Identify clusters in mixture of FACS-purified PBMC data using topic model
Peter Carbonetto
Last updated: 2020-11-23
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Knit directory: single-cell-topics/analysis/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 9167310 | Peter Carbonetto | 2020-11-23 | workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”) |
| html | 8abec44 | Peter Carbonetto | 2020-11-23 | Added PCA plots to clusters_purified_pbmc analysis. |
| Rmd | a7e6fbc | Peter Carbonetto | 2020-11-23 | Various improvements to the analysis of the PBMC data sets. |
| Rmd | 884b869 | Peter Carbonetto | 2020-11-23 | Working on new plots for clusters_purified_pbmc analysis. |
| Rmd | 4a8b2bd | Peter Carbonetto | 2020-11-23 | A couple additions to clusters_purified_pbmc.Rmd. |
| html | 1845721 | Peter Carbonetto | 2020-11-22 | Added Structure plot to clusters_purified_pbmc. |
| Rmd | 90d201b | Peter Carbonetto | 2020-11-22 | workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”) |
| html | 015e254 | Peter Carbonetto | 2020-11-22 | Fixed up some of the text and plots in clusters_purified_pbmc analysis. |
| Rmd | b512864 | Peter Carbonetto | 2020-11-22 | workflowr::wflow_publish(“clusters_purified_pbmc.Rmd”) |
| html | 7cbd5e9 | Peter Carbonetto | 2020-11-22 | First build of clusters_purified_pbmc page. |
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Here we perform PCA on the topic proportions to identify clusters in the mixture of FACS-purified PBMC data sets.
Load the packages used in the analysis below, as well as additional functions that we will use to generate some of the plots.
library(Matrix)
library(dplyr)
library(fastTopics)
library(Rtsne)
library(uwot)
library(ggplot2)
library(cowplot)
source("../code/plots.R")Load the count data.
load("../data/pbmc_purified.RData")Load the \(K = 6\) Poisson NMF model fit.
fit <- readRDS(file.path("../output/pbmc-purified/rds",
"fit-pbmc-purified-scd-ex-k=6.rds"))$fitIdentify clusters from principal components
From the PCs of the topic proportions, we define clusters for B-cells, CD14+ cells and CD34+ cells. The remaining cells are assigned to the U cluster (“U” for “unknown”).
pca <- prcomp(poisson2multinom(fit)$L)$x
n <- nrow(pca)
x <- rep("U",n)
pc1 <- pca[,1]
pc2 <- pca[,2]
pc3 <- pca[,3]
pc4 <- pca[,4]
pc5 <- pca[,5]
x[pc2 > 0.25] <- "B"
x[pc3 < -0.2 & pc4 < 0.2] <- "CD34+"
x[(pc4 + 0.1)^2 + (pc5 - 0.8)^2 < 0.07] <- "CD14+"Next, we define an NK cells cluster from the top 2 PCs of the topic proportions in the U (“unknown”) cells.
rows <- which(x == "U")
n <- length(rows)
fit2 <- select(poisson2multinom(fit),loadings = rows)
pca <- prcomp(fit2$L)$x
y <- rep("U",n)
pc1 <- pca[,1]
pc2 <- pca[,2]
y[pc1 < -0.3 & 1.1*pc1 < -pc2 - 0.57] <- "NK"
x[rows] <- yAmong the remaining cells, we define a much less distinct cluster of CD8+ cells. The rest are labeled as T-cells.
rows <- which(x == "U")
n <- length(rows)
fit2 <- select(poisson2multinom(fit),loadings = rows)
pca <- prcomp(fit2$L)$x
y <- rep("T",n)
pc1 <- pca[,1]
pc2 <- pca[,2]
y[pc1 < 0.25 & pc2 < -0.15] <- "CD8+"
x[rows] <- yIn summary, we have subdivided the cells into 6 subsets. The substructure becomes more clear when we plot T cells separately from the other cells.
cluster_colors <- c("dodgerblue","forestgreen","darkmagenta",
"red","gray","darkorange")
samples$cluster <- factor(x)
x <- with(samples,cluster == "T" | cluster == "CD8+")
rows1 <- which(!x)
rows2 <- which(x)
p1 <- pca_plot(select(poisson2multinom(fit),loadings = rows1),
fill = samples$cluster[rows1]) +
scale_fill_manual(values = cluster_colors,drop = FALSE) +
labs(fill = "cluster")
p2 <- pca_plot(select(poisson2multinom(fit),loadings = rows2),
fill = samples$cluster[rows2,drop = FALSE]) +
scale_fill_manual(values = cluster_colors,drop = FALSE) +
labs(fill = "cluster")
p3 <- pca_hexbin_plot(select(poisson2multinom(fit),loadings = rows1),bins = 28)
p4 <- pca_hexbin_plot(select(poisson2multinom(fit),loadings = rows2),bins = 28)
plot_grid(p1,p3,p2,p4,nrow = 2,ncol = 2,rel_widths = c(10,11))
This clustering corresponds closely to the Zheng et al (2017) FACS cell populations, although there are some differences—for example, the CD14+ cluster contains a large number of cells identified as CD34+ by FACS.
with(samples,table(celltype,cluster))
# cluster
# celltype B CD14+ CD34+ CD8+ NK T
# CD19+ B 10073 0 0 8 0 4
# CD14+ Monocyte 8 2420 0 138 0 46
# CD34+ 352 536 8182 141 4 17
# CD4+ T Helper2 0 0 8 49 1 11155
# CD56+ NK 0 0 17 86 8279 3
# CD8+ Cytotoxic T 0 0 0 3093 93 7023
# CD4+/CD45RO+ Memory 0 0 20 343 0 9861
# CD8+/CD45RA+ Naive Cytotoxic 3 0 0 53 2 11895
# CD4+/CD45RA+/CD25- Naive T 1 0 8 30 1 10439
# CD4+/CD25 T Reg 2 0 2 25 0 10234This close correspondence is also apparent when we layer the FACS cell population labels on the PCA plots:
facs_colors <- c("dodgerblue", # B-cells
"forestgreen", # CD14+
"darkmagenta", # CD34+
"firebrick", # T helper cells
"gray", # NK cells
"tomato", # cytotoxic T-cells
"yellow", # memory T-cells
"magenta", # naive cytotoxic
"darkorange", # naive T-cells
"gold") # regulatory T-cells
p1 <- pca_plot(select(poisson2multinom(fit),loadings = rows1),
fill = samples[rows1,"celltype"]) +
scale_fill_manual(values = facs_colors) +
labs(fill = "FACS subtype")
p2 <- pca_plot(select(poisson2multinom(fit),loadings = rows2),
fill = samples[rows2,"celltype"]) +
scale_fill_manual(values = facs_colors) +
labs(fill = "FACS subtype")
plot_grid(p1,p2)
By computing inter-cluster and inter-topic total variation distances in relative expression levels, we see that the clusters identified above show greater differentiation in gene expression, and the topics show more differentiation than the clusters.
fit_zheng <- init_poisson_nmf_from_clustering(counts,samples$celltype)
d_zheng <- totalvardist(poisson2multinom(fit_zheng)$F)
d_topics <- totalvardist(poisson2multinom(fit)$F)Here is a plot summarizing these differences:
pdat <-
rbind(data.frame(method = "zheng.et.al",d = d_zheng[upper.tri(d_zheng)]),
data.frame(method = "topics", d = d_topics[upper.tri(d_topics)]))
p3 <- ggplot(pdat,aes(x = method,y = d)) +
geom_boxplot(width = 0.25) +
labs(x = "",y = "total variation dist") +
theme_cowplot(font_size = 9)
print(p3)
Structure plot
The structure plot summarizes the topic proportions in each of these 6 subsets:
set.seed(1)
topic_colors <- c("gold","forestgreen","dodgerblue","gray","darkmagenta",
"violet")
topics <- c(5,3,2,4,1,6)
rows <- sort(c(sample(which(samples$cluster == "B"),1000),
sample(which(samples$cluster == "CD14+"),300),
sample(which(samples$cluster == "CD34+"),500),
sample(which(samples$cluster == "CD8+"),400),
sample(which(samples$cluster == "NK"),500),
sample(which(samples$cluster == "T"),1000)))
p3 <- structure_plot(select(poisson2multinom(fit),loadings = rows),
grouping = samples[rows,"cluster"],
topics = topics,colors = topic_colors[topics],
perplexity = c(70,30,30,30,30,70),
n = Inf,gap = 50,num_threads = 4,verbose = FALSE)
print(p3)
| Version | Author | Date |
|---|---|---|
| 1845721 | Peter Carbonetto | 2020-11-22 |
Note that CD8+ cells are identified as a distinctive mixture of topics capturing NK cells and T-cells.
Analysis of single-cell likelihoods
Create scatterplots comparing single-cell likelihoods using a “hard” clustering (based on the FACS subpopulations).
PCA vs. t-SNE and UMAP
Here we illustrate one of the benefits of using a simple linear dimensionality reduction technique, PCA, over more widely used nonlinear dimensionality reduction methods t-SNE and UMAP. In particular, we compare a 2-d linear embedding produced by PCA against nonlinear embeddings generated by t-SNE and UMAP.
To begin, draw a random subset of 2,000 cells from the B, CD14+ and CD34+ clusters identified above. (The main reason for taking a random subset is that we don’t want to wait a long time for t-SNE and UMAP to complete.) Then run PCA on the topic proportions for this random subset of 2,000 samples.
set.seed(5)
rows <- which(with(samples,
cluster == "B" | cluster == "CD14+" | cluster == "CD34+"))
rows <- sort(sample(rows,2000))
fit2 <- select(poisson2multinom(fit),loadings = rows)
x <- samples$cluster[rows,drop = TRUE]
p4 <- pca_plot(fit2,fill = x) + labs(fill = "cluster")Next, run t-SNE on the topic proportions.
tsne <- Rtsne(fit2$L,dims = 2,pca = FALSE,normalize = FALSE,perplexity = 100,
theta = 0.1,max_iter = 1000,eta = 200,verbose = FALSE)
tsne$x <- tsne$Y
colnames(tsne$x) <- c("tsne1","tsne2")
p5 <- pca_plot(fit2,out.pca = tsne,fill = x) + labs(fill = "cluster")Then run UMAP on the topic proportions.
out.umap <- umap(fit2$L,n_neighbors = 30,metric = "euclidean",n_epochs = 1000,
min_dist = 0.1,scale = "none",learning_rate = 1,
verbose = FALSE)
out.umap <- list(x = out.umap)
colnames(out.umap$x) <- c("umap1","umap2")
p6 <- pca_plot(fit2,out.pca = out.umap,fill = x) + labs(fill = "cluster")plot_grid(p4,p5,p6,nrow = 1)
By the projection of the samples onto the first two PCs, we see that the B-cells cluster is distinct from the others, whereas the CD14+ and CD34+ cells do not separate quite so neatly.
However, this this finer scale detail is not captured in the t-SNE and UMAP embeddings; this illustrates the tendency of t-SNE and UMAP to accentuate clusters in the data at the risk of distorting or obscure finer scale substructure.
Note that the first 2 PCs should be sufficient for capturing the full structure in the topic proportions as they explain >96% of the variance:
summary(prcomp(fit2$L))
# Importance of components:
# PC1 PC2 PC3 PC4 PC5 PC6
# Standard deviation 0.4831 0.3269 0.10351 0.03397 0.02396 3.49e-16
# Proportion of Variance 0.6618 0.3030 0.03038 0.00327 0.00163 0.00e+00
# Cumulative Proportion 0.6618 0.9647 0.99510 0.99837 1.00000 1.00e+00
sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
#
# Matrix products: default
# BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
#
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#
# attached base packages:
# [1] stats graphics grDevices utils datasets methods base
#
# other attached packages:
# [1] cowplot_1.0.0 ggplot2_3.3.0 uwot_0.1.8 Rtsne_0.15
# [5] fastTopics_0.3-184 dplyr_0.8.3 Matrix_1.2-18
#
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