Last updated: 2020-11-28

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Knit directory: single-cell-topics/analysis/

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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"))$fit

Identify 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 clusters for NK cells and dendritic cells from the top 2 PCs of the topic proportions in the U cluster.

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]
pc3  <- pca[,3]
pc4  <- pca[,4]
y[pc1 < -0.3 & 1.1*pc1 < -pc2 - 0.57] <- "NK"
y[pc3 > 0.4 & pc4 < 0.2] <- "dendritic"
x[rows] <- y

Among the remaining cells, we define a cluster for CD8+ cells, noting that this is much less distinct than the other 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] <- y

In summary, we have subdivided the cells into 7 subsets. This plot shows the clustering of the cells projected onto the top two PCs:

cluster_colors <- c("dodgerblue",  # B-cells
                    "forestgreen", # CD14+
                    "darkmagenta", # CD34+ 
                    "red",         # CD8+
                    "skyblue",     # dendritic
                    "gray",        # NK
                    "darkorange")  # T-cells
samples$cluster <- factor(x)
p1 <- pca_plot(poisson2multinom(fit),fill = samples$cluster) +
  scale_fill_manual(values = cluster_colors) +
  labs(fill = "cluster")
p2 <- pca_hexbin_plot(poisson2multinom(fit))
plot_grid(p1,p2,rel_widths = c(10,11))

Version Author Date
4781407 Peter Carbonetto 2020-11-28
48438b3 Peter Carbonetto 2020-11-26
e7411a0 Peter Carbonetto 2020-11-23

This clustering corresponds well to the Zheng et al (2017) FACS cell populations, although there are some differences.

with(samples,table(celltype,cluster))
#                               cluster
# celltype                           B CD14+ CD34+  CD8+ dendritic    NK     T
#   CD19+ B                      10073     0     0     3         7     0     2
#   CD14+ Monocyte                   8  2420     0     3       156     0    25
#   CD34+                          352   536  8182    20       121     4    17
#   CD4+ T Helper2                   0     0     8    45         9     1 11150
#   CD56+ NK                         0     0    17    82         4  8279     3
#   CD8+ Cytotoxic T                 0     0     0  3146         0    93  6970
#   CD4+/CD45RO+ Memory              0     0    20   355         1     0  9848
#   CD8+/CD45RA+ Naive Cytotoxic     3     0     0    52         2     2 11894
#   CD4+/CD45RA+/CD25- Naive T       1     0     8    27         5     1 10437
#   CD4+/CD25 T Reg                  2     0     2    24         3     0 10232

This good 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+
                 "gray",        # NK cells
                 "tomato",      # cytotoxic T-cells
                 "gold")        # T-cells
x <- as.character(samples$celltype)
x[x == "CD4+ T Helper2" | x == "CD4+/CD45RO+ Memory" |
  x == "CD8+/CD45RA+ Naive Cytotoxic" | x == "CD4+/CD45RA+/CD25- Naive T" | 
  x == "CD4+/CD45RA+/CD25- Naive T" | x == "CD4+/CD25 T Reg"] <- "T cell"
x <- factor(x)
p3 <- pca_plot(poisson2multinom(fit),fill = x) +
  scale_fill_manual(values = facs_colors) +
  labs(fill = "FACS subpopulation")
print(p3)

Version Author Date
4781407 Peter Carbonetto 2020-11-28
48438b3 Peter Carbonetto 2020-11-26
e7411a0 Peter Carbonetto 2020-11-23

This PCA plot highlights the FACS mis-labeling of the CD34+ cells:

rows <- which(with(samples,
                   cluster == "B" |
                   cluster == "CD14+" |
                   cluster == "CD34+" |
                   cluster == "dendritic"))
p4 <- pca_plot(select(poisson2multinom(fit),loadings = rows),
               fill = x[rows,drop = FALSE]) +
  scale_fill_manual(values = facs_colors,drop = FALSE) +
  labs(fill = "FACS subpopulation")
print(p4)

Version Author Date
e7411a0 Peter Carbonetto 2020-11-23
8abec44 Peter Carbonetto 2020-11-23

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$cluster == "CD34+"),500),
               which(samples$cluster == "dendritic"),
               sample(which(samples$cluster == "CD8+"),400),
               sample(which(samples$cluster == "NK"),500),
               sample(which(samples$cluster == "T"),1000)))
p5 <- structure_plot(select(poisson2multinom(fit),loadings = rows),
                     grouping = samples[rows,"cluster"],
                     topics = topics,colors = topic_colors[topics],
                     perplexity = c(70,30,30,30,30,30,70),
                     n = Inf,gap = 50,num_threads = 4,verbose = FALSE)
print(p5)

Version Author Date
4781407 Peter Carbonetto 2020-11-28
48438b3 Peter Carbonetto 2020-11-26
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: an illustration

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]
p6   <- 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")
p7 <- 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")
p8 <- pca_plot(fit2,out.pca = out.umap,fill = x) + labs(fill = "cluster")
plot_grid(p6,p7,p8,nrow = 1)

Version Author Date
e7411a0 Peter Carbonetto 2020-11-23

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

Save results

Save the clustering of the PBMC data to an RDS file.

saveRDS(samples,"clustering-pbmc-purified.rds")

sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
# 
# 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     
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.9.0        Rcpp_1.0.5           lattice_0.20-38     
#  [4] FNN_1.1.3            tidyr_1.0.0          prettyunits_1.1.1   
#  [7] assertthat_0.2.1     zeallot_0.1.0        rprojroot_1.3-2     
# [10] digest_0.6.23        R6_2.4.1             backports_1.1.5     
# [13] MatrixModels_0.4-1   evaluate_0.14        coda_0.19-3         
# [16] httr_1.4.2           pillar_1.4.3         rlang_0.4.5         
# [19] progress_1.2.2       lazyeval_0.2.2       data.table_1.12.8   
# [22] irlba_2.3.3          SparseM_1.78         hexbin_1.28.0       
# [25] whisker_0.4          rmarkdown_2.3        labeling_0.3        
# [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