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

Abstract

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 L_2,1-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.

Keywords: L2, 1-norm; Lp-norm; gene network modules; graph regularization; principal component analysis; sparse constraint; tumor clustering.

FIGURE 1

The general schematic framework of the PL21GPCA methodology.

FIGURE 2

The average performance taking the essential parameter at nine different values from 0.1 to 0.9. (A) The mean value of ACC for different cancer datasets. (B) The mean value of NMI for different cancer datasets.

FIGURE 3

A visualized comparison of low-dimensional embeddings by SPCA, gLPCA, pgLPCA, and PL21GPCA on COAD and H-C-P datasets. (A–D) Are the results of the compared methods SPCA, glPCA, gpLPCA, and PL21GPCA respectively on the CRC dataset. (E–H) Are the compared results of the four methods on the H-C-P dataset.

FIGURE 4

The first three modules of the constructed network based on the CRC data. The five marked genes SPARC, ABCC12, COL6A3, LUM, and RPS3 have been confirmed to be associated with CRC and other cancers. (A) Module 1; (B) Module 2; (C) Module 3.

FIGURE 5

The first three modules of the constructed network based on the H_C_P data. The five marked genes RPL32, EEF1G, SPRR1B, COL1A2, and MMP2 have been confirmed to be associated with multiple cancers. (A) Module 1; (B) Module 2; (C) Module 3.