# Evaluating single-cell clustering with ClustAssess

In this vignette we will illustrate several of the tools available in ClustAssess on a small single-cell RNA-seq dataset.

    library(Seurat)
    #> Attaching SeuratObject
    library(ClustAssess)

    # we will use the pbmc_small single-cell RNA-seq dataset available via Seurat
    DimPlot(pbmc_small, group.by='letter.idents')

## Proportion of ambiguously clustered pairs

The proportion of ambiguously clustered pairs (PAC) uses consensus clustering to infer the optimal number of clusters for the data, by observing how variably pairs of elements cluster together. The lower the PAC, the more stable the clustering. PAC was originally presented in https://doi.org/10.1038/srep06207.

    # retrieve scaled data for PAC calculation
    pbmc.data = GetAssayData(pbmc_small, assay='RNA', slot='scale.data')

    # perform consensus clustering
    cc.res = consensus_cluster(t(pbmc.data),
                               k_max=30,
                               n_reps=100,
                               p_sample=0.8,
                               p_feature=0.8,
                               verbose=TRUE)
    #> Calculating consensus clustering

    # assess the PAC convergence for a few values of k - each curve should
    # have converged to some value
    k.plot = c(4,6,8,10)
    pac_convergence(cc.res, k.plot)

    # visualize the final PAC across k - there seems to be a local maximum at k=7,
    # indicating that 7 clusters leads to a less stable clustering of the data than
    # nearby values of k
    pac_landscape(cc.res)

## Element-centric clustering comparison

We compare the similarity of clustering results between methods (in this case, between Louvain community detection and k-means) using element-centric similarity, which quantifies the clustering similarity per cell. Higher ECS indicates that an observation is clustered similarly across methods. ECS was introduced in https://doi.org/10.1038/s41598-019-44892-y.

    # first, cluster with Louvain algorithm
    pbmc_small = FindClusters(pbmc_small, resolution=0.8, verbose=FALSE)
    DimPlot(pbmc_small, group.by='seurat_clusters')

    # also cluster with PCA+k-means
    pbmc_pca = Embeddings(pbmc_small, 'pca')
    pbmc_small@meta.data$kmeans_clusters = kmeans(pbmc_pca,
                                                  centers=3,
                                                  nstart=10,
                                                  iter.max=1e3)$cluster
    DimPlot(pbmc_small, group.by='kmeans_clusters')

    # where are the clustering results more similar?
    pbmc_small@meta.data$ecs = element_sim_elscore(pbmc_small@meta.data$seurat_clusters,
                                                   pbmc_small@meta.data$kmeans_clusters)
    FeaturePlot(pbmc_small, 'ecs')

    mean(pbmc_small@meta.data$ecs)
    #> [1] 0.6632927

## Jaccard similarity of cluster markers

As a common step in computational single-cell RNA-seq analyses, discriminative marker genes are identified for each cluster. These markers are then used to infer the cell type of the respective cluster. Here, we compare the markers obtained for each clustering method to ask: how similarly would each cell be interpreted across clustering methods? We compare the markers per cell using the Jaccard similarity (defined as the size of the intersect divided by the size of the overlap) of the marker gene lists. The higher the JSI, the more similar are the marker genes for that cell.

    # first, we calculate the markers on the Louvain clustering
    Idents(pbmc_small) = pbmc_small@meta.data$seurat_clusters
    louvain.markers = FindAllMarkers(pbmc_small,
                                     logfc.threshold=1,
                                     min.pct=0.0,
                                     test.use='roc',
                                     verbose=FALSE)

    # then we get the markers on the k-means clustering
    Idents(pbmc_small) = pbmc_small@meta.data$kmeans_clusters
    kmeans.markers = FindAllMarkers(pbmc_small,
                                    logfc.threshold=1,
                                    min.pct=0.0,
                                    test.use='roc',
                                    verbose=FALSE)

    # next, compare the top 10 markers per cell
    pbmc_small@meta.data$marker.gene.jsi = marker_overlap(louvain.markers,
                                              kmeans.markers,
                                              pbmc_small@meta.data$seurat_clusters,
                                              pbmc_small@meta.data$kmeans_clusters,
                                              n=10,
                                              rank_by='power')
    #> Warning: Unknown or uninitialised column: `avg_logFC`.

    #> Warning: Unknown or uninitialised column: `avg_logFC`.

    # which cells have the same markers, regardless of clustering?
    FeaturePlot(pbmc_small, 'marker.gene.jsi')

    mean(pbmc_small@meta.data$marker.gene.jsi)
    #> [1] 0.6352273

## Element-wise consistency

How consistently are cells clustered by k-means? We will rerun k-means clustering 20 times to investigate.

    clustering.list = list()
    n.reps = 20
    for (i in 1:n.reps){
      # we set nstart=1 and a fairly high iter.max - this should mean that
      # the algorithm converges, and that the variability in final clusterings
      # depends mainly on the random initial cluster assignments
      km.res = kmeans(pbmc_pca, centers=3, nstart=1, iter.max=1e3)$cluster
      clustering.list[[i]] = km.res
    }

    # now, we calculate the element-wise consistency (aka frustration), which
    # performs pair-wise comparisons between all 20 clusterings; the
    # consistency is the average per-cell ECS across all comparisons. The higher
    # the consistency, the more consistently is that cell clustered across
    # random seeds.
    pbmc_small@meta.data$consistency = element_consistency(clustering.list)

    # which cells are clustered more consistently?
    FeaturePlot(pbmc_small, 'consistency')

    mean(pbmc_small@meta.data$consistency)
    #> [1] 0.6712922

## Session info

    sessionInfo()
    #> R version 4.0.3 (2020-10-10)
    #> Platform: x86_64-pc-linux-gnu (64-bit)
    #> Running under: Debian GNU/Linux 10 (buster)
    #>
    #> Matrix products: default
    #> BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.8.0
    #> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.8.0
    #>
    #> locale:
    #>  [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C
    #>  [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=C
    #>  [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8
    #>  [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C
    #>  [9] LC_ADDRESS=C               LC_TELEPHONE=C
    #> [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
    #>
    #> attached base packages:
    #> [1] stats     graphics  grDevices utils     datasets  methods   base
    #>
    #> other attached packages:
    #> [1] ClustAssess_0.3.0  SeuratObject_4.0.4 Seurat_4.1.0
    #>
    #> loaded via a namespace (and not attached):
    #>   [1] Rtsne_0.15            colorspace_2.0-2      deldir_1.0-6
    #>   [4] ellipsis_0.3.2        ggridges_0.5.3        spatstat.data_2.1-2
    #>   [7] farver_2.1.0          leiden_0.3.9          listenv_0.8.0
    #>  [10] ggrepel_0.9.1         fansi_1.0.0           codetools_0.2-18
    #>  [13] splines_4.0.3         knitr_1.37            polyclip_1.10-0
    #>  [16] jsonlite_1.7.2        ica_1.0-2             cluster_2.1.2
    #>  [19] png_0.1-7             uwot_0.1.11           shiny_1.7.1
    #>  [22] sctransform_0.3.3     spatstat.sparse_2.1-0 compiler_4.0.3
    #>  [25] httr_1.4.2            assertthat_0.2.1      Matrix_1.4-0
    #>  [28] fastmap_1.1.0         lazyeval_0.2.2        later_1.3.0
    #>  [31] prettyunits_1.1.1     htmltools_0.5.2       tools_4.0.3
    #>  [34] igraph_1.2.11         gtable_0.3.0          glue_1.6.0
    #>  [37] RANN_2.6.1            reshape2_1.4.4        dplyr_1.0.7
    #>  [40] Rcpp_1.0.8            scattermore_0.7       jquerylib_0.1.4
    #>  [43] vctrs_0.3.8           nlme_3.1-155          iterators_1.0.13
    #>  [46] lmtest_0.9-39         fastcluster_1.2.3     xfun_0.29
    #>  [49] stringr_1.4.0         globals_0.14.0        mime_0.12
    #>  [52] miniUI_0.1.1.1        lifecycle_1.0.1       irlba_2.3.5
    #>  [55] goftest_1.2-3         future_1.23.0         MASS_7.3-55
    #>  [58] zoo_1.8-9             scales_1.1.1          spatstat.core_2.3-2
    #>  [61] hms_1.1.1             promises_1.2.0.1      spatstat.utils_2.3-0
    #>  [64] parallel_4.0.3        RColorBrewer_1.1-2    yaml_2.2.1
    #>  [67] reticulate_1.22       pbapply_1.5-0         gridExtra_2.3
    #>  [70] ggplot2_3.3.5         sass_0.4.0            rpart_4.1-15
    #>  [73] stringi_1.7.6         highr_0.9             foreach_1.5.1
    #>  [76] rlang_0.4.12          pkgconfig_2.0.3       matrixStats_0.61.0
    #>  [79] evaluate_0.14         lattice_0.20-45       ROCR_1.0-11
    #>  [82] purrr_0.3.4           tensor_1.5            labeling_0.4.2
    #>  [85] patchwork_1.1.1       htmlwidgets_1.5.4     cowplot_1.1.1
    #>  [88] tidyselect_1.1.1      parallelly_1.30.0     RcppAnnoy_0.0.19
    #>  [91] plyr_1.8.6            magrittr_2.0.1        R6_2.5.1
    #>  [94] generics_0.1.1        DBI_1.1.2             pillar_1.6.4
    #>  [97] mgcv_1.8-38           fitdistrplus_1.1-6    survival_3.2-13
    #> [100] abind_1.4-5           tibble_3.1.6          future.apply_1.8.1
    #> [103] crayon_1.4.2          KernSmooth_2.23-20    utf8_1.2.2
    #> [106] spatstat.geom_2.3-1   plotly_4.10.0         rmarkdown_2.11
    #> [109] progress_1.2.2        grid_4.0.3            data.table_1.14.2
    #> [112] digest_0.6.29         xtable_1.8-4          tidyr_1.1.4
    #> [115] httpuv_1.6.5          munsell_0.5.0         viridisLite_0.4.0
    #> [118] bslib_0.3.1