stat_spantree: Calculate a minimum spanning tree among cases or variables

In corybrunson/ordr: A Tidyverse Extension for Ordinations and Biplots

Calculate a minimum spanning tree among cases or variables

Description

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.

Usage

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 for this layer. When using a ⁠stat_*()⁠ function to construct a layer, the geom argument can be used to override the default coupling between stats and geoms. The geom argument accepts the following: A Geom ggproto subclass, for example GeomPoint. A string naming the geom. To give the geom as a string, strip the function name of the geom_ prefix. For example, to use geom_point(), give the geom as "point". For more information and other ways to specify the geom, see the layer geom documentation.
position	A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following: The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position. A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter". For more information and other ways to specify the position, see the layer position documentation.
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().

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).

Value

A ggproto layer.

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

This statistical transformation is compatible with the convenience function ord_aes().

Some transformations (e.g. stat_center()) commute with projection to the lower (1 or 2)-dimensional biplot space. 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 lower-dimensional biplot when they are computed before versus after projection. If the stat layer detects these aesthetics, then the transformation is performed before projection, and the results in the first two dimensions are returned as x and y.

A small number of transformations (stat_rule()) are incompatible with ordination aesthetics but will accept ord_aes() without warning.

Computed variables

These are calculated during the statistical transformation and can be accessed with delayed evaluation.

⁠xend,yend,x,y⁠

endpoints of tree branches (segments)

References

Jolliffe IT (2002) Principal Component Analysis, Second Edition. Springer Series in Statistics, ISSN 0172-7397. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/b98835")} https://link.springer.com/book/10.1007/b98835

See Also

Other stat layers: stat_bagplot(), stat_center(), stat_chull(), stat_cone(), stat_depth(), stat_projection(), stat_rule(), stat_scale()

Examples

UScitiesD |> 
  cmdscale() |> 
  as.data.frame() |> 
  tibble::rownames_to_column(var = "city") ->
  us_mds
ggplot(us_mds, aes(-V1, -V2, label = city)) +
  stat_spantree() +
  geom_label()

corybrunson/ordr documentation built on Feb. 24, 2025, 6:34 a.m.