Add minimum spanning tree to plot, colouring by stress

To identify strain in a multidimensional scaling of distances, it can be useful to plot a minimum spanning tree (Gower 1966; Smith 2022) . Colouring each edge of the tree according to its strain can identify areas where the mapping is stretched or compressed.

MSTSegments(mapping, mstEnds, ...)

StrainCol(
  distances,
  mapping,
  mstEnds = MSTEdges(distances),
  palette = rev(hcl.colors(256L, "RdYlBu"))
)

Arguments

mapping

Two-column matrix giving x and y coordinates of plotted points.

mstEnds

Two-column matrix identifying rows of mapping at end of each edge of the MST, as output by TreeTools::MSTEdges().

...

Additional arguments to segments().

distances

Matrix or dist object giving original distances between each pair of points.

palette

Vector of colours with which to colour edges.

Value

StrainCol() returns a vector in which each entry is selected from palette, with an attribute logStrain denoting the logarithm of the mapped over original distance, shifted such that the median value is zero. Palette colours are assigned centred on the median value, with entries early in palette assigned to edges in which the ratio of mapped distance to original distance is small.

References

Gower JC (1966). “Some distance properties of latent root and vector methods used in multivariate analysis.” Biometrika, 53(3/4), 325--338. doi:10.2307/2333639 .

Smith MR (2022). “Robust analysis of phylogenetic tree space.” Systematic Biology, 71(5), 1255--1270. doi:10.1093/sysbio/syab100 .

See also

Other tree space functions: MapTrees(), MappingQuality(), SpectralEigens(), cluster-statistics, median.multiPhylo()

Author

Martin R. Smith (martin.smith@durham.ac.uk)

Examples

set.seed(0)
library("TreeTools", quietly = TRUE)
distances <- ClusteringInfoDist(as.phylo(5:16, 8))
mapping <- cmdscale(distances, k = 2)
mstEnds <- MSTEdges(distances)

# Set up blank plot
plot(mapping, asp = 1, frame.plot = FALSE, ann = FALSE, axes = FALSE,
     type = "n")
# Add MST
MSTSegments(mapping, mstEnds, 
            col = StrainCol(distances, mapping, mstEnds))
# Add points at end so they overprint the MST
points(mapping)
PlotTools::SpectrumLegend(
 "bottomleft",
 legend = c("Extended", "Median", "Contracted"),
 bty = "n",     # No box
 y.intersp = 2, # Expand in Y direction
 palette = hcl.colors(256L, "RdYlBu", rev = TRUE)
)