Calculate a minimum spanning tree among cases or variables

Source: R/stat-spantree.r

This stat layer identifies the \(n-1\) pairs among \(n\) points that form a minimum spanning tree, then calculates the segments between these poirs in the two dimensions x and y.

stat_spantree(
  mapping = NULL,
  data = NULL,
  geom = "segment",
  position = "identity",
  engine = "mlpack",
  method = "euclidean",
  show.legend = NA,
  inherit.aes = TRUE,
  ...
)

Arguments

mapping

Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.

data

The data to be displayed in this layer. There are three options:

If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot().

A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created.

A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).

geom

The geometric object to use to display the data, either as a ggproto Geom subclass or as a string naming the geom stripped of the geom_ prefix (e.g. "point" rather than "geom_point")

position

Position adjustment, either as a string naming the adjustment (e.g. "jitter" to use position_jitter), or the result of a call to a position adjustment function. Use the latter if you need to change the settings of the adjustment.

engine

A single character string specifying the package implementation to use; "mlpack", "vegan", or "ade4".

method

Passed to stats::dist() if engine is "vegan" or "ade4", ignored if "mlpack".

show.legend

logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display.

inherit.aes

If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. borders().

...

Additional arguments passed to ggplot2::layer().

Value

A ggproto layer.

Details

A minimum spanning tree (MST) on the point cloud \(X\) is a minimal connected graph on \(X\) with the smallest possible sum of distances (or dissimilarities) between linked points. These layers call stats::dist() to calculate a distance/dissimilarity object and an engine from mlpack, vegan, or ade4 to calculate the MST. The result is formatted with position aesthetics readable by ggplot2::geom_segment().

An MST calculated on x and y reflects the distances among the points in \(X\) in the reduced-dimension plane of the biplot. In contrast, one calculated on the full set of coordinates reflects distances in higher-dimensional space. Plotting this high-dimensional MST on the 2-dimensional biplot provides a visual cue as to how faithfully two dimensions can encapsulate the "true" distances between points (Jolliffe, 2002).

Biplot layers

ggbiplot() uses ggplot2::fortify() internally to produce a single data frame with a .matrix column distinguishing the subjects ("rows") and variables ("cols"). The stat layers stat_rows() and stat_cols() simply filter the data frame to one of these two.

The geom layers geom_rows_*() and geom_cols_*() call the corresponding stat in order to render plot elements for the corresponding factor matrix. geom_dims_*() selects a default matrix based on common practice, e.g. points for rows and arrows for columns.

Ordination aesthetics

The convenience function ord_aes() can be used to incorporate all coordinates of the ordination model into a statistical transformation. It maps the coordinates to the custom aesthetics ..coord1, ..coord2, etc.

Some transformations, e.g. stat_center(), are commutative with projection to the 'x' and 'y' coordinates. If they detect aesthetics of the form ..coord[0-9]+, then ..coord1 and ..coord2 are converted to x and y while any remaining are ignored.

Other transformations, e.g. stat_spantree(), yield different results in a planar biplot when they are computer before or after projection. If such a stat layer detects these aesthetics, then the lot of them are used in the transformation.

In either case, the stat layer returns a data frame with position aesthetics x and y.

References

Jolliffe IT (2002) Principal Component Analysis, Second Edition. Springer Series in Statistics, ISSN 0172-7397. doi: 10.1007/b98835 https://link.springer.com/book/10.1007/b98835

See also

Other stat layers: stat_center(), stat_chull(), stat_cone(), stat_scale()

Examples

# \dontrun{
# classical multidimensional scaling of road distances between European cities
euro_mds <- ordinate(eurodist, cmdscale_ord, k = 11)

# biplot with minimal spanning tree based on full-dimensional distances
# (as implemented in {mlpack})
euro_mds %>%
  negate_ord("PCo2") %>%
  ggbiplot() +
  stat_cols_spantree(
    ord_aes(euro_mds), engine = "mlpack",
    alpha = .5, linetype = "dotted"
  ) +
  geom_cols_text(aes(label = name), size = 3) +
  ggtitle(
    "MDS biplot of road distances between European cities",
    "Dotted segments constitute the minimal spanning tree"
  )
#> Warning: Ignoring unknown aesthetics: ..coord1, ..coord2, ..coord3, ..coord4, ..coord5,
#> ..coord6, ..coord7, ..coord8, ..coord9, ..coord10, and ..coord11

# }