Tidy a(n) svd object masquerading as list

Broom tidies a number of lists that are effectively S3 objects without a class attribute. For example, stats::optim(), svd() and interp::interp() produce consistent output, but because they do not have a class attribute, they cannot be handled by S3 dispatch.

These functions look at the elements of a list and determine if there is an appropriate tidying method to apply to the list. Those tidiers are implemented as functions of the form tidy_<function> or glance_<function> and are not exported (but they are documented!).

If no appropriate tidying method is found, they throw an error.

Usage

tidy_svd(x, matrix = "u", ...)

Arguments

x

A list with components u, d, v returned by base::svd().

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.

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).

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


library(modeldata)
data(hpc_data)

mat <- scale(as.matrix(hpc_data[, 2:5]))
s <- svd(mat)

tidy_u <- tidy(s, matrix = "u")
tidy_u
#> # A tibble: 17,324 × 3
#>      row    PC    value
#>    <int> <dbl>    <dbl>
#>  1     1     1  0.00403
#>  2     2     1 -0.00436
#>  3     3     1 -0.00196
#>  4     4     1 -0.00444
#>  5     5     1 -0.00437
#>  6     6     1 -0.00437
#>  7     7     1 -0.00431
#>  8     8     1 -0.00436
#>  9     9     1 -0.00434
#> 10    10     1 -0.00440
#> # ℹ 17,314 more rows

tidy_d <- tidy(s, matrix = "d")
tidy_d
#> # A tibble: 4 × 4
#>      PC std.dev percent cumulative
#>   <int>   <dbl>   <dbl>      <dbl>
#> 1     1    69.5   0.279      0.279
#> 2     2    67.0   0.259      0.538
#> 3     3    63.9   0.235      0.774
#> 4     4    62.6   0.226      1    

tidy_v <- tidy(s, matrix = "v")
tidy_v
#> # A tibble: 16 × 3
#>    column    PC   value
#>     <int> <dbl>   <dbl>
#>  1      1     1  0.657 
#>  2      2     1  0.409 
#>  3      3     1 -0.577 
#>  4      4     1  0.262 
#>  5      1     2 -0.0142
#>  6      2     2 -0.650 
#>  7      3     2 -0.137 
#>  8      4     2  0.747 
#>  9      1     3 -0.302 
#> 10      2     3 -0.332 
#> 11      3     3 -0.779 
#> 12      4     3 -0.438 
#> 13      1     4 -0.690 
#> 14      2     4  0.548 
#> 15      3     4 -0.205 
#> 16      4     4  0.426 

library(ggplot2)
library(dplyr)

ggplot(tidy_d, aes(PC, percent)) +
  geom_point() +
  ylab("% of variance explained")


tidy_u %>%
  mutate(class = hpc_data$class[row]) %>%
  ggplot(aes(class, value)) +
  geom_boxplot() +
  facet_wrap(~PC, scale = "free_y")