Simultaneous dimension reduction and adjustment for confounding variation

Abstract

Dimension reduction methods are commonly applied to highthroughput biological datasets. However, the results can be hindered by confounding factors, either biological or technical in origin. In this study, we extend principal component analysis (PCA) to propose AC-PCA for simultaneous dimension reduction and adjustment for confounding (AC) variation. We show that AC-PCA can adjust for (i) variations across individual donors present in a human brain exon array dataset and (ii) variations of different species in a model organism ENCODE RNA sequencing dataset. Our approach is able to recover the anatomical structure of neocortical regions and to capture the shared variation among species during embryonic development. For gene selection purposes, we extend AC-PCA with sparsity constraints and propose and implement an efficient algorithm. The methods developed in this paper can also be applied to more general settings. The R package and MATLAB source code are available at https://github.com/linzx06/AC-PCA. dimension reduction | confounding variation | transcriptome D imension reduction methods, such as multidimensional scaling (MDS) and principal component analysis (PCA), are commonly applied in high-throughput biological datasets to visualize data in a low-dimensional space, identify dominant patterns, and extract relevant features (1-6). MDS aims to place each sample in a lower-dimensional space such that the betweensample distances are preserved as much as possible (7). PCA seeks the linear combinations of the original variables such that the derived variables capture maximal variance (8). One advantage of PCA is that the principal components (PCs) are more interpretable by checking the loadings of the variables.Confounding factors, either biological or technical in origin, are commonly observed in high-throughput biological experiments. Various methods have been proposed to estimate the confounding variation, for example, regression models on known confounding factors (9) and factor models and surrogate vector analysis for unobserved confounding factors (10-15). However, limited work has been done in the context of dimension reduction. Confounding variation can affect PC-based visualization of the data points because it may obscure the desired biological variation, and it can also affect the loading of the variables in the PCs.Here we extend PCA to propose AC-PCA for simultaneous dimension reduction and adjustment for confounding (AC) variation. We introduce a class of penalty functions in PCA, which encourages the PCs to be invariant to the confounding variation. We demonstrate the performance of AC-PCA through its application to a human brain development exon array dataset (4), a model organism ENCODE (modENCODE) RNA sequencing (RNA-Seq) dataset (16, 17), and simulated data. We also implemented AC-PCA with sparsity constraints to enable variable/gene selection and better interpretation of the PCs.Results AC-PCA in a General Form. Let X denote the N × p data matrix, where N is the number of observations and p is...

Benchmarking principal component analysis for large-scale single-cell RNA-sequencing

“…PCA is widely used for data visualization [39][40][41], data QC [42], feature selection [13,[43][44][45][46][47][48][49], de-noising [50,51], imputation [52][53][54], confirmation and removal of batch effects [55][56][57], confirmation and estimation of cell-cycle effects [58], rare cell type detection [59,60], cell type and cell state similarity search [61], pseudotime inference [13,[62][63][64][65][66], and spatial reconstruction [9].…”

Reverse GWAS: Using Genetics to Identify and Model Phenotypic Subtypes

“…Finally, as MFMR seeks clusters that are unaffected by confounders like population 271 structure, age or sex, it may be useful for clustering in settings where protecting certain 272 information is important for privacy or fairness [69]. In this sense, MFMR is to GMM 273 roughly as AC-PCA [70] or contrastive PCA [71] are to ordinary PCA. We derive a novel clustering algorithm, multitrait finite mixture of regressions (MFMR), 286 beginning from the standard regression model for interaction.…”

Benchmarking principal component analysis for large-scale single-cell RNA-sequencing

“…PCA is widely used for data visualization [39][40][41], data QC [42], feature selection [13,[43][44][45][46][47][48][49], de-noising [50,51], imputation [52][53][54], confirmation and removal of batch effects [55][56][57], confirmation and estimation of cell-cycle effects [58], rare cell type detection [59,60], cell type and cell state similarity search [61], pseudotime inference [13,[62][63][64][65][66], and spatial reconstruction [9].…”