In laurenhsu1/corral: Correspondence Analysis for Single Cell Data

knitr::opts_chunk$set(echo = TRUE)
library(gridExtra)

Introduction

Data from different experimental platforms and/or batches exhibit systematic variation -- i.e., batch effects. Therefore, when conducting joint analysis of data from different batches, a key first step is to align the datasets.

corralm is a multi-table adaptation of correspondence analysis designed for single-cell data, which applies multi-dimensional optimized scaling and matrix factorization to compute integrated embeddings across the datasets. These embeddings can then be used in downstream analyses, such as clustering, cell type classification, trajectory analysis, etc.

See the vignette for corral for dimensionality reduction of a single matrix of single-cell data.

Loading packages and data

We will use the SCMixology datasets from the r Biocpkg('CellBench') package [@scmix].

library(corral)
library(SingleCellExperiment)
library(ggplot2)
library(CellBench)
library(MultiAssayExperiment)

scmix_dat <- load_all_data()[1:3]

These datasets include a mixture of three lung cancer cell lines:

H2228
H1975
HCC827

which was sequenced using three platforms:

10X
CELseq2
Dropseq

scmix_dat

Each sequencing platform captures a different set of genes. In order to apply this method, the matrices need to be matched by features (i.e., genes). We'll find the intersect of the three datasets, then subset for that as we proceed.

First, we will prepare the data by: 1. adding to the colData the sequencing platform (Method in colData for each SCE), and 2. subsetting by the intersect of the genes.

platforms <- c('10X','CELseq2','Dropseq')
for(i in seq_along(scmix_dat)) {
  colData(scmix_dat[[i]])$Method<- rep(platforms[i], ncol(scmix_dat[[i]]))
}

scmix_mae <- as(scmix_dat,'MultiAssayExperiment')
scmix_dat <- as.list(MultiAssayExperiment::experiments(MultiAssayExperiment::intersectRows(scmix_mae)))

corralm can be applied to the following types of objects:

a single r Biocpkg('SingleCellExperiment') requires specifying splitby (also see documentation of corralm_matlist for additional optional arguments that can be passed), which is a character string for the attribute in colData that is tracking the batches. In our case, this would be the "Method" attribute we just added. The output from this type of input is the same SingleCellExperiment, with the result added to the reducedDim slot under corralm.
a list of r Biocpkg('SingleCellExperiment') does not require any specific arguments. The output is a list of the input SingleCellExperiments, with the result added to the reducedDim slot under corralm.
a list of matrices (or other matrix-like objects: matrix, Matrix, tibble, data.frame, etc.) also does not require specific arguments. The output will be a concatenated list of SVD output matrices (u,d,v) where v contains a concatenated vector of the embeddings for the cells
a list of r Biocpkg('SummarizedExperiment')s does not require specific arguments. The output is the same as for a list of matrices.
r Biocpkg('MultiAssayExperiment') or ExperimentList does not require any specific arguments. corralm will identify the intersect of the rows, and use these to match the matrices. The output will be the same as for a list of matrices.

For purposes of illustration, we will walk through using corralm with a single SCE, and with a list of matrices.

`corralm` on a single `r Biocpkg('SingleCellExperiment')`

First, setting up the data to demonstrate this:

colData(scmix_dat[[2]])$non_ERCC_percent <- NULL
# need to remove this column so the objects can be concatenated

scmix_sce <- SingleCellExperiment::cbind(scmix_dat[[1]],
                                         scmix_dat[[2]],
                                         scmix_dat[[3]])

Running corralm, and specifying the splitby argument: (Note that the default is for the counts matrix to be used. To change this default, use the whichmat argument.)

scmix_sce <- corralm(scmix_sce, splitby = 'Method')

Visualizing the results:

plot_embedding_sce(sce = scmix_sce, 
                   which_embedding = 'corralm', 
                   color_attr = 'Method', 
                   color_title = 'platform', 
                   ellipse_attr = 'cell_line', 
                   plot_title = 'corralm on scmix', 
                   saveplot = FALSE)

`corralm` on a list of matrices

Again, preparing the data to be in this input format:

scmix_matlist <- sce2matlist(sce = scmix_sce, 
                             splitby = 'Method', 
                             whichmat = 'counts')

# for plotting purposes later, while we're here
platforms <- colData(scmix_sce)$Method
cell_lines <- colData(scmix_sce)$cell_line

Running corralm and visualizing output... (the embeddings are in the v matrix because these data are matched by genes in the rows and have cells in the columns; if this were reversed, with cells in the rows and genes/features in the column, then the cell embeddings would instead be in the u matrix.)

scmix_corralm <- corralm(scmix_matlist)
scmix_corralm
plot_embedding(embedding = scmix_corralm$v, 
               plot_title = 'corralm on scmix', 
               color_vec = platforms, 
               color_title = 'platform', 
               ellipse_vec = cell_lines, 
               saveplot = FALSE)

As expected, we get the same results as above. (Note that in performing SVD, the direction of the axes doesn't matter and they may be flipped between runs, as corral and corralm use irlba to perform fast approximation.)

Scaled variance plots to evaluate integration

Scaled variance plots provide a simple and fast visual summary of the integration of embeddings. It can be called using the scal_var function, and works on both corralm objects and custom embeddings (with a vector indicating batch).

When integrating embedding representations across batches, measures for cluster evaluation are effective for assessing group compactness and recovery of cell populations via clustering. However, they do not directly assess how well dataset embeddings are integrated across batches. To focus specifically on batch integration, we developed and applied a heuristic scaled variance metric, which captures the relative dispersion of each batch with respect to the entire dataset. The scaled variance of component dimension $d^$ for the subset of observations in batch $b^$, $SV_{b^,d}$, is computed with: $$SV_{b^,d} = \frac{\mathrm{Var}(\mathbf{E_{b=b^,d=d^}})}{\mathrm{Var}(\mathbf{E_{d=d^*}})}$$ where $\mathbf{E}$ is the matrix of embeddings, and $b$ indexes the rows (observations by batch) while $d$ indexes the columns to indicate which component dimension to evaluate.

scal_var(scmix_corralm)

When the datasets are well integrated, SV values for each batch are close to 1, indicating that each batch's subset has similar dispersion as compared to the entire embedding. In contrast, if there is poorer integration, the scaled variance values will be more extreme away from 1 because the variance within batches will differ more from the variance overall. This metric is appropriate when the types of cells represented in different datasets are expected to be similar, but cannot account for situations where the expected distribution of cell types (and therefore, embeddings) is fundamentally different between batches.