Robust Principal Component Analysis Regularized by Truncated Nuclear Norm for Identifying Differentially Expressed Genes

WGRLR: A Weighted Group Regularized Logistic Regression for Cancer Diagnosis and Gene Selection

Sparse regressions applied to cancer diagnosis suffer from noise reduction, gene grouping, and group significance evaluation. This paper presented the weighted group regularized logistic regression (WGRLR) for dealing with the above problems. Clean data was separated from noisy gene expression profile data, based on which gene grouping and model building were performed. An interpretable gene group significance evaluation criterion was proposed based on symmetrical uncertainty and module eigengene. A group-wise individual gene significance evaluation criterion was also presented. The performances of the proposed method were compared with WGGL, ASGL-CMI, SGL, GL, Elastic Net, and lasso on acute leukemia and brain cancer data. Experimental results demonstrate that the proposed method is superior to the other six methods in cancer diagnosis accuracy and gene selection.

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

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.

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.

A Hybrid Truncated Norm Regularization Method for Matrix Completion

Matrix completion has been widely used in image processing, in which the popular approach is to formulate this issue as a general low-rank matrix approximation problem. This paper proposes a novel regularization method referred to as truncated Frobenius norm (TFN), and presents a hybrid truncated norm (HTN) model combining the truncated nuclear norm and truncated Frobenius norm for solving matrix completion problems. To address this model, a simple and effective two-step iteration algorithm is designed. Further, an adaptive way to change the penalty parameter is introduced to reduce the computational cost. Also, the convergence of the proposed method is discussed and proved mathematically. The proposed approach could not only effectively improve the recovery performance but also greatly promote the stability of the model. Meanwhile, the use of this new method could eliminate large variations that exist when estimating complex models, and achieve competitive successes in matrix completion. Experimental results on the synthetic data, real-world images as well as recommendation systems, particularly the use of the statistical analysis strategy, verify the effectiveness and superiority of the proposed method, i.e. the proposed method is more stable and effective than other state-of-the-art approaches.