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

Gene Expression Data Analysis Using Feature Weighted Robust Fuzzy c-Means Clustering

Clustering of gene expression data has been proven to be very useful in various applications, i.e., identifying the natural structure inherent in gene expression, understanding gene functions, mining relevant information from noisy data, and understanding gene regulation. In all these applications, genes, i.e., features, play a crucial role in characterizing them into different groups. These features may be relevant, irrelevant, or redundant, but they have different contributions during the clustering process. This paper presents a novel approach by considering the effect of features during the clustering process. In the proposed method, the fuzzy c-means the objective function is modified using a weighted Euclidean distance between the features with a monotonically decreasing function. The monotonically decreasing function helps control the features' contribution during the clustering process to partition the data into more relevant clusters. The proposed approach is validated, and performance is presented in various clustering performance measures on the different standard datasets. These clustering performance measures have also been compared with multiple state-of-the-art methods.

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.