR method exceeds the existing state-of-the-art methods in aspect of tumor clustering and gene selection on integrated gene expression data.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A truncated nuclear norm and graph-Laplacian regularized low-rank representation method for tumor clustering and gene selection

Liu

2021

BMC Bioinformatics

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CNLLRR: A Novel Low-Rank Representation Method for Single-cell RNA-seq Data Analysis

Liu

Gao

et al. 2019

Preprint

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The development of single-cell RNA-sequencing (scRNA-seq) technology has enabled the measurement of gene expression in individual cells. This provides an unprecedented opportunity to explore the biological mechanisms at the cellular level. However, existing scRNA-seq analysis methods are susceptible to noise and outliers or ignore the manifold structure inherent in the data. In this paper, a novel method called Cauchy non-negative Laplacian regularized low-rank representation (CNLLRR) is proposed to alleviate the above problem. Specifically, we employ the Cauchy loss function (CLF) instead of the conventional norm constraints in the noise matrix of CNLLRR, which will enhance the robustness of the method. In addition, graph regularization term is applied to the objective function, which can capture the paired geometric relationships between cells. Then, alternating direction method of multipliers (ADMM) is adopted to solve the optimization problem of CNLLRR. Finally, extensive experiments on scRNA-seq data reveal that the proposed CNLLRR method outperforms other state-of-the-art methods for cell clustering, cell visualization and prioritization of gene markers. CNLLRR contributes to understand the heterogeneity between cell populations in complex biological systems. Author summaryAnalysis of single-cell data can help to further study the heterogeneity and complexity of cell populations. The current analysis methods are mainly to learn the similarity between cells and cells. Then they use the clustering algorithm to perform cell clustering or downstream analysis on the obtained similarity matrix. Therefore, constructing accurate cell-to-cell similarity is crucial for single-cell data analysis. In this paper, we design a novel Cauchy non-negative Laplacian regularized low-rank representation (CNLLRR) method to get a better similarity matrix. Specifically, Cauchy loss function (CLF) constraint is applied to punish noise matrix, which will improve the robustness of CNLLRR to noise and outliers. Moreover, graph regularization term is applied to the objective function, which will effectively encode the October 17, 20191/17 local manifold information of the data. Further, these will guarantee the quality of the cell-to-cell similarity matrix learned. Finally, single-cell data analysis experiments show that our method is superior to other representative methods. 2 been generated due to the development of next-generation sequencing technologies [1]. 3 At the same time, scRNA-seq data contain a wealth of information on biological 4 function and gene regulation. Analysis and research on these information pave us a way 5 to observe individual cells unprecedentedly [2]. It thus provides us possibilities to 6 explore the heterogeneity and complexity of cell population. It also offers us an 7 unprecedented opportunity to learn the biological mechanisms and functional diversity 8 at the cellular level. 9 With the help of scRNA sequencing, identification of subpopulation of cells [3] is 10 now possible. The identification can be c...

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Visualization and Analysis of Single Cell RNA-Seq Data by Maximizing Correntropy Based Non-Negative Low Rank Representation

Jiao

Liu

Wang

et al. 2022

IEEE J. Biomed. Health Inform.

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A novel low-rank representation method for identifying differentially expressed genes

Cited by 4 publications

References 0 publications

A truncated nuclear norm and graph-Laplacian regularized low-rank representation method for tumor clustering and gene selection

A truncated nuclear norm and graph-Laplacian regularized low-rank representation method for tumor clustering and gene selection

CNLLRR: A Novel Low-Rank Representation Method for Single-cell RNA-seq Data Analysis

Visualization and Analysis of Single Cell RNA-Seq Data by Maximizing Correntropy Based Non-Negative Low Rank Representation

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