Analysis of TCGA RPPA LIHC samples

Last updated: 2021-09-16

Checks: 7 0

Knit directory: Multispectral HCC/

This reproducible R Markdown analysis was created with workflowr (version 1.6.2). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

R Markdown file: up-to-date

Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Environment: empty

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

Seed: set.seed(20210728)

The command set.seed(20210728) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Session information: recorded

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Cache: none

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

File paths: relative

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Repository version: 17fc915

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version 17fc915. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:


Ignored files:
    Ignored:    .DS_Store
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    NMF_4439195520b/
    Ignored:    analysis/.DS_Store
    Ignored:    code/
    Ignored:    data/
    Ignored:    old/
    Ignored:    output/

Untracked files:
    Untracked:  omnipathr-log/

Unstaged changes:
    Modified:   analysis/cores.Rmd

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.

These are the previous versions of the repository in which changes were made to the R Markdown (analysis/tcga.Rmd) and HTML (docs/tcga.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File	Version	Author	Date	Message
Rmd	17fc915	Jovan Tanevski	2021-09-16	update hclust
Rmd	47928d9	Jovan Tanevski	2021-09-16	add silhouette based differential expression analysis, repeat nmf
html	e7709fe	Jovan Tanevski	2021-08-03	Build site.
html	f791e00	Jovan Tanevski	2021-08-03	Build site.
Rmd	e464694	Jovan Tanevski	2021-08-03	fix seed, stabilize nmf
html	51e2651	Jovan Tanevski	2021-08-03	Build site.
Rmd	7d62e48	Jovan Tanevski	2021-08-03	hclust and leiden on quantile normalized data
html	55fb7fc	Jovan Tanevski	2021-08-02	Build site.
Rmd	a152862	Jovan Tanevski	2021-08-02	add NMF based analysis
html	c25dcca	Jovan Tanevski	2021-08-02	Build site.
Rmd	21cf743	Jovan Tanevski	2021-08-02	rank normalization, leiden analysis, diff exp
html	a386eaa	Jovan Tanevski	2021-07-28	Build site.
Rmd	9ab4acc	Jovan Tanevski	2021-07-28	Build site.
Rmd	bd05dbf	Jovan Tanevski	2021-07-28	add expression profiles
html	e45bf1d	Jovan Tanevski	2021-07-28	Build site.
Rmd	dcab1bf	Jovan Tanevski	2021-07-28	set figure output to svg
html	33e71a0	Jovan Tanevski	2021-07-28	Build site.
Rmd	bb998b8	Jovan Tanevski	2021-07-28	hclust with factoextra
html	1cb80af	Jovan Tanevski	2021-07-28	Build site.
Rmd	d0b6e0f	Jovan Tanevski	2021-07-28	add pca to tcga analysis
html	d73f586	Jovan Tanevski	2021-07-28	Build site.
Rmd	c4324f5	Jovan Tanevski	2021-07-28	add umap
html	0bfae68	Jovan Tanevski	2021-07-28	Build site.
Rmd	82e3712	Jovan Tanevski	2021-07-28	add basic hclust

Setup

Load required libraries.

library(tidyverse)
library(skimr)
library(uwot)
library(factoextra)
library(cowplot)
library(FNN)
library(igraph)
library(leiden)
library(limma)
library(NMF)

Read filtered TCGA RRPA data and display summary statistics.

tcga.raw <- read_csv("data/TCGA-RPPA-LIHC_selected.csv", col_types = cols()) %>%
  select(-TumorType) %>%
  column_to_rownames("SampleID")

skim(tcga.raw)

Data summary
Name	tcga.raw
Number of rows	184
Number of columns	12
_______________________
Column type frequency:
numeric	12
________________________
Group variables	None

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
P53	1	-1.13	0.46	-2.54	-1.40	-0.96	-0.76	-0.51	▁▂▂▅▇
AKT_pS473	1	-0.63	0.71	-2.76	-1.02	-0.41	-0.15	0.96	▁▂▃▇▁
AKT_pT308	1	0.07	0.42	-1.16	-0.07	0.09	0.22	1.72	▁▃▇▁▁
BETACATENIN	1	1.50	0.72	-1.30	1.08	1.51	1.87	3.70	▁▁▇▅▁
JNK_pT183Y185	1	-0.21	0.29	-1.14	-0.36	-0.17	-0.04	0.48	▁▂▇▇▂
MEK1_pS217S221	1	-0.17	0.36	-0.82	-0.35	-0.23	-0.10	2.58	▇▃▁▁▁
P38_pT180Y182	1	0.49	0.57	-1.45	0.31	0.50	0.72	2.95	▁▂▇▁▁
P70S6K_pT389	1	-1.21	0.75	-3.22	-1.58	-0.95	-0.65	1.09	▂▃▇▃▁
PDK1_pS241	1	0.40	0.31	-0.56	0.23	0.37	0.55	1.62	▁▇▇▂▁
S6_pS235S236	1	-0.72	0.75	-3.53	-1.06	-0.67	-0.36	1.12	▁▁▅▇▂
YAP_pS127	1	2.21	0.61	0.68	1.78	2.10	2.54	4.05	▁▇▇▂▁
TRANSGLUTAMINASE	1	-0.42	0.56	-1.24	-0.83	-0.59	-0.20	2.72	▇▃▁▁▁

Quantile normalization and rank normalization for NMF as suggested in https://gdac.broadinstitute.org/runs/analyses__2016_01_28/reports/cancer/LIHC/RPPA_Clustering_CNMF/nozzle.html

tcga.norm <- normalizeQuantiles(tcga.raw)

skim(tcga.norm)

Data summary
Name	tcga.norm
Number of rows	184
Number of columns	12
_______________________
Column type frequency:
numeric	12
________________________
Group variables	None

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
P53	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
AKT_pS473	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
AKT_pT308	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
BETACATENIN	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
JNK_pT183Y185	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
MEK1_pS217S221	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
P38_pT180Y182	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
P70S6K_pT389	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
PDK1_pS241	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
S6_pS235S236	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
YAP_pS127	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁
TRANSGLUTAMINASE	1	0.01	0.52	-1.59	-0.27	0.05	0.3	1.87	▁▃▇▂▁

tcga.rank <- mutate_all(tcga.raw, rank)

Dimensionality reduction

tcga.pca <- prcomp(tcga.norm)
summary(tcga.pca)

Importance of components:
                         PC1    PC2    PC3     PC4     PC5     PC6     PC7
Standard deviation     1.052 0.6800 0.5864 0.53531 0.50548 0.47429 0.40905
Proportion of Variance 0.340 0.1421 0.1057 0.08809 0.07855 0.06915 0.05144
Cumulative Proportion  0.340 0.4821 0.5878 0.67594 0.75449 0.82364 0.87508
                           PC8     PC9    PC10    PC11    PC12
Standard deviation     0.35923 0.34052 0.28251 0.23710 0.15913
Proportion of Variance 0.03967 0.03565 0.02454 0.01728 0.00778
Cumulative Proportion  0.91475 0.95040 0.97493 0.99222 1.00000

set.seed(42)
tcga.umap <- umap(tcga.norm, n_neighbors = 10, n_epochs = 1000)

Hierarchical clustering

Perform hierarchical clustering of the data and plot the resulting dendrogram. Number of clusters to use (3) is based on gap statistic.

tcga.hclust <- eclust(tcga.norm, "hclust", 3)

Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
"none")` instead.

#fviz_gap_stat(tcga.hclust$gap_stat)

fviz_dend(tcga.hclust, rect = TRUE)

Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
"none")` instead.

Version	Author	Date
51e2651	Jovan Tanevski	2021-08-03
c25dcca	Jovan Tanevski	2021-08-02
a386eaa	Jovan Tanevski	2021-07-28

fviz_silhouette(tcga.hclust) +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1))

  cluster size ave.sil.width
1       1   65          0.09
2       2   98          0.31
3       3   21         -0.01

Version	Author	Date
51e2651	Jovan Tanevski	2021-08-03
c25dcca	Jovan Tanevski	2021-08-02

Plot in 2D PCA and UMAP

fviz_pca_ind(tcga.pca, geom = "point", col.ind = as.factor(tcga.hclust$cluster)) +
  theme_classic()

Version	Author	Date
51e2651	Jovan Tanevski	2021-08-03
c25dcca	Jovan Tanevski	2021-08-02

tcga.umap.clus <-
  tcga.umap %>%
  cbind(tcga.hclust$cluster) %>%
  `colnames<-`(c("U1", "U2", "Cluster")) %>%
  as_tibble() %>%
  mutate_at("Cluster", as.factor)

ggplot(tcga.umap.clus, aes(x = U1, y = U2, color = Cluster)) +
  geom_point() +
  theme_classic()

Version	Author	Date
f791e00	Jovan Tanevski	2021-08-03
51e2651	Jovan Tanevski	2021-08-03
c25dcca	Jovan Tanevski	2021-08-02

Expression profiles per cluster

tcga.clustered <- tcga.raw %>%
  mutate(Cluster = as.factor(tcga.hclust$cluster)) %>%
  pivot_longer(names_to = "Marker", values_to = "Z", -Cluster)

profiles <- seq_len(tcga.hclust$nbclust) %>% map(~
ggplot(
  tcga.clustered %>% filter(Cluster == .x),
  aes(x = Marker, y = Z, color = Marker)
) +
  stat_summary(fun.data = mean_sdl, show.legend = FALSE) +
  ylim(-3, 3) +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)))

plot_grid(plotlist = profiles, labels = paste("Cluster", seq_len(tcga.hclust$nbclust)))

Warning: Removed 27 rows containing non-finite values (stat_summary).

Warning: Removed 3 rows containing missing values (geom_segment).

Warning: Removed 3 rows containing non-finite values (stat_summary).

Warning: Removed 3 rows containing non-finite values (stat_summary).

Warning: Removed 1 rows containing missing values (geom_segment).

Version	Author	Date
51e2651	Jovan Tanevski	2021-08-03
c25dcca	Jovan Tanevski	2021-08-02

Differential expression analysis (limma)

design <- model.matrix(~0 + as.factor(tcga.hclust$cluster))
colnames(design) <- paste0("Cluster", seq_len(tcga.hclust$nbclust))

tcga.hclust.limma <- lmFit(t(tcga.raw), design = design)

tcga.hclust.eb <- eBayes(tcga.hclust.limma)

topTable(tcga.hclust.eb)

	Cluster1	Cluster2	Cluster3	AveExpr	F
YAP_pS127	2.4877540	2.0607184	2.0439790	2.2096629	913.18442
P53	-1.4915298	-0.8366292	-1.3823670	-1.1302653	729.46397
BETACATENIN	1.8632840	1.3984936	0.8682628	1.5021704	349.87656
P70S6K_pT389	-1.7528388	-0.7550050	-1.6956402	-1.2148558	335.71231
PDK1_pS241	0.6114473	0.2713946	0.3504661	0.4005464	156.42129
AKT_pS473	-1.1958630	-0.1776438	-0.9913925	-0.6302143	148.88894
S6_pS235S236	-1.2954581	-0.5261595	0.1387379	-0.7220376	137.29853
TRANSGLUTAMINASE	-0.4989926	-0.5342255	0.3389867	-0.4221190	64.77636
JNK_pT183Y185	-0.4004955	-0.0856420	-0.2233252	-0.2125813	62.21809
P38_pT180Y182	0.2950672	0.6794689	0.1684548	0.4853525	62.08894

tests.hclust <- decideTests(tcga.hclust.eb)

tests.hclust@.Data

                 Cluster1 Cluster2 Cluster3
P53                    -1       -1       -1
AKT_pS473              -1       -1       -1
AKT_pT308              -1        1        0
BETACATENIN             1        1        1
JNK_pT183Y185          -1       -1       -1
MEK1_pS217S221         -1       -1        0
P38_pT180Y182           1        1        0
P70S6K_pT389           -1       -1       -1
PDK1_pS241              1        1        1
S6_pS235S236           -1       -1        0
YAP_pS127               1        1        1
TRANSGLUTAMINASE       -1       -1        1

summary(tests.hclust)

       Cluster1 Cluster2 Cluster3
Down          8        7        4
NotSig        0        0        4
Up            4        5        4

Differential expression analysis (silhouette)

Select only the samples with positive silohuette scores as “core samples”

core.samples <- which(tcga.hclust$silinfo$widths[,3] > 0)
tcga.core.samples <- tcga.raw %>% add_column(Cluster = tcga.hclust$cluster) %>% 
  slice(core.samples)

Calculate difference in means (mean(cluster) - mean()), one-vs-all t-test per marker and correct for FDR. Filter q <= 0.5

unique(tcga.core.samples$Cluster) %>% map_dfr(\(c){
  tcga.core.samples %>% 
    summarize(across(-Cluster, ~t.test(.x ~ (Cluster==c))$p.value)) %>%
    pivot_longer(names_to = "Marker", values_to = "p", everything()) %>% 
    mutate(Cluster = c, Difference = -tcga.core.samples %>% 
             group_by(Cluster == c) %>% 
             select(-Cluster) %>% 
             group_split(.keep = FALSE) %>% map(colMeans) %>% reduce(`-`))
 }) %>% 
  mutate(q = p.adjust(p, method = "fdr")) %>% 
  filter(q <= 0.05) %>% arrange(q)

Marker	p	Cluster	Difference	q
AKT_pS473	0.0000000	2	0.6406739	0.0000000
P53	0.0000000	2	1.1135632	0.0000000
P70S6K_pT389	0.0000000	2	1.2202649	0.0000000
P53	0.0000000	1	1.1135632	0.0000000
AKT_pS473	0.0000000	1	0.6406739	0.0000000
P70S6K_pT389	0.0000000	1	1.2202649	0.0000000
S6_pS235S236	0.0000000	1	0.6938685	0.0000000
PDK1_pS241	0.0000000	1	-0.3926513	0.0000000
JNK_pT183Y185	0.0000000	2	0.2136928	0.0000000
JNK_pT183Y185	0.0000000	1	0.2136928	0.0000000
AKT_pT308	0.0000000	2	-0.0533286	0.0000000
PDK1_pS241	0.0000000	2	-0.3926513	0.0000000
AKT_pT308	0.0000000	1	-0.0533286	0.0000000
BETACATENIN	0.0000001	1	-1.5084240	0.0000002
P38_pT180Y182	0.0000003	2	-0.4692232	0.0000006
BETACATENIN	0.0000186	3	-1.5084240	0.0000418
S6_pS235S236	0.0000201	3	0.6938685	0.0000425
P38_pT180Y182	0.0000634	1	-0.4692232	0.0001269
TRANSGLUTAMINASE	0.0001356	3	0.4258209	0.0002569
YAP_pS127	0.0001584	1	-2.2130506	0.0002851
S6_pS235S236	0.0003887	2	0.6938685	0.0006664
YAP_pS127	0.0012609	2	-2.2130506	0.0020633
P70S6K_pT389	0.0038452	3	1.2202649	0.0060186
AKT_pS473	0.0043921	3	0.6406739	0.0065882
BETACATENIN	0.0122357	2	-1.5084240	0.0176194
TRANSGLUTAMINASE	0.0157029	2	0.4258209	0.0217425
P53	0.0278707	3	1.1135632	0.0371609

Similarity and graph based clustering

Calculate leiden clustering based on weighted shared nearest neighbor graph

tcga.knn <- knn.index(tcga.norm, 10)
jaccard.cuttoff <- 0.1

snn <- seq_len(nrow(tcga.knn) - 1) %>% map_dfr(\(id){
  to <- seq(id + 1, nrow(tcga.knn))
  jaccard <- to %>%
    map_dbl(~ length(intersect(tcga.knn[id, ], tcga.knn[.x, ])) /
      length(union(tcga.knn[id, ], tcga.knn[.x, ])))
  
  tibble(from = id, to = to, weight = jaccard) %>% filter(jaccard >= jaccard.cuttoff)
})

leiden.clusters <- graph_from_data_frame(snn, directed = FALSE) %>% leiden()

Plot in 2D PCA and UMAP

fviz_pca_ind(tcga.pca, geom = "point", col.ind = as.factor(leiden.clusters)) +
  theme_classic()

ggplot(tcga.umap.clus %>% mutate(Cluster = as.factor(leiden.clusters)), aes(x = U1, y = U2, color = Cluster, shape = Cluster)) +
  geom_point() +
  theme_classic()

Expression profiles per cluster

tcga.clustered <- tcga.raw %>%
  mutate(Cluster = as.factor(leiden.clusters)) %>%
  pivot_longer(names_to = "Marker", values_to = "Z", -Cluster)

profiles <- seq_len(max(leiden.clusters)) %>% map(~
ggplot(
  tcga.clustered %>% filter(Cluster == .x),
  aes(x = Marker, y = Z, color = Marker)
) +
  stat_summary(fun.data = mean_sdl, show.legend = FALSE) +
  ylim(-3, 3) +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)))

plot_grid(plotlist = profiles, labels = paste("Cluster", seq_len(max(leiden.clusters))))

Warning: Removed 27 rows containing non-finite values (stat_summary).

Warning: Removed 3 rows containing missing values (geom_segment).

Warning: Removed 3 rows containing non-finite values (stat_summary).

Warning: Removed 1 rows containing non-finite values (stat_summary).

Warning: Removed 2 rows containing non-finite values (stat_summary).

Warning: Removed 1 rows containing missing values (geom_segment).

Version	Author	Date
f791e00	Jovan Tanevski	2021-08-03
51e2651	Jovan Tanevski	2021-08-03
55fb7fc	Jovan Tanevski	2021-08-02

Differential expression analysis (limma)

design <- model.matrix(~0 + as.factor(leiden.clusters))
colnames(design) <- paste0("Cluster", seq_len(max(leiden.clusters)))

tcga.leiden.limma <- lmFit(t(tcga.raw), design = design)

tcga.leiden.eb <- eBayes(tcga.leiden.limma)

topTable(tcga.hclust.eb)

	Cluster1	Cluster2	Cluster3	AveExpr	F
YAP_pS127	2.4877540	2.0607184	2.0439790	2.2096629	913.18442
P53	-1.4915298	-0.8366292	-1.3823670	-1.1302653	729.46397
BETACATENIN	1.8632840	1.3984936	0.8682628	1.5021704	349.87656
P70S6K_pT389	-1.7528388	-0.7550050	-1.6956402	-1.2148558	335.71231
PDK1_pS241	0.6114473	0.2713946	0.3504661	0.4005464	156.42129
AKT_pS473	-1.1958630	-0.1776438	-0.9913925	-0.6302143	148.88894
S6_pS235S236	-1.2954581	-0.5261595	0.1387379	-0.7220376	137.29853
TRANSGLUTAMINASE	-0.4989926	-0.5342255	0.3389867	-0.4221190	64.77636
JNK_pT183Y185	-0.4004955	-0.0856420	-0.2233252	-0.2125813	62.21809
P38_pT180Y182	0.2950672	0.6794689	0.1684548	0.4853525	62.08894

tests.leiden <- decideTests(tcga.leiden.eb)

tests.leiden@.Data

                 Cluster1 Cluster2 Cluster3 Cluster4
P53                    -1       -1       -1       -1
AKT_pS473              -1       -1        0       -1
AKT_pT308              -1        1        1        0
BETACATENIN             1        1        1        1
JNK_pT183Y185          -1       -1        0        0
MEK1_pS217S221         -1       -1       -1        0
P38_pT180Y182           1        1        1        0
P70S6K_pT389           -1       -1       -1       -1
PDK1_pS241              1        1        1        1
S6_pS235S236           -1       -1       -1        0
YAP_pS127               1        1        1        1
TRANSGLUTAMINASE       -1       -1       -1        0

summary(tests.leiden)

       Cluster1 Cluster2 Cluster3 Cluster4
Down          8        7        5        3
NotSig        0        0        2        6
Up            4        5        5        3

Differential expression analysis (silhouette)

Calculate the similarity of samples using the expression and the silhouette scores based on the assigned clusters.

silhouette.leiden <- silhouette(leiden.clusters, dist(tcga.raw))
fviz_silhouette(silhouette.leiden)

  cluster size ave.sil.width
1       1   65         -0.09
2       2   60          0.13
3       3   47          0.06
4       4   12         -0.03

Version	Author	Date
f791e00	Jovan Tanevski	2021-08-03
51e2651	Jovan Tanevski	2021-08-03
55fb7fc	Jovan Tanevski	2021-08-02

Select only the samples with positive silhouette scores as “core samples”

core.samples <- which(silhouette.leiden[,3] > 0)
tcga.core.samples <- tcga.raw %>% add_column(Cluster = leiden.clusters) %>% 
  slice(core.samples)

Calculate difference in means (mean(cluster) - mean()), one-vs-all t-test per marker and correct for FDR. Filter q <= 0.5

unique(tcga.core.samples$Cluster) %>% map_dfr(\(c){
  tcga.core.samples %>% 
    summarize(across(-Cluster, ~t.test(.x ~ (Cluster==c))$p.value)) %>%
    pivot_longer(names_to = "Marker", values_to = "p", everything()) %>% 
    mutate(Cluster = c, Difference = -tcga.core.samples %>% 
             group_by(Cluster == c) %>% 
             select(-Cluster) %>% 
             group_split(.keep = FALSE) %>% map(colMeans) %>% reduce(`-`))
 }) %>% 
  mutate(q = p.adjust(p, method = "fdr")) %>% 
  filter(q <= 0.05) %>% arrange(q)

Marker	p	Cluster	Difference	q
P53	0.0000000	1	1.0772940	0.0000000
P70S6K_pT389	0.0000000	1	1.1586767	0.0000000
AKT_pS473	0.0000000	1	0.6165875	0.0000000
P53	0.0000000	3	1.0772940	0.0000000
P70S6K_pT389	0.0000000	3	1.1586767	0.0000000
BETACATENIN	0.0000000	3	-1.5451601	0.0000000
AKT_pS473	0.0000000	3	0.6165875	0.0000000
JNK_pT183Y185	0.0000000	3	0.2132549	0.0000000
JNK_pT183Y185	0.0000000	1	0.2132549	0.0000001
PDK1_pS241	0.0000003	3	-0.3557614	0.0000014
AKT_pT308	0.0000017	1	-0.0545686	0.0000073
YAP_pS127	0.0000033	3	-2.2414421	0.0000132
P38_pT180Y182	0.0000084	3	-0.4328967	0.0000310
AKT_pT308	0.0000111	3	-0.0545686	0.0000380
S6_pS235S236	0.0000208	1	0.6611220	0.0000665
BETACATENIN	0.0000411	1	-1.5451601	0.0001234
P53	0.0000569	2	1.0772940	0.0001518
P70S6K_pT389	0.0000559	4	1.1586767	0.0001518
PDK1_pS241	0.0000608	1	-0.3557614	0.0001536
AKT_pS473	0.0001065	2	0.6165875	0.0002556
S6_pS235S236	0.0001297	3	0.6611220	0.0002965
P70S6K_pT389	0.0002874	2	1.1586767	0.0006271
YAP_pS127	0.0003099	1	-2.2414421	0.0006467
BETACATENIN	0.0003851	2	-1.5451601	0.0007702
S6_pS235S236	0.0007700	4	0.6611220	0.0014784
P38_pT180Y182	0.0024050	1	-0.4328967	0.0044399
TRANSGLUTAMINASE	0.0025822	4	0.4540240	0.0045905
TRANSGLUTAMINASE	0.0029448	3	0.4540240	0.0050482
BETACATENIN	0.0078536	4	-1.5451601	0.0129991
P53	0.0082294	4	1.0772940	0.0131670
MEK1_pS217S221	0.0224278	2	0.2152544	0.0347268
P38_pT180Y182	0.0273737	4	-0.4328967	0.0410605
AKT_pT308	0.0335872	2	-0.0545686	0.0488541

Consensus NMF (9 clusters)

tcga.nmf.rank <- nmfEstimateRank(as.matrix(t(tcga.rank)), seq(2,10), nrun = 20, seed = 42)

plot(tcga.nmf.rank)

Version	Author	Date
f791e00	Jovan Tanevski	2021-08-03
51e2651	Jovan Tanevski	2021-08-03
55fb7fc	Jovan Tanevski	2021-08-02

tcga.nmf <- nmf(as.matrix(t(tcga.rank)), 9, nrun = 20, seed = 42)

For this analysis 9 clusters were selected based on consensus cophenetic correlation coefficient The analysis can also be repeated with 3 clusters as the cophenetic correlation coefficient for 3 clusters is higher (in continuation).

Extract basis of NMF (signature of cluster)

basismap(tcga.nmf)

Extract coefficients of NMF (soft clustering of samples)

coefmap(tcga.nmf)

Check for signs of overfitting

consensusmap(tcga.nmf)

Assign clusters

nmf.clusters <- apply(tcga.nmf@fit@H, 2, which.max)

Plot in 2D PCA and UMAP

fviz_pca_ind(tcga.pca, geom = "point", col.ind = as.factor(nmf.clusters)) +
  theme_classic()

ggplot(tcga.umap.clus %>% mutate(Cluster = as.factor(nmf.clusters)), aes(x = U1, y = U2, color = Cluster)) +
  geom_point() +
  theme_classic()

Expression profiles per cluster

tcga.clustered.nmf <- tcga.raw %>%
  mutate(Cluster = as.factor(nmf.clusters)) %>%
  pivot_longer(names_to = "Marker", values_to = "Z", -Cluster)

profiles <- seq_len(max(nmf.clusters)) %>% map(~
ggplot(
  tcga.clustered.nmf %>% filter(Cluster == .x),
  aes(x = Marker, y = Z, color = Marker)
) +
  stat_summary(fun.data = mean_sdl, show.legend = FALSE) +
  ylim(-3, 3) +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)))

plot_grid(plotlist = profiles, labels = paste("Cluster", seq_len(max(nmf.clusters))))

Warning: Removed 2 rows containing non-finite values (stat_summary).

Warning: Removed 1 rows containing missing values (geom_segment).

Warning: Removed 8 rows containing non-finite values (stat_summary).

Warning: Removed 1 rows containing missing values (geom_segment).

Warning: Removed 4 rows containing non-finite values (stat_summary).

Warning: Removed 2 rows containing non-finite values (stat_summary).

Warning: Removed 2 rows containing missing values (geom_segment).

Warning: Removed 2 rows containing non-finite values (stat_summary).

Warning: Removed 3 rows containing missing values (geom_segment).

Warning: Removed 4 rows containing non-finite values (stat_summary).

Warning: Removed 1 rows containing missing values (geom_segment).

Warning: Removed 5 rows containing non-finite values (stat_summary).

Warning: Removed 3 rows containing missing values (geom_segment).

Warning: Removed 4 rows containing non-finite values (stat_summary).

Warning: Removed 2 rows containing missing values (geom_segment).

Warning: Removed 2 rows containing non-finite values (stat_summary).

Differential expression analysis (limma)

design <- model.matrix(~0 + as.factor(nmf.clusters))
colnames(design) <- paste0("Cluster", seq_len(max(nmf.clusters)))

tcga.nmf.limma <- lmFit(t(tcga.raw), design = design)

tcga.nmf.eb <- eBayes(tcga.nmf.limma)

topTable(tcga.nmf.eb)

	Cluster1	Cluster2	Cluster3	Cluster4	Cluster5	Cluster6	Cluster7	Cluster8	Cluster9	AveExpr	F
YAP_pS127	2.3978952	2.6128531	2.3201659	3.1420813	2.2238593	2.3185180	2.2843542	2.7963107	1.9927770	2.2096629	317.40603
P53	-1.3898400	-1.5713606	-1.5791340	-1.6966091	-1.6871837	-1.3987109	-1.4106263	-1.4182143	-0.7678330	-1.1302653	313.60412
P70S6K_pT389	-1.5005166	-1.8855909	-1.8771042	-1.9916481	-2.1545847	-1.6546863	-1.6219767	-1.7235497	-0.6721740	-1.2148558	129.29253
BETACATENIN	1.5219449	1.9416915	1.7378802	1.6725415	1.2337905	1.6827628	1.1085864	2.5889554	1.4535112	1.5021704	112.27214
AKT_pS473	-1.0718449	-1.1911002	-1.1885023	-1.2880118	-1.6214364	0.0276857	-1.3219127	-1.0160392	-0.2052334	-0.6302143	69.34864
PDK1_pS241	0.5337273	0.8230705	0.4057842	0.4516760	0.5444971	0.5639792	0.5094236	0.4634277	0.2421504	0.4005464	55.29196
JNK_pT183Y185	-0.4204487	-0.5393783	-0.6318378	-0.5722916	-0.5929950	-0.3430688	-0.0887012	-0.5234238	-0.0614400	-0.2125813	39.72208
S6_pS235S236	-0.7697932	-1.7578225	-1.4877032	-1.2771461	0.1585755	-0.7772765	-0.7770087	-1.3703878	-0.5066805	-0.7220376	33.38019
TRANSGLUTAMINASE	0.4737129	-0.4879732	-0.7383488	-0.8834281	-0.4936744	-0.3968575	-0.2877142	-0.6573294	-0.5450193	-0.4221190	21.94286
P38_pT180Y182	0.1586131	-0.0629108	1.1912479	0.1479636	0.6498547	0.6538162	0.4270264	0.1811323	0.5655827	0.4853525	21.42125

tests.nmf <- decideTests(tcga.nmf.eb)

tests.nmf@.Data

                 Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Cluster6 Cluster7
P53                    -1       -1       -1       -1       -1       -1       -1
AKT_pS473              -1       -1       -1       -1       -1        0       -1
AKT_pT308               0       -1        0        0       -1        1       -1
BETACATENIN             1        1        1        1        1        1        1
JNK_pT183Y185          -1       -1       -1       -1       -1       -1       -1
MEK1_pS217S221         -1       -1       -1       -1        0       -1        1
P38_pT180Y182           0        0        1        0        1        1        1
P70S6K_pT389           -1       -1       -1       -1       -1       -1       -1
PDK1_pS241              1        1        1        1        1        1        1
S6_pS235S236           -1       -1       -1       -1        0       -1       -1
YAP_pS127               1        1        1        1        1        1        1
TRANSGLUTAMINASE        1       -1       -1       -1       -1       -1       -1
                 Cluster8 Cluster9
P53                    -1       -1
AKT_pS473              -1       -1
AKT_pT308               0        1
BETACATENIN             1        1
JNK_pT183Y185          -1       -1
MEK1_pS217S221         -1       -1
P38_pT180Y182           0        1
P70S6K_pT389           -1       -1
PDK1_pS241              1        1
S6_pS235S236           -1       -1
YAP_pS127               1        1
TRANSGLUTAMINASE       -1       -1

summary(tests.nmf)

       Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Cluster6 Cluster7 Cluster8
Down          6        8        7        7        6        6        7        7
NotSig        2        1        1        2        2        1        0        2
Up            4        3        4        3        4        5        5        3
       Cluster9
Down          7
NotSig        0
Up            5

Differential expression analysis (silhouette)

Calculate the similarity of samples using the expression and the silhuette scores based on the assigned clusters.

silhouette.nmf <- silhouette(nmf.clusters, dist(tcga.raw))
fviz_silhouette(silhouette.nmf)

  cluster size ave.sil.width
1       1   14         -0.09
2       2   10         -0.20
3       3    6         -0.22
4       4    3          0.01
5       5    7         -0.09
6       6   17         -0.20
7       7   31         -0.21
8       8    8          0.10
9       9   88          0.43

Select only the samples with positive silohuette scores as “core samples”

core.samples <- which(silhouette.nmf[,3] > 0)
tcga.core.samples <- tcga.raw %>% add_column(Cluster = nmf.clusters) %>% 
  slice(core.samples)

Calculate difference in means (mean(cluster) - mean()), one-vs-all t-test per marker and correct for FDR. Filter q <= 0.5

unique(tcga.core.samples$Cluster) %>% map_dfr(\(c){
  tcga.core.samples %>% 
    summarize(across(-Cluster, ~t.test(.x ~ (Cluster==c))$p.value)) %>%
    pivot_longer(names_to = "Marker", values_to = "p", everything()) %>% 
    mutate(Cluster = c, Difference = -tcga.core.samples %>% 
             group_by(Cluster == c) %>% 
             select(-Cluster) %>% 
             group_split(.keep = FALSE) %>% map(colMeans) %>% reduce(`-`))
 }) %>% 
  mutate(q = p.adjust(p, method = "fdr")) %>% 
  filter(q <= 0.05) %>% arrange(q)

Marker	p	Cluster	Difference	q
TRANSGLUTAMINASE	0.0000000	7	0.4835877	0.0000000
P70S6K_pT389	0.0000000	9	0.9057280	0.0000001
P53	0.0000000	9	0.9328523	0.0000002
PDK1_pS241	0.0000174	9	-0.3057533	0.0003535
AKT_pT308	0.0000210	6	-0.1537382	0.0003535
BETACATENIN	0.0000333	8	-1.4630194	0.0004661
PDK1_pS241	0.0000579	7	-0.3057533	0.0006952
JNK_pT183Y185	0.0001002	9	0.1337673	0.0010520
S6_pS235S236	0.0001729	8	0.6092046	0.0016137
P70S6K_pT389	0.0002544	8	0.9057280	0.0021373
AKT_pS473	0.0003231	8	0.3526431	0.0024673
P53	0.0003875	8	0.9328523	0.0027126
BETACATENIN	0.0006708	4	-1.4630194	0.0043344
P70S6K_pT389	0.0008152	1	0.9057280	0.0048903
AKT_pS473	0.0008733	6	0.3526431	0.0048903
TRANSGLUTAMINASE	0.0013948	5	0.4835877	0.0073228
AKT_pS473	0.0017123	5	0.3526431	0.0084609
JNK_pT183Y185	0.0023667	8	0.1337673	0.0110446
AKT_pT308	0.0032882	5	-0.1537382	0.0145372
AKT_pS473	0.0040119	9	0.3526431	0.0160475
MEK1_pS217S221	0.0038236	8	0.2192543	0.0160475
AKT_pS473	0.0053995	1	0.3526431	0.0206161
S6_pS235S236	0.0069532	9	0.6092046	0.0253943
TRANSGLUTAMINASE	0.0103733	8	0.4835877	0.0363067

Consensus NMF (3 clusters)

Repeat the analysis, but using 3 clusters.

tcga.nmf <- nmf(as.matrix(t(tcga.rank)), 3, nrun = 20, seed = 42)

Extract basis of NMF (signature of cluster)

basismap(tcga.nmf)

Extract coefficients of NMF (soft clustering of samples)

coefmap(tcga.nmf)

Check for signs of overfitting

consensusmap(tcga.nmf)

Assign clusters

nmf.clusters <- apply(tcga.nmf@fit@H, 2, which.max)

Plot in 2D PCA and UMAP

fviz_pca_ind(tcga.pca, geom = "point", col.ind = as.factor(nmf.clusters)) +
  theme_classic()

ggplot(tcga.umap.clus %>% mutate(Cluster = as.factor(nmf.clusters)), aes(x = U1, y = U2, color = Cluster)) +
  geom_point() +
  theme_classic()

Expression profiles per cluster

tcga.clustered.nmf <- tcga.raw %>%
  mutate(Cluster = as.factor(nmf.clusters)) %>%
  pivot_longer(names_to = "Marker", values_to = "Z", -Cluster)

profiles <- seq_len(max(nmf.clusters)) %>% map(~
ggplot(
  tcga.clustered.nmf %>% filter(Cluster == .x),
  aes(x = Marker, y = Z, color = Marker)
) +
  stat_summary(fun.data = mean_sdl, show.legend = FALSE) +
  ylim(-3, 3) +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)))

plot_grid(plotlist = profiles, labels = paste("Cluster", seq_len(max(nmf.clusters))))

Warning: Removed 9 rows containing non-finite values (stat_summary).

Warning: Removed 2 rows containing missing values (geom_segment).

Warning: Removed 21 rows containing non-finite values (stat_summary).

Warning: Removed 2 rows containing missing values (geom_segment).

Warning: Removed 3 rows containing non-finite values (stat_summary).

Differential expression analysis (limma)

design <- model.matrix(~0 + as.factor(nmf.clusters))
colnames(design) <- paste0("Cluster", seq_len(max(nmf.clusters)))

tcga.nmf.limma <- lmFit(t(tcga.raw), design = design)

tcga.nmf.eb <- eBayes(tcga.nmf.limma)

topTable(tcga.nmf.eb)

	Cluster1	Cluster2	Cluster3	AveExpr	F
YAP_pS127	2.3056243	2.8307973	2.0079290	2.2096629	1082.86252
P53	-1.5692867	-1.5852183	-0.8563584	-1.1302653	926.61353
BETACATENIN	1.0743656	2.1963955	1.4597442	1.5021704	373.80077
P70S6K_pT389	-1.8678252	-1.8760045	-0.8116854	-1.2148558	367.15157
AKT_pS473	-1.4512149	-1.1160172	-0.2172413	-0.6302143	199.61468
PDK1_pS241	0.5507008	0.6284452	0.2872053	0.4005464	147.94848
S6_pS235S236	-0.6603990	-1.4782462	-0.5374888	-0.7220376	90.44153
JNK_pT183Y185	-0.2750007	-0.5252041	-0.1062158	-0.2125813	69.30905
P38_pT180Y182	0.4358148	0.0701750	0.6151988	0.4853525	60.17513
MEK1_pS217S221	0.2105159	-0.3666276	-0.2427199	-0.1675294	44.84511

tests.nmf <- decideTests(tcga.nmf.eb)

tests.nmf@.Data

                 Cluster1 Cluster2 Cluster3
P53                    -1       -1       -1
AKT_pS473              -1       -1       -1
AKT_pT308              -1        0        1
BETACATENIN             1        1        1
JNK_pT183Y185          -1       -1       -1
MEK1_pS217S221          1       -1       -1
P38_pT180Y182           1        0        1
P70S6K_pT389           -1       -1       -1
PDK1_pS241              1        1        1
S6_pS235S236           -1       -1       -1
YAP_pS127               1        1        1
TRANSGLUTAMINASE        0       -1       -1

summary(tests.nmf)

       Cluster1 Cluster2 Cluster3
Down          6        7        7
NotSig        1        2        0
Up            5        3        5

Differential expression analysis (silhouette)

Calculate the similarity of samples using the expression and the silhuette scores based on the assigned clusters.

silhouette.nmf <- silhouette(nmf.clusters, dist(tcga.raw))
fviz_silhouette(silhouette.nmf)

  cluster size ave.sil.width
1       1   39         -0.08
2       2   31          0.11
3       3  114          0.46

Select only the samples with positive silohuette scores as “core samples”

core.samples <- which(silhouette.nmf[,3] > 0)
tcga.core.samples <- tcga.raw %>% add_column(Cluster = nmf.clusters) %>% 
  slice(core.samples)

Calculate difference in means (mean(cluster) - mean()), one-vs-all t-test per marker and correct for FDR. Filter q <= 0.5

unique(tcga.core.samples$Cluster) %>% map_dfr(\(c){
  tcga.core.samples %>% 
    summarize(across(-Cluster, ~t.test(.x ~ (Cluster==c))$p.value)) %>%
    pivot_longer(names_to = "Marker", values_to = "p", everything()) %>% 
    mutate(Cluster = c, Difference = -tcga.core.samples %>% 
             group_by(Cluster == c) %>% 
             select(-Cluster) %>% 
             group_split(.keep = FALSE) %>% map(colMeans) %>% reduce(`-`))
 }) %>% 
  mutate(q = p.adjust(p, method = "fdr")) %>% 
  filter(q <= 0.05) %>% arrange(q)

Marker	p	Cluster	Difference	q
P53	0.0000000	3	1.0646003	0.0000000
P70S6K_pT389	0.0000000	3	1.1087724	0.0000000
AKT_pS473	0.0000000	3	0.5177436	0.0000000
P53	0.0000000	2	1.0646003	0.0000000
P70S6K_pT389	0.0000000	2	1.1087724	0.0000000
BETACATENIN	0.0000000	2	-1.5370996	0.0000000
JNK_pT183Y185	0.0000000	2	0.1929598	0.0000001
AKT_pS473	0.0000001	2	0.5177436	0.0000003
S6_pS235S236	0.0000003	2	0.6813811	0.0000012
AKT_pS473	0.0000006	1	0.5177436	0.0000021
P70S6K_pT389	0.0000019	1	1.1087724	0.0000064
JNK_pT183Y185	0.0000021	3	0.1929598	0.0000064
YAP_pS127	0.0000024	2	-2.1777749	0.0000065
P53	0.0000052	1	1.0646003	0.0000134
AKT_pT308	0.0000062	3	-0.1070583	0.0000148
P38_pT180Y182	0.0000123	3	-0.4784715	0.0000278
PDK1_pS241	0.0000171	2	-0.3524044	0.0000362
YAP_pS127	0.0000189	3	-2.1777749	0.0000378
P38_pT180Y182	0.0001395	2	-0.4784715	0.0002642
PDK1_pS241	0.0003042	3	-0.3524044	0.0005476
AKT_pT308	0.0018944	2	-0.1070583	0.0031801
MEK1_pS217S221	0.0019434	1	0.2126068	0.0031801
S6_pS235S236	0.0020345	3	0.6813811	0.0031845
BETACATENIN	0.0021520	1	-1.5370996	0.0032281
MEK1_pS217S221	0.0024026	2	0.2126068	0.0034597
AKT_pT308	0.0085914	1	-0.1070583	0.0118958
TRANSGLUTAMINASE	0.0270956	1	0.4551282	0.0361275

sessionInfo()

R version 4.1.1 (2021-08-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/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] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] RColorBrewer_1.1-2  doParallel_1.0.16   iterators_1.0.13   
 [4] foreach_1.5.1       NMF_0.23.0          synchronicity_1.3.5
 [7] bigmemory_4.5.36    Biobase_2.52.0      BiocGenerics_0.38.0
[10] cluster_2.1.2       rngtools_1.5        pkgmaker_0.32.2    
[13] registry_0.5-1      limma_3.48.3        leiden_0.3.9       
[16] igraph_1.2.6        FNN_1.1.3           cowplot_1.1.1      
[19] factoextra_1.0.7    uwot_0.1.10         Matrix_1.3-4       
[22] skimr_2.1.3         forcats_0.5.1       stringr_1.4.0      
[25] dplyr_1.0.7         purrr_0.3.4         readr_2.0.1        
[28] tidyr_1.1.3         tibble_3.1.4        ggplot2_3.3.5      
[31] tidyverse_1.3.1     workflowr_1.6.2    

loaded via a namespace (and not attached):
  [1] readxl_1.3.1        uuid_0.1-4          backports_1.2.1    
  [4] Hmisc_4.5-0         plyr_1.8.6          repr_1.1.3         
  [7] splines_4.1.1       gridBase_0.4-7      digest_0.6.27      
 [10] htmltools_0.5.2     viridis_0.6.1       fansi_0.5.0        
 [13] checkmate_2.0.0     magrittr_2.0.1      tzdb_0.1.2         
 [16] openxlsx_4.2.4      modelr_0.1.8        vroom_1.5.5        
 [19] jpeg_0.1-9          colorspace_2.0-2    rvest_1.0.1        
 [22] ggrepel_0.9.1       haven_2.4.3         xfun_0.26          
 [25] crayon_1.4.1        jsonlite_1.7.2      bigmemory.sri_0.1.3
 [28] survival_3.2-13     glue_1.4.2          gtable_0.3.0       
 [31] car_3.0-11          abind_1.4-5         scales_1.1.1       
 [34] DBI_1.1.1           rstatix_0.7.0       Rcpp_1.0.7         
 [37] htmlTable_2.2.1     viridisLite_0.4.0   xtable_1.8-4       
 [40] reticulate_1.21     foreign_0.8-81      bit_4.0.4          
 [43] Formula_1.2-4       htmlwidgets_1.5.4   httr_1.4.2         
 [46] ellipsis_0.3.2      pkgconfig_2.0.3     farver_2.1.0       
 [49] nnet_7.3-16         sass_0.4.0          dbplyr_2.1.1       
 [52] utf8_1.2.2          tidyselect_1.1.1    labeling_0.4.2     
 [55] rlang_0.4.11        reshape2_1.4.4      later_1.3.0        
 [58] munsell_0.5.0       cellranger_1.1.0    tools_4.1.1        
 [61] cli_3.0.1           generics_0.1.0      broom_0.7.9        
 [64] evaluate_0.14       fastmap_1.1.0       yaml_2.2.1         
 [67] knitr_1.34          bit64_4.0.5         fs_1.5.0           
 [70] zip_2.2.0           dendextend_1.15.1   whisker_0.4        
 [73] xml2_1.3.2          compiler_4.1.1      rstudioapi_0.13    
 [76] curl_4.3.2          png_0.1-7           ggsignif_0.6.3     
 [79] reprex_2.0.1        bslib_0.3.0         stringi_1.7.4      
 [82] highr_0.9           RSpectra_0.16-0     lattice_0.20-44    
 [85] vctrs_0.3.8         pillar_1.6.2        lifecycle_1.0.0    
 [88] jquerylib_0.1.4     data.table_1.14.0   httpuv_1.6.3       
 [91] latticeExtra_0.6-29 R6_2.5.1            promises_1.2.0.1   
 [94] gridExtra_2.3       rio_0.5.27          codetools_0.2-18   
 [97] assertthat_0.2.1    rprojroot_2.0.2     withr_2.4.2        
[100] hms_1.1.0           rpart_4.1-15        grid_4.1.1         
[103] rmarkdown_2.11      carData_3.0-4       git2r_0.28.0       
[106] ggpubr_0.4.0        lubridate_1.7.10    base64enc_0.1-3

Analysis of TCGA RPPA LIHC samples

Jovan Tanevski

2021-09-16

Setup

Dimensionality reduction

Hierarchical clustering

Similarity and graph based clustering

Consensus NMF (9 clusters)

Consensus NMF (3 clusters)