tidy.prcomp: Tidy a(n) prcomp object

Description

Tidy summarizes information about the components of a model. A model component might be a single term in a regression, a single hypothesis, a cluster, or a class. Exactly what tidy considers to be a model component varies across models but is usually self-evident. If a model has several distinct types of components, you will need to specify which components to return.

Usage

# S3 method for prcomp
tidy(x, matrix = "u", ...)

Value

A tibble::tibble with columns depending on the component of PCA being tidied.

If matrix is "u", "samples", "scores", or "x" each row in the tidied output corresponds to the original data in PCA space. The columns are:

row: ID of the original observation (i.e. rowname from original data).
PC: Integer indicating a principal component.
value: The score of the observation for that particular principal component. That is, the location of the observation in PCA space.

If matrix is "v", "rotation", "loadings" or "variables", each row in the tidied output corresponds to information about the principle components in the original space. The columns are:

row: The variable labels (colnames) of the data set on which PCA was performed.
PC: An integer vector indicating the principal component.
value: The value of the eigenvector (axis score) on the indicated principal component.

If matrix is "d", "eigenvalues" or "pcs", the columns are:

PC: An integer vector indicating the principal component.
std.dev: Standard deviation explained by this PC.
percent: Fraction of variation explained by this component (a numeric value between 0 and 1).
cumulative: Cumulative fraction of variation explained by principle components up to this component (a numeric value between 0 and 1).

Arguments

x

A prcomp object returned by stats::prcomp().

matrix

Character specifying which component of the PCA should be tidied.

"u", "samples", "scores", or "x": returns information about the map from the original space into principle components space.
"v", "rotation", "loadings" or "variables": returns information about the map from principle components space back into the original space.
"d", "eigenvalues" or "pcs": returns information about the eigenvalues.

...

Additional arguments. Not used. Needed to match generic signature only. Cautionary note: Misspelled arguments will be absorbed in ..., where they will be ignored. If the misspelled argument has a default value, the default value will be used. For example, if you pass conf.lvel = 0.9, all computation will proceed using conf.level = 0.95. Two exceptions here are:

tidy() methods will warn when supplied an exponentiate argument if it will be ignored.
augment() methods will warn when supplied a newdata argument if it will be ignored.

Details

See https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca for information on how to interpret the various tidied matrices. Note that SVD is only equivalent to PCA on centered data.

Examples

Run this code

if (FALSE) { # rlang::is_installed("maps")

pc <- prcomp(USArrests, scale = TRUE)

# information about rotation
tidy(pc)

# information about samples (states)
tidy(pc, "samples")

# information about PCs
tidy(pc, "pcs")

# state map
library(dplyr)
library(ggplot2)
library(maps)

pc %>%
  tidy(matrix = "samples") %>%
  mutate(region = tolower(row)) %>%
  inner_join(map_data("state"), by = "region") %>%
  ggplot(aes(long, lat, group = group, fill = value)) +
  geom_polygon() +
  facet_wrap(~PC) +
  theme_void() +
  ggtitle("Principal components of arrest data")

au <- augment(pc, data = USArrests)

au

ggplot(au, aes(.fittedPC1, .fittedPC2)) +
  geom_point() +
  geom_text(aes(label = .rownames), vjust = 1, hjust = 1)
}