`HGC`

(short for Hierarchical Graph-based Clustering) is an R package for
conducting hierarchical clustering on large-scale single-cell RNA-seq
(scRNA-seq) data. The key idea is to construct a dendrogram of cells on
their shared nearest neighbor (SNN) graph. `HGC`

provides functions for
building cell graphs and for conducting hierarchical clustering on the graph.
Experiments on benchmark datasets showed that `HGC`

can reveal the
hierarchical structure underlying the data, achieve state-of-the-art
clustering accuracy and has better scalability to large single-cell data.
For more information, please refer to the preprint of `HGC`

on
bioRxiv.

`HGC`

could be installed from Bioconductor.

```
if (!requireNamespace("BiocManager"))
install.packages("BiocManager")
BiocManager::install("HGC")
```

The users could also get the newest version from Github.

```
if(!require(devtools))
install.packages("devtools")
devtools::install_github("XuegongLab/HGC")
```

`HGC`

takes a matrix as input where row represents cells and column
represents features. Preprocessing steps like normalization and dimension
reduction are necessary so that the constructed graph can capture the
manifold underlying the single-cell data. We recommend users to follow
the standard preprocessing steps in
`Seurat`

.
As a demo input, we stored the top 25 principal components of the
Pollen dataset (Pollen et al.)
in `HGC`

. The dataset contains 301 cells with two known labels: labels at
the tissue level and the cell line level.

```
library(HGC)
data(Pollen)
Pollen.PCs <- Pollen[["PCs"]]
Pollen.Label.Tissue <- Pollen[["Tissue"]]
Pollen.Label.CellLine <- Pollen[["CellLine"]]
dim(Pollen.PCs)
```

`## [1] 301 25`

`table(Pollen.Label.Tissue)`

```
## Pollen.Label.Tissue
## blood dermal neural pluripotent
## 113 99 65 24
```

`table(Pollen.Label.CellLine)`

```
## Pollen.Label.CellLine
## 2338 2339 BJ GW16 GW21 GW21+3 hiPSC HL60 K562 Kera NPC
## 22 17 37 26 7 17 24 54 42 40 15
```

There are two major steps for conducting the hierarchical clustering
with `HGC`

: the graph construction step and the dendrogram construction
step. `HGC`

provides functions for
building a group of graphs, including the k-nearest neighbor graph (KNN),
the shared nearest neighbor graph (SNN), the continuous k-nearest neighbor
graph (CKNN), etc. These graphs are saved as `dgCMatrix`

supported by
R package `Matrix`

. Then `HGC`

can directly build a hierarchical tree
on the graph. A self-built graph or graphs from other pipelines stored
as `dgCMatrix`

are also supported.

```
Pollen.SNN <- SNN.Construction(mat = Pollen.PCs, k = 25, threshold = 0.15)
Pollen.ClusteringTree <- HGC.dendrogram(G = Pollen.SNN)
```

The output of `HGC`

is a standard tree following the data structure `hclust()`

in R package `stats`

. The tree can be cut into specific number of clusters
with the function `cutree`

.

`cluster.k5 <- cutree(Pollen.ClusteringTree, k = 5)`

`HGC`

provides user-friendly functions to run hierarchical
clustering in the existing pipelines, like `Seurat`

,
`scran`

, etc. The section will provide the corresponding
guides.

The functions `FindClusteringTree`

and `HGC.dendrogram`

could read the graphs calculated in the pipelines.
Then they build the dendrograms and output/save the
trees. We will try our best to support the applications
of `HGC`

in more pipelines.

The `Seurat`

package is one popular
scRNA-seq data processing workflow.
It is designed for QC, analysis and exploration of scRNA-seq data.

`Seurat`

contains the graph-based clustering methods Louvain, SLM and
Leiden to find the cell clusters. They all run on the graph built by
the function `FindNeighbors`

in `Seurat`

.

Here we provide a guide to run `FindClusteringTree`

in
`Seurat`

pipeline using the SNN/KNN
graph calculated by `Seurat`

. The data comes from the
“pbmc3k_tutorial”
of `Seurat`

. We follow the tutorial to run QC, preprocessing,
dimension reduction and SNN graph construction. Then we run HGC in
the calculated graph with one order.

```
library(dplyr)
library(Seurat)
library(patchwork)
library(HGC)
# Load the PBMC dataset
pbmc.data <- Read10X(data.dir =
"../data/pbmc3k/filtered_gene_bc_matrices/hg19/")
# Initialize the Seurat object with the raw (non-normalized data).
pbmc <- CreateSeuratObject(counts = pbmc.data, project = "pbmc3k",
min.cells = 3, min.features = 200)
# QC and selecting cells for further analysis
pbmc[["percent.mt"]] <- PercentageFeatureSet(pbmc, pattern = "^MT-")
pbmc <- subset(pbmc, subset = nFeature_RNA > 200 &
nFeature_RNA < 2500 & percent.mt < 5)
# Normalizing the data
pbmc <- NormalizeData(pbmc, normalization.method = "LogNormalize",
scale.factor = 10000)
# Identification of highly variable features (feature selection)
pbmc <- FindVariableFeatures(pbmc, selection.method = "vst",
nfeatures = 2000)
# Scaling the data
all.genes <- rownames(pbmc)
pbmc <- ScaleData(pbmc, features = all.genes)
# Perform linear dimensional reduction
pbmc <- RunPCA(pbmc, features = VariableFeatures(object = pbmc))
# Determine the ‘dimensionality’ of the dataset
pbmc <- JackStraw(pbmc, num.replicate = 100)
pbmc <- ScoreJackStraw(pbmc, dims = 1:20)
# Construct the graph and cluster the cells with HGC
pbmc <- FindNeighbors(pbmc, dims = 1:10)
pbmc <- FindClusteringTree(pbmc, graph.type = "SNN")
# Output the tree
pbmc.tree <- pbmc@graphs$ClusteringTree
```

The input of `FindClusteringTree`

is the `Seurat`

object and
the function outputs a `Seurat`

object containing the
dendrogram.

`scran`

is a wildly
used step-by-step workflow for low-level analysis of scRNA-seq
data. It builds SNN graph with the function `buildSNNGraph`

and
saves the graph as `igraph`

object. The function
`HGC.dendrogram`

could run hierarchical clustering
with the `igraph`

object.

The `igraph`

package is a toolbox to do graph-related
calculations in R. It has the specific data structure to
save graphs and contains several graph-based clustering functions.
Another pipeline
`OSCA`

uses
`igraph`

to cluster the cells, and `HGC.dendrogram`

could also help.

Here we follow the tutorial of `scran`

and show how to
use the `HGC.dendrogram`

to build clustering tree on the
processed scRNA-seq data.

```
# Setting up the data
library(scRNAseq)
sce <- GrunPancreasData()
library(scuttle)
qcstats <- perCellQCMetrics(sce)
qcfilter <- quickPerCellQC(qcstats,
percent_subsets="altexps_ERCC_percent")
sce <- sce[,!qcfilter$discard]
library(scran)
clusters <- quickCluster(sce)
sce <- computeSumFactors(sce, clusters=clusters)
sce <- logNormCounts(sce)
# Variance modelling
dec <- modelGeneVar(sce)
plot(dec$mean, dec$total, xlab="Mean log-expression",
ylab="Variance")
curve(metadata(dec)$trend(x), col="blue", add=TRUE)
# Get the top 10% of genes.
top.hvgs <- getTopHVGs(dec, prop=0.1)
sce <- fixedPCA(sce, subset.row=top.hvgs)
reducedDimNames(sce)
# Automated PC choice
output <- getClusteredPCs(reducedDim(sce))
npcs <- metadata(output)$chosen
reducedDim(sce, "PCAsub") <-
reducedDim(sce, "PCA")[,1:npcs,drop=FALSE]
library(HGC)
# Graph construction
g <- buildSNNGraph(sce, use.dimred="PCAsub")
# Graph-based clustering
cluster.tree <- HGC.dendrogram(G = g)
cluster.k12 <- cutree(cluster.tree, k = 12)
colLabels(sce) <- factor(cluster.k12)
library(scater)
sce <- runTSNE(sce, dimred="PCAsub")
plotTSNE(sce, colour_by="label", text_by="label")
```

The input of `HGC.dendrogram`

is the graph saved as `igraph`

object, and the output is the tree saved as `hclust`

object.
The document of `HGC.dendrogram`

contains more details.

With various published methods in R, results of `HGC`

can be visualized easily.
Here we use the R package `dendextend`

as an example to visualize the results
on the Pollen dataset. The tree has been cut into five clusters. And for a
better visualization, the height of the tree has been log-transformed.

```
Pollen.ClusteringTree$height = log(Pollen.ClusteringTree$height + 1)
Pollen.ClusteringTree$height = log(Pollen.ClusteringTree$height + 1)
HGC.PlotDendrogram(tree = Pollen.ClusteringTree,
k = 5, plot.label = FALSE)
```

`## [1] 1`

We can also add a colour bar of the known label under the dendrogram as a comparison of the achieved clustering results.

```
Pollen.labels <- data.frame(Tissue = Pollen.Label.Tissue,
CellLine = Pollen.Label.CellLine)
HGC.PlotDendrogram(tree = Pollen.ClusteringTree,
k = 5, plot.label = TRUE,
labels = Pollen.labels)
```

`## [1] 1`

For datasets with known labels, the clustering results of `HGC`

can be
evaluated by comparing the consistence between the known labels and the
achieved clusters. Adjusted Rand Index (ARI) is a wildly used statistics
for this purpose. Here we calculate the ARIs of the clustering results at
different levels of the dendrogram with the two known labels.

```
ARI.mat <- HGC.PlotARIs(tree = Pollen.ClusteringTree,
labels = Pollen.labels)
```

Our work shows that the dendrogram construction in `HGC`

has a linear time
complexity. For advanced users, `HGC`

provides functions to conduct time
complexity analysis on their own data. The construction of the dendrogram
is a recursive procedure of two steps: 1. find the nearest neighbour pair,
2. merge the node pair and update the graph. For different data structures of
graph, there’s a trade-off between the time consumptions of the two steps.
Generally speaking, storing more information about the graph makes it faster
to find the nearest neighbour pair (step 1) but slower to update the graph
(step 2). We have experimented several datasets and chosen the best data
structure for the overall efficiency.

The key parameters related to the time consumptions of the two steps are the
length of the nearest neighbor chains and the number of nodes needed to be
updated in each iteration, respectively (for more details, please refer to
our preprint).`HGC`

provides
functions to record and visualize these parameters.

```
Pollen.ParameterRecord <- HGC.parameter(G = Pollen.SNN)
HGC.PlotParameter(Pollen.ParameterRecord, parameter = "CL")
```

`## [1] 1`

`HGC.PlotParameter(Pollen.ParameterRecord, parameter = "ANN")`

`## [1] 1`