Author: Mirek Kratochvil
Date: 2026-03-08

# EmbedSOM basic embedding

#### Mirek Kratochvil

#### 2026-03-08

# Basic embedding with EmbedSOM

## Dataset

We will embed a small dataset created from gaussian clusters positioned in vertices of a 5-dimensional hypercube.

    #create the seed dataset
    n <- 1024
    data <- matrix(c(rep(0,n),rep(1,n)),ncol=1)

    #add dimensions
    for(i in 2:5) data <- cbind(c(rep(0,dim(data)[1]), rep(1, dim(data)[1])),rbind(data,data))

    #scatter the points to clusters
    set.seed(1)
    data <- data + 0.2*rnorm(dim(data)[1]*dim(data)[2])
    colnames(data) <- paste0('V',1:5)

This looks relatively nicely from the side (each corner in fact hides 8 separate clusters):

    plot(data, pch=19, col=rgb(0,0,0,0.2))

Linear dimensionality reduction doesn’t help much with seeing all 32 clusters:

    plot(data.frame(prcomp(data)$x), pch='.', col=rgb(0,0,0,0.2))

Let’s use the non-linear EmbedSOM instead.

## Getting the SOM ready

EmbedSOM works on a self-organizing map that you need to create first:

    set.seed(1)
    map <- EmbedSOM::SOM(data, xdim=24, ydim=24)

EmbedSOM provides some level of compatibility with FlowSOM that can be used to simplify some commands. FlowSOM-originating maps and whole FlowSOM object may be used as well:

    fs <- FlowSOM::ReadInput(as.matrix(data.frame(data)))
    fs <- FlowSOM::BuildSOM(fsom=fs, xdim=24, ydim=24)

\(24\times24\) is the recommended SOM size for getting something interesting from EmbedSOM – it provides a good amount of detail, and still runs quite quickly.

## Embedding

When the SOM is ready, a matrix of 2-dimensional coordinates is obtained using the `EmbedSOM` function:

    e <- EmbedSOM::EmbedSOM(data=data, map=map)

Alternatively, FlowSOM objects are supported to be used instead of `data` and `map` parameters in most EmbedSOM commands:

    e <- EmbedSOM::EmbedSOM(fsom=fs)

Several extra parameters may be specified; e.g. the following code makes the embedding a bit smoother and faster (but not necessarily better). See the EmbedSOM paper for details on parameters.

    e <- EmbedSOM::EmbedSOM(data=data, map=map, smooth=2, k=10)

Finally, `e` now contains the dimensionality-reduced 2D coordinates of the original data that can be used for plotting.

    head(e)

    ##      EmbedSOM1 EmbedSOM2
    ## [1,]  23.47801  13.42236
    ## [2,]  22.86703  12.98544
    ## [3,]  23.63919  14.31299
    ## [4,]  21.65178  12.51104
    ## [5,]  22.58825  13.94369
    ## [6,]  23.12144  13.64124

## Plotting the data

The embedding can be plotted using the standard graphics function, nicely showing all clusters next to each other.

    plot(e, pch=19, cex=.5, col=rgb(0,0,0,0.2))

EmbedSOM provides specialized plotting function which is useful in many common use cases; for example for displaying density:

    EmbedSOM::PlotEmbed(e, pch=19, cex=.5, nbin=100)

Or for seeing colored expression of a single marker (`value=1` specifies a column number; column names can be used as well):

    EmbedSOM::PlotEmbed(e, data=data, pch=19, cex=.5, alpha=0.3, value=1)

(Notice that it is necessary to pass in the original data frame. When working with FlowSOM, the same can be done using `fsom=fs`.)

Or multiple markers:

    EmbedSOM::PlotEmbed(e, data=data, pch=19, cex=.5, alpha=0.3, red=2, green=4)

Or perhaps for coloring the clusters. The following example uses the FlowSOM-style clustering to find the original 32 clusters in the scattered data. If that works right, each cluster should have its own color. (See FlowSOM documentation on how the meta-clustering works.)

    n_clusters <- 32
    hcl <- hclust(dist(map$codes))
    metaclusters <- cutree(hcl,n_clusters)[map$mapping[,1]]

    EmbedSOM::PlotEmbed(e, pch=19, cex=.5, clust=metaclusters, alpha=.3)

Custom colors are also supported (this is colored according to the dendrogram order):

    colors <- topo.colors(24*24, alpha=.3)[Matrix::invPerm(hcl$order)[map$mapping[,1]]]

    EmbedSOM::PlotEmbed(e, pch=19, cex=.5, col=colors)

`ggplot2` interoperability is provided using function `PlotGG`:

    EmbedSOM::PlotGG(e, data=data) + ggplot2::geom_hex(bins=80)

    ## Warning: Computation failed in `stat_binhex()`.
    ## Caused by error in `compute_group()`:
    ## ! The package "hexbin" is required for `stat_bin_hex()`.

(You may also get the ggplot-compatible data object using `PlotData` function.)