Convex hulls and hull peelings

Source: R/stat-chull.r

Restrict planar data to the boundary points of its convex hull, or of nested convex hulls containing specified fractions of points.

stat_chull(
  mapping = NULL,
  data = NULL,
  geom = "polygon",
  position = "identity",
  show.legend = NA,
  inherit.aes = TRUE,
  ...
)

stat_peel(
  mapping = NULL,
  data = NULL,
  geom = "polygon",
  position = "identity",
  breaks = c(0.5),
  cut = c("above", "below"),
  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.

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().

breaks

A numeric vector of fractions (between 0 and 1) of the data to contain in each hull.

cut

Character; one of "above" and "below", indicating whether each hull should contain at least or at most breaks of the data, respectively.

Value

A ggproto layer.

Details

As used in a ggplot2 vignette, stat_chull() restricts a dataset with x and y variables to the points that lie on its convex hull.

Building on this, stat_peel() returns hulls from a convex hull peeling: a subset of sequentially removed hulls containing specified fractions of the data.

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.

hull

the position of breaks that defines each hull

frac

the value of breaks that defines each hull

prop

the actual proportion of data within each hull

References

Barnett V (1976) "The Ordering of Multivariate Data". Journal of the Royal Statistical Society: Series A (General), 139(3): 318–344. doi:10.2307/2344839

See also

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

Examples

# correspondence analysis of combined female and male hair and eye color data
HairEyeColor %>%
  rowSums(dims = 2L) %>%
  MASS::corresp(nf = 2L) %>%
  as_tbl_ord() %>%
  augment_ord() %>%
  print() -> hec_ca
#> # A tbl_ord of class 'correspondence': (4 x 2) x (4 x 2)'
#> # 2 coordinates: Can1 and Can2
#> # 
#> # Rows (standard): [ 4 x 2 | 1 ]
#>     Can1   Can2 |   name 
#>                 |   <chr>
#> 1 -1.10   1.44  | 1 Black
#> 2 -0.324 -0.219 | 2 Brown
#> 3 -0.283 -2.14  | 3 Red  
#> 4  1.83   0.467 | 4 Blond
#> # 
#> # Columns (standard): [ 4 x 2 | 1 ]
#>     Can1   Can2 |   name 
#>                 |   <chr>
#> 1 -1.08   0.592 | 1 Brown
#> 2  1.20   0.556 | 2 Blue 
#> 3 -0.465 -1.12  | 3 Hazel
#> 4  0.354 -2.27  | 4 Green
# inertia across artificial coordinates (all singular values < 1)
get_inertia(hec_ca)
#>       Can1       Can2 
#> 0.20877265 0.02222661 

# in row-principal biplot, row coordinates are weighted averages of columns
hec_ca %>%
  confer_inertia("rows") %>%
  ggbiplot(aes(color = .matrix, fill = .matrix, shape = .matrix)) +
  theme_bw() +
  stat_cols_chull(alpha = .1) +
  geom_cols_point() +
  geom_rows_point() +
  ggtitle("Row-principal CA of hair & eye color")

# in column-principal biplot, column coordinates are weighted averages of rows
hec_ca %>%
  confer_inertia("cols") %>%
  ggbiplot(aes(color = .matrix, fill = .matrix, shape = .matrix)) +
  theme_bw() +
  stat_rows_chull(alpha = .1) +
  geom_rows_point() +
  geom_cols_point() +
  ggtitle("Column-principal CA of hair & eye color")

judge_pca <- ordinate(USJudgeRatings, princomp)
ggbiplot(judge_pca, axis.type = "predictive") +
  geom_cols_axis() +
  geom_rows_point(elements = "score") +
  stat_rows_peel(
    aes(alpha = after_stat(hull)), color = "black", elements = "score",
    breaks = c(.9, .5, .1)
  )
#> Warning: Using alpha for a discrete variable is not advised.

ggbiplot(judge_pca, axis.type = "predictive") +
  geom_cols_axis() +
  geom_rows_point(elements = "score") +
  stat_rows_peel(
    aes(alpha = after_stat(hull)), color = "black", elements = "score",
    breaks = c(.9, .5, .1), cut = "below"
  )
#> Warning: Using alpha for a discrete variable is not advised.


iris_pca <- ordinate(iris, cols = 1:4, model = prcomp)
ggbiplot(iris_pca) +
  geom_rows_point(aes(color = Species), shape = "circle open") +
  stat_rows_peel(
    aes(fill = Species, alpha = after_stat(hull)),
    breaks = c(.9, .5, .1)
  )
#> Warning: Using alpha for a discrete variable is not advised.