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Rmd | c8dd3af | Peter Carbonetto | 2020-09-16 | Implemented basic_pca_plot; improved labeled_pca_plot function. |
Here we perform PCA on the topic proportions to identify clusters in the droplet data.
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(ggplot2)
library(cowplot)
source("../code/plots.R")
Load the droplet data.
load("../data/droplet.RData")
Load the \(k = 7\) Poisson NMF model fit.
fit <- readRDS("../output/droplet/rds/fit-droplet-scd-ex-k=7.rds")$fit
To identify clusters, we begin by plotting PCs computed from the topic proportions. (Note that only 6 PCs are needed for 7 topics.)
p1 <- pca_plot(poisson2multinom(fit),pcs = 1:2,fill = "none")
p2 <- pca_plot(poisson2multinom(fit),pcs = 3:4,fill = "none")
p3 <- pca_plot(poisson2multinom(fit),pcs = 5:6,fill = "none")
plot_grid(p1,p2,p3,nrow = 1,ncol = 3)
Some of the structure is more evident from “hexbin” plots showing the density of the points.
breaks <- c(0,1,5,10,100,Inf)
p4 <- pca_hexbin_plot(poisson2multinom(fit),pcs = 1:2,breaks = breaks)
p5 <- pca_hexbin_plot(poisson2multinom(fit),pcs = 3:4,breaks = breaks)
p6 <- pca_hexbin_plot(poisson2multinom(fit),pcs = 5:6,breaks = breaks)
p4 <- p4 + guides(fill = "none")
p5 <- p5 + guides(fill = "none")
p6 <- p6 + guides(fill = "none")
plot_grid(p4,p5,p6,nrow = 1,ncol = 3)
From these PCA plots, we define 4 clusters, labeled A, Cil, G and T+N. (The reasoning behind these labels will become clear later.) Points that do not fit in any of these clusters are assigned to a “background cluster”, labeled U.
pca <- prcomp(poisson2multinom(fit)$L)$x
x <- rep("U",nrow(pca))
pc1 <- pca[,1]
pc2 <- pca[,2]
pc6 <- pca[,6]
x[pc2 > -0.15] <- "A"
x[pc1 > 0.3 & pc2 < -0.75] <- "Cil"
x[pc1 <= 0.3 & pc2 >= -0.75 & pc2 < -0.4] <- "T+N"
x[pc6 < -0.05] <- "G"
There is additional substructure in cluster A, which is more apparent in the projection onto the top 2 PCs computed from cluster A only.
rows <- which(x == "A")
fit2 <- select(poisson2multinom(fit),loadings = rows)
p7 <- pca_plot(fit2,fill = "none")
p8 <- pca_hexbin_plot(fit2,breaks = breaks) + guides(fill = "none")
plot_grid(p7,p8)
The variation in PCs 1 and 2 is mostly produced by topics 2, 4 and 5.
p9 <- pca_plot(fit2,k = c(2,4,5))
print(p9)
Topic 4 in particular corresponds closely to expression of Krt13 which was identified as being uniquely expressed by transitional “hillock” cells.
p10 <- pca_plot(fit2,fill = log10(counts[rows,"Krt13"])) +
labs(fill = "log10(count)",title = "Krt13")
print(p10)
Version | Author | Date |
---|---|---|
d707238 | Peter Carbonetto | 2020-10-06 |
ab1ed99 | Peter Carbonetto | 2020-09-27 |
bf299b9 | Peter Carbonetto | 2020-09-27 |
0a8b571 | Peter Carbonetto | 2020-09-21 |
db6135c | Peter Carbonetto | 2020-09-21 |
4172024 | Peter Carbonetto | 2020-09-20 |
5361fdf | Peter Carbonetto | 2020-09-19 |
311b4e8 | Peter Carbonetto | 2020-09-19 |
We label the three more-or-less distinct subclusters as B, C and H, and assign the remaining “in between” data points to a new “background cluster”, B+C.
pca <- prcomp(fit2$L)$x
pc1 <- pca[,1]
pc2 <- pca[,2]
y <- rep("B+C",nrow(pca))
y[pc1 < 0.1] <- "B"
y[pc1 > 0.4 & pc2 < 0.45] <- "C"
y[pc2 > 0.55] <- "H"
x[rows] <- y
In summary, we have subdivided the droplet data into 8 subsets.
samples$cluster <- factor(x,c("B","C","B+C","H","Cil","T+N","G","U"))
cluster_colors <- c("royalblue", # B
"forestgreen", # C
"slategray", # B+C
"turquoise", # H
"firebrick", # Cil
"darkorange", # T+N
"gold", # G
"gainsboro") # U
p11 <- pca_plot(poisson2multinom(fit),pcs = 1:2,fill = samples$cluster) +
scale_fill_manual(values = cluster_colors) +
labs(fill = "cluster")
p12 <- pca_plot(poisson2multinom(fit),pcs = 3:4,fill = samples$cluster) +
scale_fill_manual(values = cluster_colors) +
labs(fill = "cluster")
p13 <- pca_plot(poisson2multinom(fit),pcs = 5:6,fill = samples$cluster) +
scale_fill_manual(values = cluster_colors) +
labs(fill = "cluster")
plot_grid(p11,p12,p13,nrow = 1,ncol = 3)
The clusters identified here correspond well to the Montoro et al (2018) clustering, with some exceptions (e.g., we do not identify an ionocytes cluster, and the neuroendocrine and tuft cells are included in the same cluster).
with(samples,table(tissue,cluster))
# cluster
# tissue B C B+C H Cil T+N G U
# Basal 3682 16 142 5 0 0 0 0
# Ciliated 1 13 4 0 371 5 0 31
# Club 93 1878 411 192 0 0 2 2
# Goblet 2 20 1 0 0 0 42 0
# Ionocyte 9 0 1 0 0 1 1 14
# Neuroendocrine 27 4 6 0 0 51 0 8
# Tuft 27 5 5 0 1 111 2 7
By computing inter-cluster and inter-topic expression differences by the total variation distance in relative expression levels, we see that the clusters identified above show greater differentiation in gene expression, and the topics show more differentiation than the clusters.
fit_montoro <- init_poisson_nmf_from_clustering(counts,samples$tissue)
fit_cluster <- init_poisson_nmf_from_clustering(counts,samples$cluster)
fit_merge <- merge_topics(poisson2multinom(fit),c("k5","k7"))
d_montoro <- totalvardist(poisson2multinom(fit_montoro)$F)
d_cluster <- totalvardist(poisson2multinom(fit_cluster)$F[,-c(3,8)])
d_topics <- totalvardist(fit_merge$F[,-3])
cat("Montoro et al (2018) clustering:\n")
print(d_montoro,digits = 3)
cat("Our clustering:\n")
print(d_cluster,digits = 3)
cat("Topics:\n")
print(d_topics,digits = 3)
# Montoro et al (2018) clustering:
# Basal Ciliated Club Goblet Ionocyte Neuroendocrine Tuft
# Basal 0.000 0.362 0.446 0.579 0.262 0.236 0.272
# Ciliated 0.362 0.000 0.487 0.587 0.362 0.340 0.351
# Club 0.446 0.487 0.000 0.445 0.497 0.425 0.472
# Goblet 0.579 0.587 0.445 0.000 0.589 0.515 0.553
# Ionocyte 0.262 0.362 0.497 0.589 0.000 0.275 0.294
# Neuroendocrine 0.236 0.340 0.425 0.515 0.275 0.000 0.214
# Tuft 0.272 0.351 0.472 0.553 0.294 0.214 0.000
# Our clustering:
# B C H Cil T+N G
# B 0.000 0.511 0.347 0.390 0.351 0.626
# C 0.511 0.000 0.523 0.579 0.632 0.574
# H 0.347 0.523 0.000 0.422 0.436 0.659
# Cil 0.390 0.579 0.422 0.000 0.391 0.658
# T+N 0.351 0.632 0.436 0.391 0.000 0.681
# G 0.626 0.574 0.659 0.658 0.681 0.000
# Topics:
# k1 k2 k4 k6 k5+k7
# k1 0.000 0.821 0.826 0.810 0.797
# k2 0.821 0.000 0.381 0.409 0.695
# k4 0.826 0.381 0.000 0.427 0.681
# k6 0.810 0.409 0.427 0.000 0.705
# k5+k7 0.797 0.695 0.681 0.705 0.000
Here is a plot summarizing these differences:
pdat <-
rbind(data.frame(method="montoro.et.al",d=d_montoro[upper.tri(d_montoro)]),
data.frame(method="clusters", d=d_cluster[upper.tri(d_cluster)]),
data.frame(method="topics", d=d_topics[upper.tri(d_topics)]))
p14a <- ggplot(pdat,aes(x = method,y = d)) +
geom_boxplot(width = 0.25) +
labs(x = "",y = "total variation dist") +
theme_cowplot(font_size = 9)
print(p14a)
Version | Author | Date |
---|---|---|
b6374a1 | Peter Carbonetto | 2020-10-11 |
This next plot provides a more direct comparison of the total variation distances among the 5 clusters that are comparable to the Montoro et al clusters:
fit_montoro <- merge_topics(poisson2multinom(fit_montoro),
c("Tuft","Neuroendocrine"))
d_montoro <- totalvardist(fit_montoro$F[,c("Basal","Ciliated","Club","Goblet",
"Tuft+Neuroendocrine")])
d_cluster <-
totalvardist(poisson2multinom(fit_cluster)$F[,c("B","Cil","C","G","T+N")])
pdat <- data.frame(montoro = d_montoro[upper.tri(d_montoro)],
clusters = d_cluster[upper.tri(d_cluster)])
p14b <- ggplot(pdat,aes(x = montoro,y = clusters)) +
geom_point(shape = 21,size = 2,color = "white",fill = "dodgerblue") +
geom_abline(intercept = 0,slope = 1,color = "black",linetype = "dotted") +
xlim(0.2,0.7) +
ylim(0.2,0.7) +
labs(x = "Montoro et al clusters",y = "our clusters") +
theme_cowplot(font_size = 9)
print(p14b)
The structure plot summarizes the topic proportions in each of these 8 subsets:
set.seed(1)
topic_colors <- c("gold","royalblue","salmon","turquoise","olivedrab",
"firebrick","forestgreen")
topics <- c(3,4,5,1,7,2,6)
rows <- sort(c(sample(which(samples$cluster == "B"),800),
sample(which(samples$cluster == "C"),800),
which(samples$cluster == "B+C"),
which(samples$cluster == "H"),
which(samples$cluster == "Cil"),
which(samples$cluster == "T+N"),
which(samples$cluster == "G"),
which(samples$cluster == "U")))
p15 <- structure_plot(select(poisson2multinom(fit),loadings = rows),
grouping = samples[rows,"cluster"],
topics = topics,colors = topic_colors[topics],
perplexity = c(70,70,30,30,50,30,12,18),
n = Inf,gap = 30,num_threads = 4,verbose = FALSE)
print(p15)
Based on this structure plot, and the above results, we roughly subdivide the droplet data into two: (1) the Cil, T+N and G clusters that give rise to well-separated clusters, and (2) the B, C, B+C and H subsets that contain interesting substructure but much less distinct clustering. Therefore,the cluster labels B, C, B+C and H are useful as a guide but should be taken with a grain of salt as the boundaries between these clusters are somewhat arbitrary.
Note the distribution of the topics in cluster C suggests that there is further substantial heterogeneity in these cells beyond what can be captured by identifying “hard” clusters. In particular, there is additional continuous variation in gene expression primarily captured by topics 5 and 7:
rows <- which(is.element(x,c("B","C","H","B+C")))
fit2 <- select(poisson2multinom(fit),loadings = rows)
p16 <- pca_plot(fit2,pcs = 2:3,k = c(4,5,7))
print(p16)
Although subtle, there is variation in topics 2 and 6 within the T+N cluster that tracks closely with the tuft (here signaled by gene Gnat3) and pulmonary neuroendocrine (Chga) cell-types:
p17 <- pca_plot(poisson2multinom(fit),k = 2)
p18 <- pca_plot(poisson2multinom(fit),k = 6)
p19 <- pca_plot(poisson2multinom(fit),fill = log10(counts[,"Chga"])) +
labs(fill = "log10(count)",title = "Chga")
p20 <- pca_plot(poisson2multinom(fit),fill = log10(counts[,"Gnat3"])) +
labs(fill = "log10(count)",title = "Gnat3")
plot_grid(p17,p18,p19,p20)
Save the clustering of the droplet data to an RDS file.
saveRDS(samples,"clustering-droplet.rds")
sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.6
#
# 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 fastTopics_0.3-179 dplyr_0.8.3
# [5] Matrix_1.2-18
#
# loaded via a namespace (and not attached):
# [1] ggrepel_0.9.0 Rcpp_1.0.5 lattice_0.20-38
# [4] tidyr_1.0.0 prettyunits_1.1.1 assertthat_0.2.1
# [7] zeallot_0.1.0 rprojroot_1.3-2 digest_0.6.23
# [10] R6_2.4.1 backports_1.1.5 MatrixModels_0.4-1
# [13] evaluate_0.14 coda_0.19-3 httr_1.4.2
# [16] pillar_1.4.3 rlang_0.4.5 progress_1.2.2
# [19] lazyeval_0.2.2 data.table_1.12.8 irlba_2.3.3
# [22] SparseM_1.78 hexbin_1.28.0 whisker_0.4
# [25] rmarkdown_2.3 labeling_0.3 Rtsne_0.15
# [28] stringr_1.4.0 htmlwidgets_1.5.1 munsell_0.5.0
# [31] compiler_3.6.2 httpuv_1.5.2 xfun_0.11
# [34] pkgconfig_2.0.3 mcmc_0.9-6 htmltools_0.4.0
# [37] tidyselect_0.2.5 tibble_2.1.3 workflowr_1.6.2.9000
# [40] quadprog_1.5-8 viridisLite_0.3.0 crayon_1.3.4
# [43] withr_2.1.2 later_1.0.0 MASS_7.3-51.4
# [46] grid_3.6.2 jsonlite_1.6 gtable_0.3.0
# [49] lifecycle_0.1.0 git2r_0.26.1 magrittr_1.5
# [52] scales_1.1.0 RcppParallel_4.4.2 stringi_1.4.3
# [55] farver_2.0.1 fs_1.3.1 promises_1.1.0
# [58] vctrs_0.2.1 tools_3.6.2 glue_1.3.1
# [61] purrr_0.3.3 hms_0.5.2 yaml_2.2.0
# [64] colorspace_1.4-1 plotly_4.9.2 knitr_1.26
# [67] quantreg_5.54 MCMCpack_1.4-5