---
title: "Exploring scRNA-seq data from 5 cancer cell lines with scBubbletree"
author: "Simo Kitanovski (simo.kitanovski@uni-due.de)"
output:
  BiocStyle::html_document
vignette: >
  %\VignetteIndexEntry{User Manual: scBubbletree}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---


```{r setup, include = FALSE, warning = FALSE}
knitr::opts_chunk$set(comment = FALSE, 
                      warning = FALSE, 
                      message = FALSE)
```


# Background

Over the last decade, we have seen exponential growth of the scale of scRNA-seq 
datasets to millions of cells sequenced in a single study. This has enabled 
researchers to characterize the gene expression profiles of various cell types 
across tissues. The rapid growth of scRNA-seq data has also created an unique 
set of challenges, for instance, there is a pressing need for scalable 
approaches for scRNA-seq data visualization.

This vignette introduces `r Biocpkg("scBubbletree")`, a transparent workflow 
for quantitative exploration of single cell RNA-seq data. 

In short, the algorithm of `r Biocpkg("scBubbletree")` performs clustering 
to identify clusters (bubbles) of transcriptionally similar cells, and then 
visualizes these clusters as leafs in a hierarchical dendrogram (bubbletree) 
which describes their natural relationships. The workflow comprises four 
steps: 1. determining the clustering resolution, 2. clustering, 3. hierarchical 
cluster grouping and 4. visualization. We explain each step in the following
using real scRNA-seq dataset of five cancer cell lines.

To run this vignette we need to load a few R-packages:

```{r}
library(scBubbletree)
library(ggplot2)
library(ggtree)
library(patchwork)
```



# Data[^1]

Here we will analyze a scRNA-seq dataset containing a mixture of 3,918 cells 
from five human lung adenocarcinoma cell lines (HCC827, H1975, A549, H838 and 
H2228). The dataset is available here[^2].
  
The library has been prepared with 10x Chromium platform and sequenced with 
Illumina NextSeq 500 platform. Raw data has been processed with Cellranger. 
The tool demuxlet has been used to predict the identity of each cell based on 
known genetic differences between the different cell lines. 


# Data processing

Data processing was performed with R-package `r CRANpkg("Seurat")`. Gene 
expressions were normalized with the function `r CRANpkg("SCTransform")` 
using default parameters, and principal component analysis (PCA) was performed 
with function *RunPCA* based on the 5,000 most variable genes in the dataset 
identified with the function *FindVariableFeatures*. 

In both datasets we saw that the first 15 principal components capture most 
of the variance in the data, and the proportion of variance explained by each 
subsequent principal component was negligible. Thus, we used the single cell 
projections (embeddings) in 15-dimensional feature space, $A^{3,918\times 15}$.

```{r}
# # This script can be used to generate data("d_ccl", package = "scBubbletree")
# 
# # create directory
# dir.create(path = "case_study/")
# 
# # download the data from:
# https://github.com/LuyiTian/sc_mixology/raw/master/data/
#   sincell_with_class_5cl.RData
# 
# # load the data
# load(file = "case_study/sincell_with_class_5cl.RData")
# 
# # we are only interested in the 10x data object 'sce_sc_10x_5cl_qc'
# d <- sce_sc_10x_5cl_qc
# 
# # remove the remaining objects (cleanup)
# rm(sc_Celseq2_5cl_p1, sc_Celseq2_5cl_p2, sc_Celseq2_5cl_p3, sce_sc_10x_5cl_qc)
# 
# # get the meta data for each cell
# meta <- colData(d)[,c("cell_line_demuxlet","non_mt_percent","total_features")]
# 
# # create Seurat object from the raw counts and append the meta data to it
# d <- Seurat::CreateSeuratObject(counts = d@assays$data$counts,
#                                 project = '')
# 
# # check if all cells are matched between d and meta
# # table(rownames(d@meta.data) == meta@rownames)
# d@meta.data <- cbind(d@meta.data, meta@listData)
# 
# # cell type predictions are provided as part of the meta data
# table(d@meta.data$cell_line)
# 
# # select 5,000 most variable genes
# d <- Seurat::FindVariableFeatures(object = d,
#                                   selection.method = "vst",
#                                   nfeatures = 5000)
# 
# # Preprocessing with Seurat: SCT transformation + PCA
# d <- SCTransform(object = d,
#                  variable.features.n = 5000)
# d <- RunPCA(object = d,
#             npcs = 50,
#             features = VariableFeatures(object = d))
# 
# # perform UMAP + t-SNE
# d <- RunUMAP(d, dims = 1:15)
# d <- RunTSNE(d, dims = 1:15)
# 
# # save the preprocessed data
# save(d, file = "case_study/d.RData")
# 
# # save the PCA matrix 'A', meta data 'm' and
# # marker genes matrix 'e'
# d <- get(load(file ="case_study/d.RData"))
# A <- d@reductions$pca@cell.embeddings[, 1:15]
# m <- d@meta.data
# e <- t(as.matrix(d@assays$SCT@data[
#   rownames(d@assays$SCT@data) %in%
#     c("ALDH1A1",
#       "PIP4K2C",
#       "SLPI",
#       "CT45A2",
#       "CD74"), ]))
# 
# d_ccl <- list(A = A, m = m, e = e)
# save(d_ccl, file = "data/d_ccl.RData")
```


Load the processed PCA matrix and the meta data

```{r}
data("d_ccl", package = "scBubbletree")
A <- d_ccl$A
m <- d_ccl$m
e <- d_ccl$e
```



# scBubbletree workflow
   
We will analyze this data with `r Biocpkg("scBubbletree")`. 

As first input `r Biocpkg("scBubbletree")` uses matrix $A^{n\times f}$ which 
represents a low-dimensional projection of the original scRNA-seq data, with 
$n$ rows as cells and $f$ columns as low-dimension features. 

We will use the PCA data generated by `r CRANpkg("Seurat")` as $A$. In 
particular, we will use the first 15 principal components (PCs) as every 
additional PC explains negligible amount of variance in the data.

**Important remark about $A$**: the `r Biocpkg("scBubbletree")` workflow 
works directly with the numeric matrix $A^{n\times f}$ and is agnostic to 
the initial data processing protocol. This enables seamless integration 
of `r Biocpkg("scBubbletree")` with computational pipelines using objects 
generated by the R-packages `r CRANpkg("Seurat")` and 
`r Biocpkg("SingleCellExperiment")`. The users simply have to extract $A$ 
from the corresponding `r CRANpkg("Seurat")` or 
`r Biocpkg("SingleCellExperiment")` objects.

```{r}
# A has n=cells as rows, f=features as columns (e.g. from PCA)
dim(A)
```
The `r Biocpkg("scBubbletree")` workflow performs the following steps:
  
  1. determine the clustering resolution (clusters $k$ or resolution $r$)
  2. graph-based community detection (e.g. with Louvain) or k-means clustering
  3. hierarchical organization of clusters (bubbles)
  4. visualization

## 1. determine the clustering resolution
If we use graph-based community detection (**recommended for scRNA-seq**) with
e.g. the Louvain or Leiden method, then we need to find appropriate value for 
the resolution parameter $r$. Otherwise, we can use the simpler k-means 
clustering algorithm in which case we need to find an appropriate value of the 
number of clusters $k$.

### 1.1 determining the number of clusters $k$
How many clusters (cell types) are there are in the data? Can we guess a 
reasonable value of $k$? 

To find a reasonable value of $k$ we can study the literature or databases such 
as the human protein atlas database (HPA). We can also use the function `get_k` 
for data-driven inference of $k$ based on the Gap statistic and the within-
cluster sum of squares (WCSS).

As this is a toy dataset, we will skip the first approach and perform a 
data-driven search for $k$ using `get_k`. As input we need to provide the 
matrix $A$ as input and a vector of $k$s. The output will be the Gap 
statistic and WCSS estimates for each $k$.
  
Lets run `get_k` now:

```{r}
b_k <- get_k(B_gap = 5,
             ks = 1:10,
             x = A,
             n_start = 50, 
             iter_max = 200,
             kmeans_algorithm = "MacQueen", 
             cores = 1)
```

The Gap statistic and WCSS curves have a noticeable knee (elbow) at $k=5$. 
Hence, $k$=5 appears to be reasonable first choice of $k$. Means (points) and 
95% confidence intervals are shown for the Gap statistic at each $k$ computed
using `B_gap`=5 MCMC simulations.

```{r}
g0 <- ggplot(data = b_k$gap_stats_summary)+
  geom_line(aes(x = k, y = gap_mean))+
  geom_point(aes(x = k, y = gap_mean), size = 1)+
  geom_errorbar(aes(x = k, y = gap_mean, ymin = L95, ymax = H95), width = 0.1)+
  ylab(label = "Gap")|
ggplot(data = b_k$wcss_stats_summary)+
  geom_line(aes(x = k, y = wcss_mean))+
  geom_point(aes(x = k, y = wcss_mean), size = 1)+
  ylab(label = "WCSS")+
  scale_y_log10()+
  annotation_logticks(base = 10, sides = "l")
```


```{r, fig.width=7, fig.height=2.5, fig.align='center'}
g0
```

### 1.2 determining the resolution parameter $r$
For Louvain clustering we need to select a clustering resolution $r$. Higher 
resolutions lead to more communities and lower resolutions lead to fewer 
communities. We can use the same strategy as before to find a reasonable 
reasonable value of $r$.

Lets use the function `get_r` for data-driven estimation of $r$ based on 
the Gap statistic and WCSS. As input we need to provide the matrix $A$ and 
a vector of $r$s. The output will be the Gap statistic and WCSS estimate 
for each $r$ (or the number of communities $k'$ detected at resolution $r$).

```{r}
b_r <- get_r(B_gap = 5,
             rs = 10^seq(from = -4, to = 0, by = 0.35),
             x = A,
             n_start = 10, 
             iter_max = 50,
             algorithm = "original",
             knn_k = 50,
             cores = 1)
```


The Gap statistic and WCSS curves have noticeable knees (elbows) at $k'=5$ 
($r=0.0025$). Means (points) and 95% confidence intervals are shown for the 
Gap statistic at each $k$ computed using `B_gap`=5 MCMC simulations.

```{r}
g0_r <- (ggplot(data = b_r$gap_stats_summary)+
  geom_line(aes(x = k, y = gap_mean))+
  geom_point(aes(x = k, y = gap_mean), size = 1)+
  geom_errorbar(aes(x = k, y = gap_mean, ymin = L95, ymax = H95), width = 0.1)+
  ylab(label = "Gap")+
  xlab(label = "k'")|
ggplot(data = b_r$gap_stats_summary)+
  geom_line(aes(x = r, y = gap_mean))+
  geom_point(aes(x = r, y = gap_mean), size = 1)+
  geom_errorbar(aes(x = r, y = gap_mean, ymin = L95, ymax = H95), width = 0.1)+
  ylab(label = "Gap")+
  xlab(label = "r")+
  scale_x_log10()+
  annotation_logticks(base = 10, sides = "b"))/
(ggplot(data = b_r$wcss_stats_summary)+
  geom_line(aes(x = k, y = wcss_mean))+
  geom_point(aes(x = k, y = wcss_mean), size = 1)+
  ylab(label = "WCSS")+
  xlab(label = "k'")|
ggplot(data = b_r$wcss_stats_summary)+
  geom_line(aes(x = r, y = wcss_mean))+
  geom_point(aes(x = r, y = wcss_mean), size = 1)+
  ylab(label = "WCSS")+
  xlab(label = "r")+
  scale_x_log10()+
  annotation_logticks(base = 10, sides = "b"))
```


```{r, fig.width=6, fig.height=4, fig.align='center'}
g0_r
```


A range of resolutions yields $k=5$ number of communities, i.e. $r = 0.0025$ 
and $r = 0.125$ result in $k=5$. Lets use $r=0.1$ for clustering

```{r, fig.width=4, fig.height=3, fig.align='center'}
ggplot(data = b_r$gap_stats_summary)+
    geom_point(aes(x = r, y = k), size = 1)+
    xlab(label = "r")+
    ylab(label = "k'")+
  scale_x_log10()+
  annotation_logticks(base = 10, sides = "b")
```


```{r}
knitr::kable(x = b_r$gap_stats_summary[b_r$gap_stats_summary$k == 5, ],
             digits = 4, row.names = FALSE)
```


## 2. clustering

### 2.1 with k-means
Now that we found out that $k=5$ is a reasonable choice based on the data, 
we will perform k-means clustering with $k=5$ and $A$ as inputs. For this 
we will use the function kmeans (R-package stats) which offers various 
variants of k-means. Here we will use MacQueen's k-means variant and 
perform $n_\textit{start} = 1000$ (default in `r Biocpkg("scBubbletree")`) 
random starts and a maximum number of iterations $iter_\textit{max}=300$. 

**Important remark**: for smaller datasets (e.g. $n<50,000$) $n_{start}=1000$ 
and $n_{iter} = 300$ are unnecessarily high, however for larger datasets this 
is necessary to make sure that k-means converges.


## 3. hierarchical grouping
After the clustering is complete we will organize the bubbles in a natural
hierarchy. For this we perform $B$ bootstrap iterations (default $B=200$). 
In iteration $b$ the algorithm draws a random subset of $N_\textit{eff}$ 
(default $N_\textit{eff}=200$) cells with replacement from each cluster and 
computes the average inter-cluster Euclidean distances. This data is used to 
populate the distance matrix ($D^{k\times k}_b$), which is provided as input 
for hierarchical clustering with average linkage to generate a hierarchical 
clustering dendrogram $H_b$. 

The collection of distance matrices that are computed during $B$ iterations are 
used to compute a consensus (average) distance matrix ($\hat{D}^{k\times k}$) 
and from this a corresponding consensus hierarchical dendrogram (bubbletree; 
$\hat{H}$) is constructed. The collection of dendrograms are used to quantify 
the robustness of the bubbletree topology, i.e. to count the number of times 
each branch in the bubbletree is found among the topologies of the bootstrap 
dendrograms. Branches can have has variable degrees of support ranging between 
0 (no support) and $B$ (complete support). Distances between bubbles (inter-
bubble relationships) are described quantitatively in the bubbletree as sums 
of branch lengths. 

Steps 2.1 and 3. are performed next

```{r}
k5_kmeans <- get_bubbletree_kmeans(
  x = A,
  k = 5,
  cores = 1,
  B = 200,
  N_eff = 200,
  round_digits = 1,
  show_simple_count = FALSE,
  kmeans_algorithm = "MacQueen")
```

... and plot the bubbletree

```{r, fig.width=4, fig.height=3, fig.align='center'}
k5_kmeans$tree
```


Lets describe the bubbletree:

**bubbles**: The bubbletree has `k=5` bubbles (clusters) shown as leaves. The 
absolute and relative cell frequencies in each bubble and the bubble IDs are 
shown as labels. Bubble radii scale linearly with absolute cell count in each 
bubble, i.e. large bubbles have many cells and small bubbles contain few cells. 

Bubble 1 is the largest one in the dendrogram and contains 1,253 cells 
($\approx$ 32% of all cells in the dataset). Bubble 4 is the smallest one 
and contains only 436 cells ($\approx$ 11% of all cells in the dataset). 

We can access the bubble data shown in the bubbletree

```{r}
knitr::kable(k5_kmeans$tree_meta, 
             digits = 2, row.names = FALSE)
```

**topology**: inter-bubble distances are represented by sums of branch 
lengths in the dendrogram. Branches of the bubbletree are annotated with 
their bootstrap support values (red branch labels). The branch support 
value tells us how manytimes a given branch from the bubbletree was found 
among the $B$ bootstrap dendrograms. We ran `get_bubbletree_kmeans` with 
$B=200$. All but one branch have complete (200 out of 200) support, and 
one branch has lower support of 179 (85%). This tells us that the branch 
between bubbles (3, 4) and 1 is not as robust.



### 2.2 with Louvain
Lets also perform clustering with the Louvain algorithm (function FindClusters, 
R-package `r CRANpkg("Seurat")`) and resolution parameter $r=0.1$. There are 
numerous variants of the Louvain algorithm. Here we will use the original 
implementation. We will do clustering with $n_\textit{start} = 20$ random 
starts and a maximum number of iterations $iter_\textit{max} = 100$. 

Steps 2.2 and 3. (hierarchical clustering) are performed next

```{r}
k5_louvain <- get_bubbletree_graph(x = A,
                                   r = 0.0025,
                                   n_start = 20,
                                   iter_max = 100,
                                   algorithm = "original",
                                   knn_k = 50,
                                   cores = 1,
                                   B = 200,
                                   N_eff = 200,
                                   round_digits = 1,
                                   show_simple_count = FALSE)
```


... and plot the bubbletree. We see nearly identical dendrogram as the one 
generated by kmeans clustering. The bubble IDs are different but we see similar 
bubble sizes, topology and branch robustness values.

```{r, fig.width=4, fig.height=3, fig.align='center'}
k5_louvain$tree
```


The two dendrograms shown side-by-side:

```{r, fig.width=7, fig.height=3, fig.align='center'}
k5_kmeans$tree|k5_louvain$tree
```


Given the high degree of similarity between the two clustering solutions we 
proceed in the next with the k-means results.




## 4. visualization

To extract biologically useful information from the bubbletree (and also for 
2D UMAP or t-SNE plots) we need to adorn it with biologically relevant cell 
features. This includes both **numeric** and **categorical** cell features.

Numeric cell features:

  * gene expression
  * % of mitochondrial transcripts
  * number of UMIs, genes detected
  * ...

Categorical cell features:

  * cell type label (e.g. B-cells, T-cells, moncytes, ...)
  * cell cycle phase (e.g. S, M, G1, ...)
  * sample name (e.g. S1, S2, S3, ...)
  * treatment group (e.g. cancer vs. control cell)
  * multiplet status (e.g. singlet, doublet or multiplet)
  * ...


In the next two paragraph we will explain how to 'attach' numeric and 
categorical features to the bubbletree using `r Biocpkg("scBubbletree")`.


## Attaching categorical features

Categorical cell features can be 'attached' to the bubbletree using the function
`get_cat_tiles`. Here we will show the relative frequency of cell type labels 
across the bubbles (parameter `integrate_vertical=TRUE`).

Interpretation of the figure below: 
  
  * we see high degree of co-occurrence between cell lines and bubbles, i.e. 
    each bubble is made up of cells from a distinct cell line
  * for instance, 99.8% of cells that have feature HCC827 are found in bubble 2
  * columns in the tile plot integrate to 100%

```{r, fig.width=7, fig.height=4, fig.align='center'}
w1 <- get_cat_tiles(btd = k5_kmeans,
                    f = m$cell_line_demuxlet,
                    integrate_vertical = TRUE,
                    round_digits = 1,
                    x_axis_name = 'Cell line',
                    rotate_x_axis_labels = TRUE,
                    tile_text_size = 2.75)

(k5_kmeans$tree|w1$plot)+
  patchwork::plot_layout(widths = c(1, 1))
```

We can also show the inter-bubble cell type composition, i.e. the relative 
frequencies of different cell types in a specific bubble (with parameter 
`integrate_vertical=FALSE`).

Interpretation of the figure below: 
  
  * the bubbles appear to be "pure" $\rightarrow$ made up of cells from 
    distinct cell lines
  * the cell line composition of bubble 2 is: 0.1% H838, 99.9% H2228, 0.1% 
    A549, 0.1% H1975 and 0% HCC827 cells
  * rows integrate to 100%

```{r, fig.width=7, fig.height=4, fig.align='center'}
w2 <- get_cat_tiles(btd = k5_kmeans,
                    f = m$cell_line_demuxlet,
                    integrate_vertical = FALSE,
                    round_digits = 1,
                    x_axis_name = 'Cell line',
                    rotate_x_axis_labels = TRUE,
                    tile_text_size = 2.75)

(k5_kmeans$tree|w2$plot)+
  patchwork::plot_layout(widths = c(1, 1))
```

`r Biocpkg("scBubbletree")` uses R-package `r Biocpkg("ggtree")` to 
visualize the bubbletree, and `r CRANpkg("ggplot2")` to visualize 
annotations. Furthermore, R-package `r CRANpkg("patchwork")` is used to 
combine plots.

```{r, fig.width=9, fig.height=4, fig.align='center'}
(k5_kmeans$tree|w1$plot|w2$plot)+
  patchwork::plot_layout(widths = c(1, 2, 2))+
  patchwork::plot_annotation(tag_levels = "A")
```



## Gini impurity index

To quantify the purity of a cluster (or bubble) $i$ with $n_i$ number of cells, 
each of which carries one of $L$ possible labels (e.g. cell lines), we can 
compute the Gini impurity index:

$\textit{GI}_i=\sum_{j=1}^{L} \pi_{ij}(1-\pi_{ij})$,

with $\pi_{ij}$ as the relative frequency of label $j$ in cluster $i$. In 
homogeneous (`pure`) clusters most cells carry a distinct label. Hence, the 
$\pi$'s are close to either 1 or 0, and *GI* takes on a small value close to 
zero. In `impure` clusters cells carry a mixture of different labels. In 
this case most $\pi$ are far from either 1 or 0, and *GI* diverges from 0 
and approaches 1. If the relative frequencies of the different labels in 
cluster $i$ are equal to the (background) relative frequencies of the labels 
in the sample, then cluster $i$ is completely `impure`.

To compute the overall Gini impurity of a bubbletree, which represents a 
clustering solution with $k$ bubbles, we estimated the weighted Gini impurity 
(*WGI*) by computing the weighted (by the cluster size) average of the 

$\textit{WGI}=\sum_{i=1}^{k} \textit{GI}_i \dfrac{n_i}{n}$,

with $n_i$ as the number of cells in cluster $i$ and $n=\sum_i n_i$. 


The Gini impurity results are shown below:

```{r}
# gini
get_gini(labels = m$cell_line_demuxlet, 
         clusters = k5_kmeans$cluster)$gi
```

All cluster-specific *GI*s are close to 0 and hence also *WGI* is close to 0. 
This indicates nearly perfect mapping of cell lines to bubbles. This analysis 
performed for different values of $k$ with function `get_gini_k`, which takes 
as main input the output of `get_k` or `get_r`

```{r}
gini_boot <- get_gini_k(labels = m$cell_line_demuxlet,
                        obj = b_k)
```

From the figure we can conclude that WGI drops to 0 at `k=5`, and all labels 
are nearly perfectly split across the bubbles with each bubble containing cells 
exclusively from one cell type.

```{r, fig.width=4, fig.height=3, fig.align='center'}
g1 <- ggplot(data = gini_boot$wgi_summary)+
  geom_point(aes(x = k, y = wgi), size = 0.75)+
  ylab(label = "WGI")+
  ylim(c(0, 1))

g1
```


## Attaching numeric features

We can also "attach" numeric cell features to the bubbletree. We will "attach" 
the expression of five marker genes, i.e. one marker gene for each of the five 
cancer cell lines. 

We can visualize numeric features in *two* ways.

First, we can show numeric feature aggregates (e.g. "mean", "median", "sum",
"pct nonzero" or "pct zero") in the different bubbles with `get_num_tiles`

```{r, fig.width=8, fig.height=4, fig.align='center'}
w3 <- get_num_tiles(btd = k5_kmeans,
                    fs = e,
                    summary_function = "mean",
                    x_axis_name = 'Gene expression',
                    rotate_x_axis_labels = TRUE,
                    round_digits = 1,
                    tile_text_size = 2.75)

(k5_kmeans$tree|w3$plot)+
  patchwork::plot_layout(widths = c(1, 1))
```


Second, we can visualize the distributions of the numeric cell features in each
bubble as violins with `get_num_violins`

```{r, fig.width=10, fig.height=4, fig.align='center'}
w4 <- get_num_violins(btd = k5_kmeans,
                      fs = e,
                      x_axis_name = 'Gene expression',
                      rotate_x_axis_labels = TRUE)

(k5_kmeans$tree|w3$plot|w4$plot)+
  patchwork::plot_layout(widths = c(1.5, 2, 2.5))+
  patchwork::plot_annotation(tag_levels = 'A')
```

## Quality control with `r Biocpkg("scBubbletree")`
What is the percent of UMIs coming from mitochondrial genes in each bubble? 

```{r, fig.width=9, fig.height=4, fig.align='center'}
w_mt_dist <- get_num_violins(btd = k5_kmeans,
                             fs = 1-m$non_mt_percent,
                             x_axis_name = 'MT [%]',
                             rotate_x_axis_labels = TRUE)

w_umi_dist <- get_num_violins(btd = k5_kmeans,
                              fs = m$nCount_RNA/1000,
                              x_axis_name = 'RNA count (in thousands)',
                              rotate_x_axis_labels = TRUE)

w_gene_dist <- get_num_violins(btd = k5_kmeans,
                               fs = m$nFeature_RNA,
                               x_axis_name = 'Gene count',
                               rotate_x_axis_labels = TRUE)


(k5_kmeans$tree|w_mt_dist$plot|w_umi_dist$plot|w_gene_dist$plot)+
  patchwork::plot_layout(widths = c(0.7, 1, 1, 1))+
  patchwork::plot_annotation(tag_levels = 'A')
```


The clustering of both algorithms seems to work well, i.e. cells from specific 
cell lines are clustered together. Two potential issues:

1. overplotting: points are stacked on top of each other $\rightarrow$ loss 
   of information about cell density distribution $\rightarrow$ we are
   unable to accurately answer two questions: 
      * which cell line contains most cells?
      * what are the relative frequencies of cells across cell lines?

2. preservation of long-range cell distances: UMAP and t-SNE focus on 
   preserving local cell distance (at the cost of global distances)
   $\rightarrow$ are there pairs of cell lines that are more similar to each
   other than the remaining ones in the sample?
 
These challenges will become more severe in real datasets (e.g. PBMC samples, 
see case study B) which contain many clusters of cells that are not clearly 
separable.




## scBubbletree can incorporate results from other clustering approaches

Wide range of clustering approaches are used for clustering of scRNA-seq data. 
`r Biocpkg("scBubbletree")` implements the function `get_bubbletree_dummy` to 
allow users to incorporate results from various clustering approaches together
with our workflow. With this function we skip the k-means clustering portion of 
the workflow and proceed with computing distances between the clusters and 
generation of the bubbletree.

Lets try `get_bubbletree_dummy`. First, will perform k-medoids clustering with
R-package `r CRANpkg("cluster")` and then generate the bubbletree:

```{r, fig.width=7, fig.height=4, fig.align='center'}
pam_k5 <- cluster::pam(x = A, 
                       k = 5, 
                       metric = "euclidean")

dummy_k5_pam <- get_bubbletree_dummy(x = A,
                                     cs = pam_k5$clustering,
                                     B = 200,
                                     N_eff = 200,
                                     cores = 2,
                                     round_digits = 1)

dummy_k5_pam$tree|
  get_cat_tiles(btd = dummy_k5_pam, 
                f = m$cell_line_demuxlet,
                integrate_vertical = TRUE,
                round_digits = 1,
                tile_text_size = 2.75,
                x_axis_name = 'Cell line',
                rotate_x_axis_labels = TRUE)$plot
```



## Summary

`r Biocpkg("scBubbletree")` promotes simple and transparent visual exploration 
of scRNA-seq. It is *not a black-box* approach and the user *is encouraged* to 
explore the data with different values of $k$ and $r$ or custom clustering 
solutions. Attaching of cell features to the bubbletree is necessary for 
biological interpretation of the individual bubbles and their relationships 
which are described by the bubbletree topology.




[^1]: Tian, Luyi, et al. "Benchmarking single cell RNA-sequencing analysis 
pipelines using mixture control experiments." Nature methods 16.6 (2019): 
479-487.
[^2]: https://github.com/LuyiTian/sc_mixology/blob/master/data/
sincell_with_class_5cl.RData


## Session Info

```{r}
sessionInfo()
```

