Render interpolation of new rows from columns (or vice-versa)

geom_interpolation() renders a geometric construction that interpolates a new data matrix (row or column) element from its entries to its artificial coordinates.

Usage

geom_interpolation(
  mapping = NULL,
  data = NULL,
  stat = "identity",
  position = "identity",
  new_data = NULL,
  type = c("centroid", "sequence"),
  arrow = default_arrow,
  ...,
  point.fill = NA,
  na.rm = FALSE,
  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)).

stat

The statistical transformation to use on the data for this layer. When using a geom_*() function to construct a layer, the stat argument can be used the override the default coupling between geoms and stats. The stat argument accepts the following:

A Stat ggproto subclass, for example StatCount.
A string naming the stat. To give the stat as a string, strip the function name of the stat_ prefix. For example, to use stat_count(), give the stat as "count".
For more information and other ways to specify the stat, see the layer stat 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.

new_data

A list (best structured as a data.frame) of row (geom_cols_interpolation()) or column (geom_rows_interpolation()) values to interpolate.

type

Character value matched to "centroid" or "sequence"; the type of operations used to visualize interpolation.

arrow

Specification for arrows, as created by grid::arrow(), or else NULL for no arrows.

...

Additional arguments passed to ggplot2::layer().

point.fill

Default aesthetics for markers. Set to NULL to inherit from the data's aesthetics.

na.rm

Passed to ggplot2::layer().

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().

Details

Interpolation answers the following question: Given a new data element that might have appeared as a row (respectively, column) in the singular-value-decomposed data matrix, where should we expect the marker for this element to appear in the biplot? The solution is the vector sum of the column (row) units weighted by their values in the new row (column). Gower, Gardner–Lubbe, & le Roux (2011) provide two visualizations of this calculation: a tail-to-head sequence of weighted units (type = "sequence"), and a centroid of the weighted units scaled by the number of units (type = "centroid").

WARNING: This layer is appropriate only with axes in standard coordinates (usually confer_inertia(p = "rows")) and interpolative calibration (ggbiplot(axis.type = "interpolative")).

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.

Aesthetics

geom_interpolation() requires the custom interpolate aesthetic, which tells the internals which columns of the new_data parameter contain the variables to be used for interpolation. Except in rare cases, new_data should contain the same rows or columns as the ordinated data and interpolate should be set to name (procured by augment_ord()). geom_interpolation() additionally understands the following aesthetics (required aesthetics are in bold):

alpha
colour
linetype
size
fill
shape
stroke
center, scale
group

References

Gower JC, Gardner–Lubbe S, & le Roux NJ (2011) Understanding Biplots. Wiley, ISBN: 978-0-470-01255-0. https://www.wiley.com/go/biplots

Examples

iris[, -5] %>%
  prcomp(scale = TRUE) %>%
  as_tbl_ord() %>%
  print() -> iris_pca
#> # A tbl_ord of class 'prcomp': (150 x 4) x (4 x 4)'
#> # 4 coordinates: PC1, PC2, ..., PC4
#> # 
#> # Rows (principal): [ 150 x 4 | 0 ]
#>     PC1    PC2     PC3 ... | 
#>                            | 
#> 1 -2.26 -0.478  0.127      | 
#> 2 -2.07  0.672  0.234      | 
#> 3 -2.36  0.341 -0.0441 ... | 
#> 4 -2.29  0.595 -0.0910     | 
#> 5 -2.38 -0.645 -0.0157     | 
#> # ℹ 145 more rows     | 
#> 
#> # 
#> # Columns (standard): [ 4 x 4 | 0 ]
#>      PC1     PC2    PC3 ... | 
#>                             | 
#> 1  0.521 -0.377   0.720     | 
#> 2 -0.269 -0.923  -0.244 ... | 
#> 3  0.580 -0.0245 -0.142     | 
#> 4  0.565 -0.0669 -0.634     | 
iris_pca <- mutate_rows(iris_pca, species = iris$Species)
iris_pca <- augment_ord(iris_pca)

# sample of one of each species, with some missing measurements
new_data <- iris[c(42, 61, 110), seq(5, 1), drop = FALSE]
new_data[3L, "Sepal.Width"] <- NA
new_data[1L, "Petal.Length"] <- NA
print(new_data)
#>        Species Petal.Width Petal.Length Sepal.Width Sepal.Length
#> 42      setosa         0.3           NA         2.3          4.5
#> 61  versicolor         1.0          3.5         2.0          5.0
#> 110  virginica         2.5          6.1          NA          7.2

# centroid interpolation method
iris_pca %>%
  augment_ord() %>%
  mutate_rows(obs = dplyr::row_number()) %>%
  mutate_cols(measure = name) %>%
  ggbiplot() +
  theme_bw() +
  scale_color_brewer(type = "qual", palette = 2) +
  geom_origin(marker = "cross", alpha = .5) +
  geom_cols_interpolation(
    aes(center = center, scale = scale, interpolate = name), size = 3,
    new_data = new_data, type = "centroid", alpha = .5
  ) +
  geom_rows_text(aes(label = obs, color = species), alpha = .5, size = 3)


# missing an entire variable
new_data$Petal.Length <- NULL

# sequence interpolation method
iris_pca %>%
  augment_ord() %>%
  mutate_rows(obs = dplyr::row_number()) %>%
  mutate_cols(measure = name) %>%
  ggbiplot() +
  theme_bw() +
  scale_color_brewer(type = "qual", palette = 2) +
  geom_origin(marker = "circle", alpha = .5) +
  geom_cols_interpolation(
    aes(center = center, scale = scale, interpolate = name,
        linetype = measure),
    new_data = new_data, type = "sequence", alpha = .5
  ) +
  geom_rows_text(aes(label = obs, color = species), alpha = .5, size = 3)