A Class-Information-Based Sparse Component Analysis Method to Identify Differentially Expressed Genes on RNA-Seq Data

A two-way rectification method for identifying differentially expressed genes by maximizing the co-function relationship

BACKGROUND

The identification of differentially expressed genes (DEGs) is an important task in many biological studies. The currently widely used methods often calculate a score for each gene by estimating the significance level in terms of the differential expression. However, biological experiments often have only three duplications, plus plenty of noises contain in gene expression datasets, which brings a great challenge to statistical analysis methods. Moreover, the abundance of gene expression levels are not evenly distributed. Thus, those low expressed genes are more easily to be detected by fold-change based methods, which may results in high false positives among the DEG list. Since phenotypical changes result from DEGs should be strongly related to several distinct cellular functions, a more robust method should be designed to increase the true positive rate of the functional related DEGs.

RESULTS

In this study, we propose a two-way rectification method for identifying DEGs by maximizing the co-function relationships between genes and their enriched cellular pathways. An iteration strategy is employed to sequentially narrow down the group of identified DEGs and their associated biological functions. Functional analyses reveal that the identified DEGs are well organized in the form of functional modules, and the enriched pathways are very significant with lower p-value and larger gene count.

CONCLUSIONS

An integrative rectification method was proposed to identify key DEGs and their related functions simultaneously. The experimental validations demonstrate that the method has high interpretability and feasibility. It performs very well in terms of the identification of remarkable functional related genes.

Joint Lp-Norm and L2,1-Norm Constrained Graph Laplacian PCA for Robust Tumor Sample Clustering and Gene Network Module Discovery

The dimensionality reduction method accompanied by different norm constraints plays an important role in mining useful information from large-scale gene expression data. In this article, a novel method named Lp-norm and L2,1-norm constrained graph Laplacian principal component analysis (PL21GPCA) based on traditional principal component analysis (PCA) is proposed for robust tumor sample clustering and gene network module discovery. Three aspects are highlighted in the PL21GPCA method. First, to degrade the high sensitivity to outliers and noise, the non-convex proximal Lp-norm (0 < p < 1)constraint is applied on the loss function. Second, to enhance the sparsity of gene expression in cancer samples, the L2,1-norm constraint is used on one of the regularization terms. Third, to retain the geometric structure of the data, we introduce the graph Laplacian regularization item to the PL21GPCA optimization model. Extensive experiments on five gene expression datasets, including one benchmark dataset, two single-cancer datasets from The Cancer Genome Atlas (TCGA), and two integrated datasets of multiple cancers from TCGA, are performed to validate the effectiveness of our method. The experimental results demonstrate that the PL21GPCA method performs better than many other methods in terms of tumor sample clustering. Additionally, this method is used to discover the gene network modules for the purpose of finding key genes that may be associated with some cancers.

Edge-group sparse PCA for network-guided high dimensional data analysis

Motivation

Principal component analysis (PCA) has been widely used to deal with high-dimensional gene expression data. In this study, we proposed an Edge-group Sparse PCA (ESPCA) model by incorporating the group structure from a prior gene network into the PCA framework for dimension reduction and feature interpretation. ESPCA enforces sparsity of principal component (PC) loadings through considering the connectivity of gene variables in the prior network. We developed an alternating iterative algorithm to solve ESPCA. The key of this algorithm is to solve a new k-edge sparse projection problem and a greedy strategy has been adapted to address it. Here we adopted ESPCA for analyzing multiple gene expression matrices simultaneously. By incorporating prior knowledge, our method can overcome the drawbacks of sparse PCA and capture some gene modules with better biological interpretations.

Results

We evaluated the performance of ESPCA using a set of artificial datasets and two real biological datasets (including TCGA pan-cancer expression data and ENCODE expression data), and compared their performance with PCA and sparse PCA. The results showed that ESPCA could identify more biologically relevant genes, improve their biological interpretations and reveal distinct sample characteristics.

Availability and implementation

An R package of ESPCA is available at http://page.amss.ac.cn/shihua.zhang/.

Supplementary information

Supplementary data are available at Bioinformatics online.

Supervised Discriminative Sparse PCA for Com-Characteristic Gene Selection and Tumor Classification on Multiview Biological Data

Principal component analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the so-called sparse PCA, which focuses on seeking sparse loadings. However, the performance of these methods is still far from satisfactory due to their limitation of using unsupervised learning methods; moreover, the class ambiguity within the sample is high. To overcome this problem, this paper developed a new PCA method, which is named the supervised discriminative sparse PCA (SDSPCA). The main innovation of this method is the incorporation of discriminative information and sparsity into the PCA model. Specifically, in contrast to the traditional sparse PCA, which imposes sparsity on the loadings, here, sparse components are obtained to represent the data. Furthermore, via the linear transformation, the sparse components approximate the given label information. On the one hand, sparse components improve interpretability over the traditional PCA, while on the other hand, they are have discriminative abilities suitable for classification purposes. A simple algorithm is developed, and its convergence proof is provided. SDSPCA has been applied to the common-characteristic gene selection and tumor classification on multiview biological data. The sparsity and classification performance of SDSPCA are empirically verified via abundant, reasonable, and effective experiments, and the obtained results demonstrate that SDSPCA outperforms other state-of-the-art methods.

Robust and Efficient Biomolecular Clustering of Tumor Based on ${p}$ -Norm Singular Value Decomposition

High dimensionality has become a typical feature of biomolecular data. In this paper, a novel dimension reduction method named p-norm singular value decomposition (PSVD) is proposed to seek the low-rank approximation matrix to the biomolecular data. To enhance the robustness to outliers, the Lp-norm is taken as the error function and the Schatten p-norm is used as the regularization function in the optimization model. To evaluate the performance of PSVD, the Kmeans clustering method is then employed for tumor clustering based on the low-rank approximation matrix. Extensive experiments are carried out on five gene expression data sets including two benchmark data sets and three higher dimensional data sets from the cancer genome atlas. The experimental results demonstrate that the PSVD-based method outperforms many existing methods. Especially, it is experimentally proved that the proposed method is more efficient for processing higher dimensional data with good robustness, stability, and superior time performance.

Joint L1/2-Norm Constraint and Graph-Laplacian PCA Method for Feature Extraction

Principal Component Analysis (PCA) as a tool for dimensionality reduction is widely used in many areas. In the area of bioinformatics, each involved variable corresponds to a specific gene. In order to improve the robustness of PCA-based method, this paper proposes a novel graph-Laplacian PCA algorithm by adopting L_1/2 constraint (L_1/2 gLPCA) on error function for feature (gene) extraction. The error function based on L_1/2-norm helps to reduce the influence of outliers and noise. Augmented Lagrange Multipliers (ALM) method is applied to solve the subproblem. This method gets better results in feature extraction than other state-of-the-art PCA-based methods. Extensive experimental results on simulation data and gene expression data sets demonstrate that our method can get higher identification accuracies than others.

Characteristic Gene Selection Based on Robust Graph Regularized Non-Negative Matrix Factorization

Many methods have been considered for gene selection and analysis of gene expression data. Nonetheless, there still exists the considerable space for improving the explicitness and reliability of gene selection. To this end, this paper proposes a novel method named robust graph regularized non-negative matrix factorization for characteristic gene selection using gene expression data, which mainly contains two aspects: Firstly, enforcing L₂₁-norm minimization on error function which is robust to outliers and noises in data points. Secondly, it considers that the samples lie in low-dimensional manifold which embeds in a high-dimensional ambient space, and reveals the data geometric structure embedded in the original data. To demonstrate the validity of the proposed method, we apply it to gene expression data sets involving various human normal and tumor tissue samples and the results demonstrate that the method is effective and feasible.

Feature selection methods for big data bioinformatics: A survey from the search perspective

This paper surveys main principles of feature selection and their recent applications in big data bioinformatics. Instead of the commonly used categorization into filter, wrapper, and embedded approaches to feature selection, we formulate feature selection as a combinatorial optimization or search problem and categorize feature selection methods into exhaustive search, heuristic search, and hybrid methods, where heuristic search methods may further be categorized into those with or without data-distilled feature ranking measures.

Block-Constraint Robust Principal Component Analysis and its Application to Integrated Analysis of TCGA Data

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.