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.

Installation

HGC could be installed from Github.

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. 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)
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.

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.

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.

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.

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.

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.

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).HGC provides functions to record and visualize these parameters.

Pollen.ParameterRecord <- HGC.parameter(G = Pollen.SNN)

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