Exploring High-Dimensional Biological Data with Sparse Contrastive Principal Component Analysis

Abstract

Motivation: Statistical analyses of high-throughput sequencing data have re-shaped the biological sciences. In spite of myriad advances, recovering interpretable biological signal from data corrupted by technical noise remains a prevalent open problem. Several classes of procedures, among them classical dimensionality reduction techniques, and others incorporating subject-matter knowledge, have provided e ective advances; however, no procedure currently satisfies the dual objectives of recovering stable and relevant features simultaneously. Results: Inspired by recent proposals for making use of control data in the removal of unwanted variation, we propose a variant of principal component analysis that extracts sparse, stable, interpretable, and relevant biological signal. The new methodology is compared to competing dimensionality reduction approaches through a simulation study as well as via analyses of several publicly available protein expression, microarray gene expression, and single-cell transcriptome sequencing datasets. Availability:A free and open-source software implementation of the methodology, the scPCA R package, is made available via the Bioconductor Project. Code for all analyses presented in the paper are also made available via GitHub.

scPCA: A toolbox for sparse contrastive principal component analysis in R

“…Although SPCA and cPCA have proven useful in resolving individual shortcomings of PCA, neither is capable of tackling the issues of stability and relevance simultaneously. The scPCA R package implements sparse constrastive PCA (scPCA) (Boileau, Hejazi, & Dudoit, 2019), a combination of these methods, drawing on cPCA to remove unwanted effects and on SPCA to sparsify the principal component loadings. In both simulation studies and data analysis, Boileau et al (2019) provided practical demonstrations of scPCA's ability to extract stable, interpretable, and uncontaminated signal from high-dimensional biological data.…”

“…The scPCA R package implements sparse constrastive PCA (scPCA) (Boileau, Hejazi, & Dudoit, 2019), a combination of these methods, drawing on cPCA to remove unwanted effects and on SPCA to sparsify the principal component loadings. In both simulation studies and data analysis, Boileau et al (2019) provided practical demonstrations of scPCA's ability to extract stable, interpretable, and uncontaminated signal from high-dimensional biological data. Indeed, scPCA was found to produce more informative and interpretable embeddings than linear (e.g.…”

“…As the scPCA software package was specially designed for use in disentangling biological signal from technical noise in high-throughput sequencing data, a free and open-source software implementation has been made available via the Bioconductor Project (Gentleman, Carey, Huber, Irizarry, & Dudoit, 2006;Gentleman et al, 2004;Huber et al, 2015) for the R language and environment for statistical computing (R Core Team, 2020). The scPCA package also implements cPCA, previously unavailable in the R language, in two flavors: (1) the semiautomated version of Abid et al (2018) and (2) the automated version formulated by Boileau et al (2019). In order to interface seamlessly with data structures common in computational biology, the scPCA package integrates fully with the SingleCellExperiment container class (Lun & Risso, 2019), using the class to store the cPCA and scPCA representations generated via the reducedDims accessor method.…”

Probabilistic Contrastive Principal Component Analysis

“…Specifically, in any of these algorithms, one can consider replacing the distance by the "constrastive distance." For example, sparse CPCA has been developed following this philosophy (Boileau et al, 2020), although without this justification. However, it is important to note that the contrastive distance is not a well-defined distance, which may violate the assumptions of traditional distance-based algorithms, and so cannot be used to replace distance metrics in existing algorithms without some luck.…”

scPNMF: sparse gene encoding of single cells to facilitate gene selection for targeted gene profiling

“…Specifically, genes can be selected based on their contributions to the projected low dimensions found by PCA or NMF [17–19]. Although many variants of PCA and NMF algorithms have been developed for scRNA-seq data analysis, they are not designed for gene selection [20–26].…”