geom_interpolation: Render interpolation of new rows from columns (or vice-versa)
In corybrunson/ordr: A Tidyverse Extension for Ordinations and Biplots

geom_interpolation

R Documentation

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

Description

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
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)

# 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)

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