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.
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:
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.
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)
# 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.
Clustering on a 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.
g <- buildSNNGraph(sce, k = 5, use.dimred = "MNN")
sce$louvain_SNNk5 <- factor(cluster_louvain(g)$membership)
g <- buildSNNGraph(sce, k = 10, use.dimred = "MNN")
sce$louvain_SNNk10 <- factor(cluster_louvain(g)$membership)
g <- buildSNNGraph(sce, k = 15, use.dimred = "MNN")
sce$louvain_SNNk15 <- factor(cluster_louvain(g)$membership)
plot_grid(ncol = 3, plotReducedDim(sce, dimred = "UMAP_on_MNN", colour_by = "louvain_SNNk5") +
ggplot2::ggtitle(label = "louvain_SNNk5"), plotReducedDim(sce, dimred = "UMAP_on_MNN",
colour_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")
K-means clustering
K-means is a generic clustering algorithm that has been used in many application areas. In R, it can be applied via the kmeans function. Typically, it is applied to a reduced dimension representation of the expression data (most often PCA, because of the interpretability of the low-dimensional distances). We need to define the number of clusters in advance. Since the results depend on the initialization of the cluster centers, it is typically recommended to run K-means with multiple starting configurations (via the nstart argument).
sce$kmeans_5 <- factor(kmeans(x = reducedDim(sce, "MNN"), centers = 5)$cluster)
sce$kmeans_10 <- factor(kmeans(x = reducedDim(sce, "MNN"), centers = 10)$cluster)
sce$kmeans_15 <- factor(kmeans(x = reducedDim(sce, "MNN"), centers = 15)$cluster)
plot_grid(ncol = 3, plotReducedDim(sce, dimred = "UMAP_on_MNN", colour_by = "kmeans_5") +
ggplot2::ggtitle(label = "KMeans5"), plotReducedDim(sce, dimred = "UMAP_on_MNN",
colour_by = "kmeans_10") + ggplot2::ggtitle(label = "KMeans10"), plotReducedDim(sce,
dimred = "UMAP_on_MNN", colour_by = "kmeans_15") + ggplot2::ggtitle(label = "KMeans15"))
clustree(sce, prefix = "kmeans_")
Hierarchical clustering
Defining distance between cells
The base R stats package already contains a function
dist that calculates distances between all pairs of
samples. Since we want to compute distances between samples, rather than
among genes, we need to transpose the data before applying it to the
dist function. This can be done by simply adding the
transpose function t() to the data. The distance methods
available in dist are: “euclidean”, “maximum”, “manhattan”,
“canberra”, “binary” or “minkowski”.
d <- dist(reducedDim(sce, "MNN"), method = "euclidean")As you might have realized, correlation is not a method implemented
in the dist function. However, we can create our own
distances and transform them to a distance object. We can first compute
sample correlations using the cor function. As you already
know, correlation range from -1 to 1, where 1 indicates that two samples
are closest, -1 indicates that two samples are the furthest and 0 is
somewhat in between. This, however, creates a problem in defining
distances because a distance of 0 indicates that two samples are
closest, 1 indicates that two samples are the furthest and distance of
-1 is not meaningful. We thus need to transform the correlations to a
positive scale (a.k.a. adjacency):
\[adj = \frac{1- cor}{2}\]
Once we transformed the correlations to a 0-1 scale, we can simply
convert it to a distance object using as.dist function. The
transformation does not need to have a maximum of 1, but it is more
intuitive to have it at 1, rather than at any other number.
# Compute sample correlations
sample_cor <- cor(Matrix::t(reducedDim(sce, "MNN")))
# Transform the scale from correlations
sample_cor <- (1 - sample_cor)/2
# Convert it to a distance object
d2 <- as.dist(sample_cor)Clustering cells
After having calculated the distances between samples calculated, we
can now proceed with the hierarchical clustering per-se. We will use the
function hclust for this purpose, in which we can simply
run it with the distance objects created above. The methods available
are: “ward.D”, “ward.D2”, “single”, “complete”, “average”, “mcquitty”,
“median” or “centroid”. It is possible to plot the dendrogram for all
cells, but this is very time consuming and we will omit for this
tutorial.
# euclidean
h_euclidean <- hclust(d, method = "ward.D2")
# correlation
h_correlation <- hclust(d2, method = "ward.D2")Once your dendrogram is created, the next step is to define which
samples belong to a particular cluster. After identifying the
dendrogram, we can now literally cut the tree at a fixed threshold (with
cutree) at different levels to define the clusters. We can
either define the number of clusters or decide on a height. We can
simply try different clustering levels.
#euclidean distance
sce$hc_euclidean_5 <- factor( cutree(h_euclidean,k = 5) )
sce$hc_euclidean_10 <- factor( cutree(h_euclidean,k = 10) )
sce$hc_euclidean_15 <- factor( cutree(h_euclidean,k = 15) )
#correlation distance
sce$hc_corelation_5 <- factor( cutree(h_correlation,k = 5) )
sce$hc_corelation_10 <- factor( cutree(h_correlation,k = 10) )
sce$hc_corelation_15 <- factor( cutree(h_correlation,k = 15) )
plot_grid(ncol = 3,
plotReducedDim(sce,dimred = "UMAP_on_MNN",colour_by = "hc_euclidean_5")+
ggplot2::ggtitle(label ="HC_euclidean_5"),
plotReducedDim(sce,dimred = "UMAP_on_MNN",colour_by = "hc_euclidean_10")+
ggplot2::ggtitle(label ="HC_euclidean_10"),
plotReducedDim(sce,dimred = "UMAP_on_MNN",colour_by = "hc_euclidean_15")+
ggplot2::ggtitle(label ="HC_euclidean_15"),
plotReducedDim(sce,dimred = "UMAP_on_MNN",colour_by = "hc_corelation_5")+
ggplot2::ggtitle(label ="HC_correlation_5"),
plotReducedDim(sce,dimred = "UMAP_on_MNN",colour_by = "hc_corelation_10")+
ggplot2::ggtitle(label ="HC_correlation_10"),
plotReducedDim(sce,dimred = "UMAP_on_MNN",colour_by = "hc_corelation_15")+
ggplot2::ggtitle(label ="HC_correlation_15")
)
Finally, lets save the integrated data for further analysis.
saveRDS(sce, "data/results/covid_qc_dr_int_cl.rds")Your turn
By now you should know how to plot different features onto your data. Take the QC metrics that were calculated in the first exercise, that should be stored in your data object, and plot it as violin plots per cluster using the clustering method of your choice. For example, plot number of UMIS, detected genes, percent mitochondrial reads.
Then, check carefully if there is any bias in how your data is separated due to quality metrics. Could it be explained biologically, or could you have technical bias there?
Session Info
sessionInfo()## R version 4.1.3 (2022-03-10)
## Platform: x86_64-apple-darwin13.4.0 (64-bit)
## Running under: macOS Big Sur/Monterey 10.16
##
## Matrix products: default
## BLAS/LAPACK: /Users/asabjor/miniconda3/envs/scRNAseq2023/lib/libopenblasp-r0.3.21.dylib
##
## locale:
## [1] C/UTF-8/C/C/C/C
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] clustree_0.5.0 ggraph_2.1.0
## [3] igraph_1.3.5 pheatmap_1.0.12
## [5] rafalib_1.0.0 cowplot_1.1.1
## [7] scran_1.22.1 scater_1.22.0
## [9] ggplot2_3.4.0 scuttle_1.4.0
## [11] SingleCellExperiment_1.16.0 SummarizedExperiment_1.24.0
## [13] Biobase_2.54.0 GenomicRanges_1.46.1
## [15] GenomeInfoDb_1.30.1 IRanges_2.28.0
## [17] S4Vectors_0.32.4 BiocGenerics_0.40.0
## [19] MatrixGenerics_1.6.0 matrixStats_0.63.0
## [21] RJSONIO_1.3-1.7 optparse_1.7.3
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