SPARCoC: A New Framework for Molecular Pattern Discovery and Cancer Gene Identification

Abstract

It is challenging to cluster cancer patients of a certain histopathological type into molecular subtypes of clinical importance and identify gene signatures directly relevant to the subtypes. Current clustering approaches have inherent limitations, which prevent them from gauging the subtle heterogeneity of the molecular subtypes. In this paper we present a new framework: SPARCoC (Sparse-CoClust), which is based on a novel Common-background and Sparse-foreground Decomposition (CSD) model and the Maximum Block Improvement (MBI) co-clustering technique. SPARCoC has clear advantages compared with widely-used alternative approaches: hierarchical clustering (Hclust) and nonnegative matrix factorization (NMF). We apply SPARCoC to the study of lung adenocarcinoma (ADCA), an extremely heterogeneous histological type, and a significant challenge for molecular subtyping. For testing and verification, we use high quality gene expression profiling data of lung ADCA patients, and identify prognostic gene signatures which could cluster patients into subgroups that are significantly different in their overall survival (with p-values < 0.05). Our results are only based on gene expression profiling data analysis, without incorporating any other feature selection or clinical information; we are able to replicate our findings with completely independent datasets. SPARCoC is broadly applicable to large-scale genomic data to empower pattern discovery and cancer gene identification.

Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems

“…(1.9) in [24] with the bounded constraints added to u in order to get a background image with physical meanings. A similar model was considered by Ma et al in [30] for molecular pattern discovery and cancer gene identification. We refer the interested readers to [24] and [30] for more details of this problem.…”

“…For solving (13) using the 3-block ADMM (4), see [35]. [24,30]. This problem aims to extract the static background from a surveillance video.…”

Machine learning based imputation techniques for estimating phylogenetic trees from incomplete distance matrices

“…Matrix Factorization has previously been used in imputing missing data in various domains of bioinformatics, including analyzing scRNA-seq with missing data [53], handling missing data in genome-wide association studies (GWAS) [54], and identifying cancerous genes [55]. In this study, we successfully adapted this idea for imputing missing entries in a distance matrix for phylogenetic estimation.…”

Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants

“…As a special case of RPCA, one can consider that all columns of the low-rank matrix L are identical. That is, the given matrix M is a superposition of a special rank-one matrix L and a sparse matrix S. This special RPCA finds many interesting applications in practice such as video processing [55], [56] and bioinformatics [57]. For instance, in the background extraction of surveillance video, if the background is static, then the low-rank matrix L that corresponds to the background should have identical columns.…”

“…Here, one can use PALM algorithm [64] to generate a sequence that converges to a critical point of Ψ ν which is a KL function -also see [65], [32] for some other related work on nonconvex optimization. Note that instead of solving the smooth approximation given in (56), it is preferable to solve the following nonconvex formulation in (57), which is equivalent to (2).…”