# HGC: fast hierarchical clustering for large-scale single-cell data
## Introduction
`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](https://doi.org/10.1101/2021.02.07.430106).
## Installation
`HGC` could be installed from Github.
```{r Github install, eval = FALSE}
if(!require(devtools))
install.packages("devtools")
devtools::install_github("XuegongLab/HGC")
```
## Quick Start
### Input data
`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`](https://satijalab.org/seurat/articles/get_started.html).
As a demo input, we stored the top 25 principal components of the
Pollen dataset ([Pollen et al.](https://www.nature.com/articles/nbt.2967))
in `HGC`. The dataset contains 301 cells with two known labels: labels at
the tissue level and the cell line level.
```{r, message=FALSE, warning=FALSE}
library(HGC)
data(Pollen)
Pollen.PCs <- Pollen[["PCs"]]
Pollen.Label.Tissue <- Pollen[["Tissue"]]
Pollen.Label.CellLine <- Pollen[["CellLine"]]
dim(Pollen.PCs)
table(Pollen.Label.Tissue)
table(Pollen.Label.CellLine)
```
### Run HGC
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.
```{r}
Pollen.SNN <- SNN.Construction(mat = Pollen.PCs, k = 25, threshold = 0.15)
Pollen.ClusteringTree <- HGC.dendrogram(G = Pollen.SNN)
```
The user could also give `HGC.dendrogram` an adjacency matrix directly, for instance, to read a matrix from `igraph` object and use it to run `HGC`.
```{r}
require(igraph)
g <- sample_gnp(10, 2/10)
G <- as_adjacency_matrix(g, sparse = TRUE)
G.ClusteringTree <- HGC.dendrogram(G = G)
```
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`.
```{r}
cluster.k5 <- cutree(Pollen.ClusteringTree, k = 5)
```
### Visualization
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.
```{r, fig.height = 4.5}
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)
```
We can also add a colour bar of the known label under the dendrogram as a
comparison of the achieved clustering results.
```{r, fig.height = 4.5}
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)
```
### Evaluation of the clustering results
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.
```{r}
ARI.mat <- HGC.PlotARIs(tree = Pollen.ClusteringTree,
labels = Pollen.labels)
```
## Time complexity analysis of HGC
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](https://doi.org/10.1101/2021.02.07.430106)).`HGC` provides
functions to record and visualize these parameters.
```{r}
Pollen.ParameterRecord <- HGC.parameter(G = Pollen.SNN)
HGC.PlotParameter(Pollen.ParameterRecord, parameter = "CL")
HGC.PlotParameter(Pollen.ParameterRecord, parameter = "ANN")
```
