Clustering

In this tutorial we will continue the analysis of the integrated dataset. We will use the integrated PCA to perform the clustering. First we will construct a \(k\)-nearest neighbour graph in order to perform a clustering on the graph. We will also show how to perform hierarchical clustering and k-means clustering on PCA space.

Let’s first load all necessary libraries and also the integrated dataset from the previous step.

if (!require(clustree)) {
    install.packages("clustree", dependencies = FALSE)
}
## Loading required package: clustree
## Loading required package: ggraph
## Loading required package: ggplot2
suppressPackageStartupMessages({
    library(scater)
    library(scran)
    library(cowplot)
    library(ggplot2)
    library(rafalib)
    library(pheatmap)
    library(igraph)
})

sce <- readRDS("data/results/covid_qc_dr_int.rds")

Graph clustering


The procedure of clustering on a Graph can be generalized as 3 main steps:

  1. Build a kNN graph from the data

  2. Prune spurious connections from kNN graph (optional step). This is a SNN graph.

  3. Find groups of cells that maximizes the connections within the group compared other groups.

Building kNN / SNN graph

The first step into graph clustering is to construct a k-nn graph, in case you don’t have one. For this, we will use the PCA space. Thus, as done for dimensionality reduction, we will use ony the top N PCA dimensions for this purpose (the same used for computing UMAP / tSNE).

# These 2 lines are for demonstration purposes only
g <- buildKNNGraph(sce, k = 30, use.dimred = "MNN")
reducedDim(sce, "KNN") <- igraph::as_adjacency_matrix(g)

# These 2 lines are the most recommended
g <- buildSNNGraph(sce, k = 30, use.dimred = "MNN")
reducedDim(sce, "SNN") <- as_adjacency_matrix(g, attr = "weight")

We can take a look at the kNN graph. It is a matrix where every connection between cells is represented as \(1\)s. This is called a unweighted graph (default in Seurat). Some cell connections can however have more importance than others, in that case the scale of the graph from \(0\) to a maximum distance. Usually, the smaller the distance, the closer two points are, and stronger is their connection. This is called a weighted graph. Both weighted and unweighted graphs are suitable for clustering, but clustering on unweighted graphs is faster for large datasets (> 100k cells).

# plot the KNN graph
pheatmap(reducedDim(sce, "KNN")[1:200, 1:200], col = c("white", "black"), border_color = "grey90", 
    legend = F, cluster_rows = F, cluster_cols = F, fontsize = 2)