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Rmd f8bea96 kevinlkx 2020-10-20 clustering with k = 13 topics

Here we explore the structure in the Cusanovich et al (2018) ATAC-seq data inferred from the multinomial topic model with \(k = 13\).

Load packages and some functions used in this analysis.

library(Matrix)
library(dplyr)
library(ggplot2)
library(cowplot)
library(fastTopics)
source("code/plots.R")

Load the data. The counts are no longer needed at this stage of the analysis.

data.dir <- "/project2/mstephens/kevinluo/scATACseq-topics/data/Cusanovich_2018/processed_data/"
load(file.path(data.dir, "Cusanovich_2018.RData"))
rm(counts)

Plot PCs of the topic proportions

We first use PCA to explore the structure inferred from the multinomial topic model with \(k = 13\):

Load the \(k = 13\) Poisson NMF fit.

out.dir <- "/project2/mstephens/kevinluo/scATACseq-topics/output/Cusanovich_2018"
fit <- readRDS(file.path(out.dir, "/fit-Cusanovich2018-scd-ex-k=13.rds"))$fit

Plot PCs of the topic proportions.

p.pca1.1 <- pca_plot(poisson2multinom(fit),pcs = 1:2,fill = "none")
p.pca1.2 <- pca_plot(poisson2multinom(fit),pcs = 3:4,fill = "none")
p.pca1.3 <- pca_plot(poisson2multinom(fit),pcs = 5:6,fill = "none")
p.pca1.4 <- pca_plot(poisson2multinom(fit),pcs = 7:8,fill = "none")
p.pca1.5 <- pca_plot(poisson2multinom(fit),pcs = 9:10,fill = "none")
p.pca1.6 <- pca_plot(poisson2multinom(fit),pcs = 11:12,fill = "none")

plot_grid(p.pca1.1,p.pca1.2,p.pca1.3,p.pca1.4,p.pca1.5,p.pca1.6)

Version Author Date
a38788b kevinlkx 2020-10-20

Some of the structure is more evident from “hexbin” plots showing the density of the points.

breaks <- c(0,1,5,10,100,Inf)
p.pca2.1 <- pca_hexbin_plot(poisson2multinom(fit), pcs = 1:2, breaks = breaks) + guides(fill = "none")
p.pca2.2 <- pca_hexbin_plot(poisson2multinom(fit), pcs = 3:4, breaks = breaks) + guides(fill = "none")
p.pca2.3 <- pca_hexbin_plot(poisson2multinom(fit), pcs = 5:6, breaks = breaks) + guides(fill = "none")
p.pca2.4 <- pca_hexbin_plot(poisson2multinom(fit), pcs = 7:8, breaks = breaks) + guides(fill = "none")
p.pca2.5 <- pca_hexbin_plot(poisson2multinom(fit), pcs = 9:10, breaks = breaks) + guides(fill = "none")
p.pca2.6 <- pca_hexbin_plot(poisson2multinom(fit), pcs = 11:12, breaks = breaks) + guides(fill = "none")

plot_grid(p.pca2.1,p.pca2.2,p.pca2.3,p.pca2.4,p.pca2.5,p.pca2.6)

Version Author Date
a38788b kevinlkx 2020-10-20

Layer the tissue and cell labels onto the PC plots

Next, we layer the tissue and cell labels onto the PC plots.

PCs 1 and 2:

p.pca3.1 <- labeled_pca_plot(fit,1:2,samples$tissue,font_size = 7,
                       legend_label = "tissue")
p.pca3.2 <- labeled_pca_plot(fit,1:2,samples$cell_label,font_size = 7,
                        legend_label = "cell_label")
plot_grid(p.pca3.1,p.pca3.2,rel_widths = c(8,11))

Version Author Date
a38788b kevinlkx 2020-10-20

PCs 3 and 4:

p.pca3.3 <- labeled_pca_plot(fit,3:4,samples$tissue,font_size = 7,
                        legend_label = "tissue")
p.pca3.4 <- labeled_pca_plot(fit,3:4,samples$cell_label,font_size = 7,
                        legend_label = "cell_label")
plot_grid(p.pca3.3,p.pca3.4,rel_widths = c(8,11))

Version Author Date
a38788b kevinlkx 2020-10-20

PCs 5 and 6:

p.pca3.5 <- labeled_pca_plot(fit,5:6,samples$tissue,font_size = 7,
                       legend_label = "tissue")
p.pca3.6 <- labeled_pca_plot(fit,5:6,samples$cell_label,font_size = 7,
                        legend_label = "cell_label")
plot_grid(p.pca3.5,p.pca3.6,rel_widths = c(8,11))

Version Author Date
a38788b kevinlkx 2020-10-20

PCs 7 and 8:

p.pca3.7 <- labeled_pca_plot(fit,7:8,samples$tissue,font_size = 7,
                       legend_label = "tissue")
p.pca3.8 <- labeled_pca_plot(fit,7:8,samples$cell_label,font_size = 7,
                        legend_label = "cell_label")
plot_grid(p.pca3.7,p.pca3.8,rel_widths = c(8,11))

Version Author Date
a38788b kevinlkx 2020-10-20

PCs 9 and 10:

p.pca3.9 <- labeled_pca_plot(fit,9:10,samples$tissue,font_size = 7,
                       legend_label = "tissue")
p.pca3.10 <- labeled_pca_plot(fit,9:10,samples$cell_label,font_size = 7,
                        legend_label = "cell_label")
plot_grid(p.pca3.9,p.pca3.10,rel_widths = c(8,11))

Version Author Date
a38788b kevinlkx 2020-10-20

PCs 11 and 12:

p.pca3.11 <- labeled_pca_plot(fit,11:12,samples$tissue,font_size = 7,
                       legend_label = "tissue")
p.pca3.12 <- labeled_pca_plot(fit,11:12,samples$cell_label,font_size = 7,
                        legend_label = "cell_label")
plot_grid(p.pca3.11,p.pca3.12,rel_widths = c(8,11))

Version Author Date
a38788b kevinlkx 2020-10-20

Visualize by structure plot grouped by tissues

set.seed(10)
colors_topics <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99","#e31a1c",
                   "#fdbf6f","#ff7f00","#cab2d6","#6a3d9a","#ffff99","#b15928",
                   "gray")
rows <- sample(nrow(fit$L),4000)
samples$tissue <- as.factor(samples$tissue)

p.structure.1 <- structure_plot(select(poisson2multinom(fit),loadings = rows),
                     grouping = samples[rows, "tissue"],n = Inf,gap = 40,
                     perplexity = 50,topics = 1:13,colors = colors_topics,
                     num_threads = 4,verbose = FALSE)
# Perplexity automatically changed to 42 because original setting of 50 was too large for the number of samples (132)
# Perplexity automatically changed to 40 because original setting of 50 was too large for the number of samples (124)

print(p.structure.1)

k-means clustering on topic proportions

Define clusters using k-means, and then create structure plot based on the clusters from k-means.

Define clusters using k-means with 15 clusters:

set.seed(10)

clusters.15 <- factor(kmeans(poisson2multinom(fit)$L,centers = 15)$cluster)
print(table(clusters.15))
# clusters.15
#     1     2     3     4     5     6     7     8     9    10    11    12    13 
#  2740  3868  3775  3879  3645  3651 12037  2955  6045 12026  6068  3582  9319 
#    14    15 
#  3411  4172

Structure plot based on 15 clusters

colors_topics <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99","#e31a1c",
            "#fdbf6f","#ff7f00","#cab2d6","#6a3d9a","#ffff99","#b15928",
            "gray")
rows <- sample(nrow(fit$L),4000)

p.structure.kmeans.15 <- structure_plot(select(poisson2multinom(fit),loadings = rows),
                                        grouping = clusters.15[rows],n = Inf,gap = 20,
                                        perplexity = 50,topics = 1:13,colors = colors_topics,
                                        num_threads = 4,verbose = FALSE)
# Perplexity automatically changed to 42 because original setting of 50 was too large for the number of samples (130)
# Perplexity automatically changed to 46 because original setting of 50 was too large for the number of samples (144)
print(p.structure.kmeans.15)

Version Author Date
9d31a9f kevinlkx 2020-10-21
32ed5ae kevinlkx 2020-10-21
a38788b kevinlkx 2020-10-20

Refine k-means clusters: - Split cluster 10 into two clusters. - (maybe also merge cluster 4 and 9)

set.seed(10)
clusters.refined <- as.numeric(clusters.15)

idx_cluster10 <- which(clusters.15 == 10)
cluster10.refined <- kmeans(poisson2multinom(fit)$L[idx_cluster10, ],centers = 2)$cluster+15
clusters.refined[idx_cluster10] <- cluster10.refined
clusters.refined <- factor(clusters.refined, labels = paste0("c", c(1:length(unique(clusters.refined)))))

print(table(clusters.refined))

samples$cluster_kmeans <- clusters.refined
# clusters.refined
#    c1    c2    c3    c4    c5    c6    c7    c8    c9   c10   c11   c12   c13 
#  2740  3868  3775  3879  3645  3651 12037  2955  6045  6068  3582  9319  3411 
#   c14   c15   c16 
#  4172  6423  5603

Structure plot based on refined clusters

colors_topics <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99","#e31a1c",
            "#fdbf6f","#ff7f00","#cab2d6","#6a3d9a","#ffff99","#b15928",
            "gray")
rows <- sample(nrow(fit$L),4000)

p.structure.kmeans.refined <- structure_plot(select(poisson2multinom(fit),loadings = rows),
                                             grouping = clusters.refined[rows],n = Inf,gap = 40,
                                             perplexity = 50,topics = 1:13,colors = colors_topics,
                                             num_threads = 4,verbose = FALSE)
# Perplexity automatically changed to 41 because original setting of 50 was too large for the number of samples (129)
# Perplexity automatically changed to 46 because original setting of 50 was too large for the number of samples (144)
print(p.structure.kmeans.refined)

Group samples by k-means clusters first, then by tissue labels:

p.structure.kmeans.refined <- structure_plot(select(poisson2multinom(fit),loadings = rows),
                     grouping = clusters.refined[rows],
                     rows = order(samples[rows, "tissue"]), # samples are grouped by clusters first, then by tissue labels
                     n = Inf,gap = 40,
                     perplexity = 50,topics = 1:13,colors = colors_topics,
                     num_threads = 4,verbose = FALSE)
print(p.structure.kmeans.refined)

The clusters defined by k-means on topic proportions reasonably identify the clusters shown in the PCA hexbin plots (below).

p.pca.4.1 <- labeled_pca_plot(fit,1:2,samples$cluster_kmeans,font_size = 7,
                       legend_label = "cluster_kmeans")
p.pca.4.2 <- labeled_pca_plot(fit,3:4,samples$cluster_kmeans,font_size = 7,
                       legend_label = "cluster_kmeans")
p.pca.4.3 <- labeled_pca_plot(fit,5:6,samples$cluster_kmeans,font_size = 7,
                       legend_label = "cluster_kmeans")
p.pca.4.4 <- labeled_pca_plot(fit,7:8,samples$cluster_kmeans,font_size = 7,
                       legend_label = "cluster_kmeans")
p.pca.4.5 <- labeled_pca_plot(fit,9:10,samples$cluster_kmeans,font_size = 7,
                       legend_label = "cluster_kmeans")
p.pca.4.6 <- labeled_pca_plot(fit,11:12,samples$cluster_kmeans,font_size = 7,
                       legend_label = "cluster_kmeans")
plot_grid(p.pca.4.1,p.pca.4.2,p.pca.4.3,p.pca.4.4,p.pca.4.5,p.pca.4.6)

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plot_grid(p.pca2.1,p.pca2.2,p.pca2.3,p.pca2.4,p.pca2.5,p.pca2.6)

Version Author Date
32ed5ae kevinlkx 2020-10-21
a38788b kevinlkx 2020-10-20

We then label the cells in each cluster with the known tissue labels.

Tissues:

samples$tissue <- as.factor(samples$tissue)
cat(length(levels(samples$tissue)), "tissues. \n")
table(samples$tissue)

colors_tissues <- c("darkblue", "darkgray", "red", "lightgreen", "brown", "purple", "skyblue", "black",
                    "darkgreen", "pink", "yellow", "orange", "lightgray")
# 13 tissues. 
# 
#       BoneMarrow       Cerebellum            Heart           Kidney 
#             8403             2278             7650             6431 
#   LargeIntestine            Liver             Lung PreFrontalCortex 
#             7086             6167             9996             5959 
#   SmallIntestine           Spleen           Testes           Thymus 
#             4077             4020             2723             7617 
#       WholeBrain 
#             8766

Plot the distribution of tissues by cluster.

Stacked barplot for the counts of tissues by clusters:

library(plyr);library(dplyr)
# ------------------------------------------------------------------------------
# You have loaded plyr after dplyr - this is likely to cause problems.
# If you need functions from both plyr and dplyr, please load plyr first, then dplyr:
# library(plyr); library(dplyr)
# ------------------------------------------------------------------------------
# 
# Attaching package: 'plyr'
# The following objects are masked from 'package:dplyr':
# 
#     arrange, count, desc, failwith, id, mutate, rename, summarise,
#     summarize
library(RColorBrewer)

freq_cluster_tissue <- count(samples, vars=c("cluster_kmeans","tissue")) 

# stacked barplot for the counts of tissues by clusters
p.barplot.1 <- ggplot(freq_cluster_tissue, aes(fill=tissue, y=freq, x=cluster_kmeans)) + 
  geom_bar(position="stack", stat="identity") +
  theme_classic() + xlab("Cluster") + ylab("Number of cells") +
  scale_fill_manual(values = colors_tissues) +
  guides(fill=guide_legend(ncol=2)) +
  theme(
  legend.title = element_text(size = 10),
  legend.text = element_text(size = 8)
  )
print(p.barplot.1)

Version Author Date
32ed5ae kevinlkx 2020-10-21
b8a48b9 kevinlkx 2020-10-20

Percent stacked barplot for the counts of tissues by clusters:


p.barplot.2 <- ggplot(freq_cluster_tissue, aes(fill=tissue, y=freq, x=cluster_kmeans)) + 
  geom_bar(position="fill", stat="identity") +
  theme_classic() + xlab("Cluster") + ylab("Proportion of cells") +
  scale_fill_manual(values = colors_tissues) +
  guides(fill=guide_legend(ncol=2)) +
  theme(
  legend.title = element_text(size = 10),
  legend.text = element_text(size = 8)
  )
print(p.barplot.2)

Version Author Date
32ed5ae kevinlkx 2020-10-21
b8a48b9 kevinlkx 2020-10-20
  • We can see a few clusters are tissue specific:
  • cluster c3 is heart specific;
  • cluster c8 is kidney specific;
  • cluster c16 is liver specific;
  • cluster c1 is primarily bone marrow;
  • cluster c12 is primarily thymus.

Some clusters are combinations of related tissues: - cluster c9 is half lung and half spleen; - cluster c5 and c15 are mainly from pre-frontal cortex, whole brain (and cerebellum) -- all neuron related. - cluster c14 is also from whole brain and cerebellum. - cluster c11 is mainly from Kidney, LargeIntestine, and Lung.

Some clusters are more heterogeneous mixtures of different tissues: e.g. c2, c6, c7, c12.

freq_table_cluster_tissue <- with(samples,table(tissue,cluster_kmeans))
print(freq_table_cluster_tissue)
#                   cluster_kmeans
# tissue               c1   c2   c3   c4   c5   c6   c7   c8   c9  c10  c11  c12
#   BoneMarrow       2455   15    0 1399    0   33 1060    0  276 3063    0  102
#   Cerebellum          0   51    0    7  525   44  191    0   30   42    0    0
#   Heart               0 1374 3768  126    3 1225  803    5   68  259    3   13
#   Kidney              0  757    0   47    0  402   98 2950   48  280 1614   19
#   LargeIntestine      0   73    1  107    4  665 2778    0   71  172  441   94
#   Liver               0  268    0   97    0   84   31    0   39   50    1   34
#   Lung                2 1093    5 1324    2  659 1010    0 2678  465 1521  773
#   PreFrontalCortex    0   75    0   84 1169   48  118    0  131   49    0    1
#   SmallIntestine      0   22    0   75    0  341 2112    0    9 1457    1   27
#   Spleen             43    3    0  427    0    5   24    0 2510  116    0  892
#   Testes            240   19    0    1    0   37 2379    0    2   38    0    0
#   Thymus              0    2    1   82    0    9   32    0   90   30    1 7363
#   WholeBrain          0  116    0  103 1942   99 1401    0   93   47    0    1
#                   cluster_kmeans
# tissue              c13  c14  c15  c16
#   BoneMarrow          0    0    0    0
#   Cerebellum         15 1177  196    0
#   Heart               3    0    0    0
#   Kidney            215    0    0    1
#   LargeIntestine   2680    0    0    0
#   Liver               4    1    0 5558
#   Lung              434    2    2   26
#   PreFrontalCortex   19    4 4261    0
#   SmallIntestine     18    0    0   15
#   Spleen              0    0    0    0
#   Testes              4    0    0    3
#   Thymus              7    0    0    0
#   WholeBrain         12 2988 1964    0

Plot the distribution of cell labels by cluster.

Stacked barplot for the counts of cell labels by clusters:

freq_cluster_celllabel <- count(samples, vars=c("cluster_kmeans","cell_label")) 

colors_celllabels <- colorRampPalette(brewer.pal(12, "Set3"))(40)

# stacked barplot for the counts of tissues by clusters
p.barplot.3 <- ggplot(freq_cluster_celllabel, aes(fill=cell_label, y=freq, x=cluster_kmeans)) + 
  geom_bar(position="stack", stat="identity") +
  theme_classic() + xlab("Cluster") + ylab("Number of cells") +
  scale_fill_manual(values = colors_celllabels) +
  guides(fill=guide_legend(ncol=3)) +
  theme(
  legend.title = element_text(size = 9),
  legend.text = element_text(size = 7)
  )
print(p.barplot.3)

Percent stacked barplot for the counts of tissues by clusters:


p.barplot.4 <- ggplot(freq_cluster_celllabel, aes(fill=cell_label, y=freq, x=cluster_kmeans)) + 
  geom_bar(position="fill", stat="identity") +
  theme_classic() + xlab("Cluster") + ylab("Proportion of cells") +
  scale_fill_manual(values = colors_celllabels) +
  guides(fill=guide_legend(ncol=3)) +
  theme(
  legend.title = element_text(size = 9),
  legend.text = element_text(size = 7)
  )
print(p.barplot.4)

freq_table_cluster_celllabel <- with(samples,table(cell_label,cluster_kmeans))
print(freq_table_cluster_celllabel)
#                             cluster_kmeans
# cell_label                     c1   c2   c3   c4   c5   c6   c7   c8   c9  c10
#   Activated B cells             0    0    0  146    0    0    0    0  331   23
#   Alveolar macrophages          0    0    0  322    0    2   16    0  185   34
#   Astrocytes                    0    0    0    0 1574   11   58    0    0   20
#   B cells                       0    0    0  470    0    3  648    0 4616   34
#   Cardiomyocytes                0   15 3773    1    0   42  169    0    0   76
#   Cerebellar granule cells      0    0    0    9    0    3  306    0    0   19
#   Collecting duct               0    0    0    0    0   10    0    0    0    5
#   Collisions                    6    2    0  296  423   15  166    0   44   64
#   DCT/CD                        0    0    0    0    0    1    0    1    0    6
#   Dendritic cells               1    0    0  416    0    2   12    0  424  102
#   Distal convoluted tubule      0    0    0    0    0    0    0    0    0    6
#   Endothelial I (glomerular)    0  386    0    0    0  158    0    0    0    8
#   Endothelial I cells           0  512    0    0    0  438    1    0    0    1
#   Endothelial II cells          0 2405    0   15    0  574    7    0    0   15
#   Enterocytes                   0    0    0    0    1   11 1585    0    0   54
#   Erythroblasts              2420    0    0   37    0    0   79    0    0  275
#   Ex. neurons CPN               0    0    0    0    0    0   10    0    0    0
#   Ex. neurons CThPN             0    0    0    0    0    0   91    0    0    0
#   Ex. neurons SCPN              0    0    0    0    0    0   40    0    0   32
#   Hematopoietic progenitors     0    0    0   26    0    1  899    0    0 2499
#   Hepatocytes                   0    0    0    2    0    5   11    0    0   44
#   Immature B cells              0    0    0  285    0    0    0    0   68  218
#   Inhibitory neurons            0    0    0    3   68   27  754    0    0    8
#   Loop of henle                 0    1    0    0    0    8    2    1    0   11
#   Macrophages                   0    0    0  337    0   14  191    0  127   42
#   Microglia                     0    1    0  159    1    3   31    0  226    1
#   Monocytes                    69    0    0 1010    0    1   50    0    9   32
#   NK cells                      0    0    0  231    0    1    2    0    0   16
#   Oligodendrocytes              0    0    0    1 1506    1   30    0    0   17
#   Podocytes                     0  369    0    0    0  113    0    0    0   16
#   Proximal tubule               0    1    0    1    0   16   33 2361    0  132
#   Proximal tubule S3            0    0    0    0    0    0    2  592    0    0
#   Purkinje cells                0    0    0    0    1    2   50    0    0    0
#   Regulatory T cells            3    0    0   17    0    1    7    0    0    4
#   SOM+ Interneurons             0    0    0    0    7    8   66    0    0    5
#   Sperm                       240    0    0    0    0    1 1814    0    0   32
#   T cells                       1    1    0   35    1    7  104    0    0   50
#   Type I pneumocytes            0    0    0    1    0    3    0    0    0   27
#   Type II pneumocytes           0    8    0    0    0   14    0    0    0    1
#   Unknown                       0  167    2   59   63 2155 4803    0   15 2139
#                             cluster_kmeans
# cell_label                    c11  c12  c13  c14  c15  c16
#   Activated B cells             0    0    0    0    0    0
#   Alveolar macrophages          0    0    0    0    0    0
#   Astrocytes                    0    0    0    0    3    0
#   B cells                       0    0    1    0    0    0
#   Cardiomyocytes                0    0    0    0    0    0
#   Cerebellar granule cells      0    0    0 3762    0    0
#   Collecting duct             124    0   25    0    0    0
#   Collisions                    0   11    8   97   86    0
#   DCT/CD                      441    0   57    0    0    0
#   Dendritic cells               0    0    1    0    0    0
#   Distal convoluted tubule    301    0   12    0    0    0
#   Endothelial I (glomerular)    0    0    0    0    0    0
#   Endothelial I cells           0    0    0    0    0    0
#   Endothelial II cells          0    1    1    1    0    0
#   Enterocytes                 442    0 2690    0    0    0
#   Erythroblasts                 0    0    0    0    0    0
#   Ex. neurons CPN               0    0    0    0 1822    0
#   Ex. neurons CThPN             0    0    0    0 1449    0
#   Ex. neurons SCPN              0    0    0    0 1394    0
#   Hematopoietic progenitors     0    0    0    0    0    0
#   Hepatocytes                   0    0    0    0    0 5602
#   Immature B cells              0    0    0    0    0    0
#   Inhibitory neurons            0    0    0    3  965    0
#   Loop of henle               718    0   74    0    0    0
#   Macrophages                   0    0    0    0    0    0
#   Microglia                     0    0    0    0    0    0
#   Monocytes                     0    2    0    0    0    0
#   NK cells                      0   71    0    0    0    0
#   Oligodendrocytes              0    0    0    0    3    0
#   Podocytes                     0    0    0    0    0    0
#   Proximal tubule               7    0   19    0    0    0
#   Proximal tubule S3            0    0    0    0    0    0
#   Purkinje cells                0    0    0  262    5    0
#   Regulatory T cells            0  475    0    0    0    0
#   SOM+ Interneurons             0    0    0    1  466    0
#   Sperm                         0    0    2    0    0    0
#   T cells                       0 8753    2    0    0    0
#   Type I pneumocytes         1415    6  170    0    0    0
#   Type II pneumocytes          66    0   68    0    0    0
#   Unknown                      68    0  281   46  230    1

sessionInfo()
# R version 3.6.1 (2019-07-05)
# Platform: x86_64-pc-linux-gnu (64-bit)
# Running under: Scientific Linux 7.4 (Nitrogen)
# 
# Matrix products: default
# BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so
# 
# locale:
#  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
#  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
# [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] RColorBrewer_1.1-2 plyr_1.8.6         fastTopics_0.3-180 cowplot_1.1.0     
# [5] ggplot2_3.3.2      dplyr_1.0.2        Matrix_1.2-18      workflowr_1.6.2   
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.8.2      Rcpp_1.0.5         lattice_0.20-41    tidyr_1.1.2       
#  [5] prettyunits_1.1.1  rprojroot_1.3-2    digest_0.6.27      R6_2.5.0          
#  [9] backports_1.2.0    MatrixModels_0.4-1 evaluate_0.14      coda_0.19-3       
# [13] httr_1.4.2         pillar_1.4.7       rlang_0.4.8        progress_1.2.2    
# [17] lazyeval_0.2.2     data.table_1.13.2  irlba_2.3.3        SparseM_1.77      
# [21] whisker_0.4        hexbin_1.28.1      rmarkdown_2.5      labeling_0.4.2    
# [25] Rtsne_0.15         stringr_1.4.0      htmlwidgets_1.5.2  munsell_0.5.0     
# [29] compiler_3.6.1     httpuv_1.5.4       xfun_0.19          pkgconfig_2.0.3   
# [33] mcmc_0.9-7         htmltools_0.5.0    tidyselect_1.1.0   tibble_3.0.4      
# [37] quadprog_1.5-7     viridisLite_0.3.0  crayon_1.3.4       withr_2.3.0       
# [41] later_1.1.0.1      MASS_7.3-53        grid_3.6.1         jsonlite_1.6      
# [45] gtable_0.3.0       lifecycle_0.2.0    git2r_0.27.1       magrittr_1.5      
# [49] scales_1.1.1       RcppParallel_5.0.2 stringi_1.5.3      farver_2.0.3      
# [53] fs_1.3.1           promises_1.1.1     ellipsis_0.3.1     generics_0.0.2    
# [57] vctrs_0.3.5        tools_3.6.1        glue_1.4.2         purrr_0.3.4       
# [61] hms_0.5.3          yaml_2.2.0         colorspace_2.0-0   plotly_4.9.0      
# [65] knitr_1.30         quantreg_5.41      MCMCpack_1.4-4