Impact of Data Preprocessing on Integrative Matrix Factorization of Single Cell Data

Abstract

Integrative, single-cell analyses may provide unprecedented insights into cellular and spatial diversity of the tumor microenvironment. The sparsity, noise, and high dimensionality of these data present unique challenges. Whilst approaches for integrating single-cell data are emerging and are far from being standardized, most data integration, cell clustering, cell trajectory, and analysis pipelines employ a dimension reduction step, frequently principal component analysis (PCA), a matrix factorization method that is relatively fast, and can easily scale to large datasets when used with sparse-matrix representations. In this review, we provide a guide to PCA and related methods. We describe the relationship between PCA and singular value decomposition, the difference between PCA of a correlation and covariance matrix, the impact of scaling, log-transforming, and standardization, and how to recognize a horseshoe or arch effect in a PCA. We describe canonical correlation analysis (CCA), a popular matrix factorization approach for the integration of single-cell data from different platforms or studies. We discuss alternatives to CCA and why additional preprocessing or weighting datasets within the joint decomposition should be considered.

Rampant False Detection of Adaptive Phenotypic Optimization by ParTI-Based Pareto Front Inference

“…2014 ). Likewise, transcriptomes of single cells are often nonindependent due to spatial or temporal autocorrelation, which might create similar artifacts such as the horseshoe effect ( Edelaar 2013 ; Hsu and Culhane 2020 ). Although we did not simulate the evolution of optimized traits, our results suggest that, even when the phenotypes are Pareto optimal, the Pareto front and archetypes identified by ParTI may be biased by the phylogenetic relationship or population structure in the data.…”

A single-mode associates global patterns of brain network structure and behavior across the human lifespan

“…Critically, one recent report has sparked interest by suggesting that adding nonlinear interactions to data modelling may provide negligible improvement over linear models when comparing brain-behavior interactions [130]. In selecting the best models (linear or nonlinear) might also depend on data preprocessing [131,132]. The effectiveness of data preprocessing may vary depending on the characteristics of the data domains.…”

Correspondence analysis for dimension reduction, batch integration, and visualization of single-cell RNA-seq data

“…Because of the size and complexity of the data, the datasets are orders of magnitude greater than those encountered when analyzing "bulk" RNAseq data from tissue samples. While such fine resolution data have the potential to reveal new biological findings, scRNAseq data exhibit sparsity, noisiness, and technical artefacts beyond those seen for bulk RNA samples (1,2), necessitating scRNAseq specific pre-processing and normalization (3,4). Typically scRNAseq analysis includes the use of dimension reduction, as it attenuates noise and ensures computational tractability, but the choice of method considerably influences downstream analyses, results, and conclusions (3,5).…”

“…As such, use of principal component analysis (PCA) requires that discrete and sparse scRNAseq count data be transformed prior to dimension reduction with this method (6). PCA is a linear dimension reduction method that obtains a low-dimensional data representation along orthogonal linear axes such that the proportion of variance accounted on each axis is maximized in Euclidean space (4,(8)(9)(10)(11). Because PCA is most suitable for continuous data that is approximately normally distributed, it may exhibit artefacts when applied to data with gradients or noncontinuous data (such as counts); one such artefact, called the "arch" or "horseshoe" effect, has been found to occur when PCA is applied to scRNAseq data without log-transformation (4,6,12).…”

“…Another matrix factorization method that emerged in the duality diagram framework is correspondence analysis (CA), a fast dimension reduction method appropriate for non-negative, count-based data and can identify relationships between categorical data types that is popular among ecologists for analyzing species-by-site abundance count matrices (8,24). In practice, PCA is often computed by singular value decomposition (SVD) of column centered or Z-score normalized data (Figure 1A) (4,25) and CA is computed by SVD of the Pearson residuals to reveal the row-column associations that deviate from expectation (26). The principal components in CA partition the codependence between the rows and columns such that a higher weight indicates a stronger dependence or association between row and column; for scRNAseq data, CA principal components can identify codependence between gene expression counts and particular cells.…”