A P-Norm Robust Feature Extraction Method for Identifying Differentially Expressed 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.

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.

PCA Based on Graph Laplacian Regularization and P-Norm for Gene Selection and Clustering

In modern molecular biology, the hotspots and difficulties of this field are identifying characteristic genes from gene expression data. Traditional reconstruction-error-minimization model principal component analysis (PCA) as a matrix decomposition method uses quadratic error function, which is known sensitive to outliers and noise. Hence, it is necessary to learn a good PCA method when outliers and noise exist. In this paper, we develop a novel PCA method enforcing P-norm on error function and graph-Laplacian regularization term for matrix decomposition problem, which is called as PgLPCA. The heart of the method designing for reducing outliers and noise is a new error function based on non-convex proximal P-norm. Besides, Laplacian regularization term is used to find the internal geometric structure in the data representation. To solve the minimization problem, we develop an efficient optimization algorithm based on the augmented Lagrange multiplier method. This method is used to select characteristic genes and cluster the samples from explosive biological data, which has higher accuracy than compared methods.

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.

An NMF-L2,1-Norm Constraint Method for Characteristic Gene Selection

Recent research has demonstrated that characteristic gene selection based on gene expression data remains faced with considerable challenges. This is primarily because gene expression data are typically high dimensional, negative, non-sparse and noisy. However, existing methods for data analysis are able to cope with only some of these challenges. In this paper, we address all of these challenges with a unified method: nonnegative matrix factorization via the L_2,1-norm (NMF-L_2,1). While L_2,1-norm minimization is applied to both the error function and the regularization term, our method is robust to outliers and noise in the data and generates sparse results. The application of our method to plant and tumor gene expression data demonstrates that NMF-L_2,1 can extract more characteristic genes than other existing state-of-the-art methods.