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.

```
suppressPackageStartupMessages({
library(scater)
library(scran)
library(cowplot)
library(ggplot2)
library(rafalib)
library(pheatmap)
library(igraph)
})
<- readRDS("data/results/covid_qc_dr_int.rds") sce
```

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

Build a kNN graph from the data

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

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

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
<- buildKNNGraph(sce, k = 30, use.dimred = "MNN")
g reducedDim(sce, "KNN") <- igraph::as_adjacency_matrix(g)
# These 2 lines are the most recommended
<- buildSNNGraph(sce, k = 30, use.dimred = "MNN")
g 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)
```

```
# or the SNN graph
pheatmap(reducedDim(sce, "SNN")[1:200, 1:200], col = colorRampPalette(c("white",
"yellow", "red", "black"))(20), border_color = "grey90", legend = T, cluster_rows = F,
cluster_cols = F, fontsize = 2)
```

As you can see, the way Scran computes the SNN graph is different to Seurat. It gives edges to all cells that shares a neighbor, but weights the edges by how similar the neighbors are. Hence, the SNN graph has more edges than the KNN graph.

Once the graph is built, we can now perform graph clustering. The clustering is done respective to a resolution which can be interpreted as how coarse you want your cluster to be. Higher resolution means higher number of clusters.

```
<- buildSNNGraph(sce, k = 5, use.dimred = "MNN")
g $louvain_SNNk5 <- factor(cluster_louvain(g)$membership)
sce
<- buildSNNGraph(sce, k = 10, use.dimred = "MNN")
g $louvain_SNNk10 <- factor(cluster_louvain(g)$membership)
sce
<- buildSNNGraph(sce, k = 15, use.dimred = "MNN")
g $louvain_SNNk15 <- factor(cluster_louvain(g)$membership)
sce
plot_grid(ncol = 3, plotReducedDim(sce, dimred = "UMAP_on_MNN", colour_by = "louvain_SNNk5") +
::ggtitle(label = "louvain_SNNk5"), plotReducedDim(sce, dimred = "UMAP_on_MNN",
ggplot2colour_by = "louvain_SNNk10") + ggplot2::ggtitle(label = "louvain_SNNk10"), plotReducedDim(sce,
dimred = "UMAP_on_MNN", colour_by = "louvain_SNNk15") + ggplot2::ggtitle(label = "louvain_SNNk15"))
```

We can now use the `clustree`

package to visualize how
cells are distributed between clusters depending on resolution.

```
suppressPackageStartupMessages(library(clustree))
clustree(sce, prefix = "louvain_SNNk")
```