# Combined or independent SuperCell runs for different samples

Comparing a combined (i.e., processing samples together) and an independent (i.e., processing samples separately) construction of metacells with SuperCell (related to @daskelly question https://github.com/GfellerLab/SuperCell/issues/11#issuecomment-1090916447).

    library(SuperCell)
    library(Matrix)
    data(cell_lines)

    GE <- cell_lines$GE
    cell.meta <- cell_lines$meta

    gamma <- 20 # graining level
    n.pc  <- 10 # number of PCs

To compare results, we use 2 samples that correspond to two different cancer cell lines (data from Tian et al., 2019)

    cell.idx.HCC827 <- which(cell.meta == "HCC827")
    cell.idx.H838   <- which(cell.meta == "H838")

## A combined analysis – construction of metacells processing two samples together

    SC.HCC827.H838 <- SCimplify(
      GE[,c(cell.idx.HCC827, cell.idx.H838)],  # log-normalized gene expression matrix
      gamma = gamma, # graining level
      cell.split.condition = cell.meta[c(cell.idx.HCC827, cell.idx.H838)], # metacell do not mix cells from different cell lines
      n.pc = n.pc) # number of proncipal components to use

    genes.use <- SC.HCC827.H838$genes.use

    SC.HCC827.H838$cell.line <- supercell_assign(cell.meta[c(cell.idx.HCC827, cell.idx.H838)],
                                                 supercell_membership = SC.HCC827.H838$membership)

    SC.GE.HCC827.H838 <- supercell_GE(GE[,c(cell.idx.HCC827, cell.idx.H838)], groups = SC.HCC827.H838$membership)

    SC.HCC827.H838$SC_PCA <- supercell_prcomp(
      Matrix::t(SC.GE.HCC827.H838),
      supercell_size = SC.HCC827.H838$supercell_size,
      genes.use = genes.use)

    SC.HCC827.H838$SC_UMAP <- supercell_UMAP(
      SC.HCC827.H838,
      n_neighbors = 10)

    supercell_plot_UMAP(
        SC.HCC827.H838,
        group = "cell.line",
        title = paste0("Combined construction of HCC827 and H838 metacells")
      )

## Independent analysis – construction of metacells for each sample independently (applying the same granularity `gamma` and the same set of features `genes.use`)

    SC.HCC827 <- SCimplify(GE[,cell.idx.HCC827],  # log-normalized gene expression matrix
                    gamma = gamma, # graining level
                    n.pc = n.pc, # number of proncipal components to use
                    genes.use = genes.use) # using the same set of genes as for the combined analysis

    SC.HCC827$cell.line <- supercell_assign(cell.meta[cell.idx.HCC827], supercell_membership = SC.HCC827$membership)

    SC.H838 <- SCimplify(GE[,cell.idx.H838],  # log-normalized gene expression matrix
                    gamma = gamma, # graining level
                    n.pc = n.pc, # number of proncipal components to use
                    genes.use = genes.use) # using the same set of genes as for the combined analysis
    SC.H838$cell.line <- supercell_assign(cell.meta[cell.idx.H838], supercell_membership = SC.H838$membership)

    SC.merged <- supercell_merge(list(SC.HCC827, SC.H838), fields = c("cell.line"))

    # compute metacell gene expression for SC.HCC827
    SC.GE.HCC827 <- supercell_GE(GE[, cell.idx.HCC827], groups = SC.HCC827$membership)
    # compute metacell gene expression for SC.H838
    SC.GE.H838 <- supercell_GE(GE[, cell.idx.H838], groups = SC.H838$membership)
    # merge GE matricies
    SC.GE.merged <- supercell_mergeGE(list(SC.GE.HCC827, SC.GE.H838))

    SC.merged$SC_PCA <- supercell_prcomp(
      Matrix::t(SC.GE.merged),
      supercell_size = SC.merged$supercell_size,
      genes.use = genes.use)

    SC.merged$SC_UMAP <- supercell_UMAP(
      SC.merged,
      n_neighbors = 10)

    g <- supercell_plot_UMAP(
        SC.merged,
        group = "cell.line",
        title = paste0("Independent construction of HCC827 and H838 metacells")
      )

## Combined and independent analyses do not result in the same metacell construction.

As the dimensionality reductions (even on the same set of features) are different for the combined (HCC827+H838) dataset and for the independent (HCC827 and H838 separately) datasets. The first PCA basen on global variability between two cell lines and the PCAs from the second approach represent local variability within each cell line. (sample).

    heatmap(as.matrix(table(SC.merged$membership, SC.HCC827.H838$membership)), scale = "none")

Metacell size distribution

    summary(SC.merged$supercell_size)
    summary(SC.HCC827.H838$supercell_size)

Also, in the combined analysis, the graining level does not mean that each cell line (or sample) will have this particular graining level. For instance, in the combined analysis, the graining level for HCC827 is `18.6` and for H838 is `21.8`, but this difference might be even more prominent if the heterogeneity and complexity of two samples are more different.

    ## Combined analysis
    # actual graining level for H838 cell line
    length(cell.idx.H838)/sum(SC.HCC827.H838$cell.line == "H838")
    # actual graining level for H838 cell line
    length(cell.idx.HCC827)/sum(SC.HCC827.H838$cell.line == "HCC827")

    ## Independent analysis
    # actual graining level for H838 cell line
    length(cell.idx.H838)/sum(SC.merged$cell.line == "H838")
    # actual graining level for HCC827 cell line
    length(cell.idx.HCC827)/sum(SC.merged$cell.line == "HCC827")
    # actual overall graining level in the combined analysis
    length(SC.merged$membership)/max(SC.merged$membership)