How to build Principal Component Analysis (PCA) correlation circle from PCA object made with the package recipes?
Context: Tidymodels framework make use of a common grammar to build model. However, the FactoMineR and factoextra packages are not part of it. Instead, the package recipes is used.
Problem: in order to standardize my data analysis workflow, I try to use recipes and the tidymodels grammar to make an PCA. However, I cannot figure out how to get comparable outputs from the FactoMineR and the recipes approaches.
Question: How to build the correlation circle and other graphical representations, similar to FactoMineR::PCA() from an object made with recipes::step_pca()?
What I tried so far: I compared the PCA output form packages recipes, FactoMineR and stats, trying to identify "equivalent" information. However I do not understand how to make graphical representations equivalent to those made with FactoMineR, but using recipes + ggplot.
Here is some code to work with:
Using recipes:
# Using recipes ----
library(recipes)
rec_iris <- recipe(~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data = iris) %>%
step_normalize(all_numeric_predictors()) %>%
step_pca(all_predictors())
prep_rec <- prep(rec_iris)
bake(prep_rec, new_data = NULL)
#> # A tibble: 150 × 4
#> PC1 PC2 PC3 PC4
#> <dbl> <dbl> <dbl> <dbl>
#> 1 -2.26 -0.478 0.127 0.0241
#> 2 -2.07 0.672 0.234 0.103
#> 3 -2.36 0.341 -0.0441 0.0283
#> 4 -2.29 0.595 -0.0910 -0.0657
#> 5 -2.38 -0.645 -0.0157 -0.0358
#> 6 -2.07 -1.48 -0.0269 0.00659
#> 7 -2.44 -0.0475 -0.334 -0.0367
#> 8 -2.23 -0.222 0.0884 -0.0245
#> 9 -2.33 1.11 -0.145 -0.0268
#> 10 -2.18 0.467 0.253 -0.0398
#> # ℹ 140 more rows
# I can get useful information using:
prep_rec %>% tidy(2, type = "variance")
#> # A tibble: 16 × 4
#> terms value component id
#> <chr> <dbl> <int> <chr>
#> 1 variance 2.92 1 pca_OMBbk
#> 2 variance 0.914 2 pca_OMBbk
#> 3 variance 0.147 3 pca_OMBbk
#> 4 variance 0.0207 4 pca_OMBbk
#> 5 cumulative variance 2.92 1 pca_OMBbk
#> 6 cumulative variance 3.83 2 pca_OMBbk
#> 7 cumulative variance 3.98 3 pca_OMBbk
#> 8 cumulative variance 4 4 pca_OMBbk
#> 9 percent variance 73.0 1 pca_OMBbk
#> 10 percent variance 22.9 2 pca_OMBbk
#> 11 percent variance 3.67 3 pca_OMBbk
#> 12 percent variance 0.518 4 pca_OMBbk
#> 13 cumulative percent variance 73.0 1 pca_OMBbk
#> 14 cumulative percent variance 95.8 2 pca_OMBbk
#> 15 cumulative percent variance 99.5 3 pca_OMBbk
#> 16 cumulative percent variance 100 4 pca_OMBbk
prep_rec %>% tidy(2, type = "coef")
#> # A tibble: 16 × 4
#> terms value component id
#> <chr> <dbl> <chr> <chr>
#> 1 Sepal.Length 0.521 PC1 pca_OMBbk
#> 2 Sepal.Width -0.269 PC1 pca_OMBbk
#> 3 Petal.Length 0.580 PC1 pca_OMBbk
#> 4 Petal.Width 0.565 PC1 pca_OMBbk
#> 5 Sepal.Length -0.377 PC2 pca_OMBbk
#> 6 Sepal.Width -0.923 PC2 pca_OMBbk
#> 7 Petal.Length -0.0245 PC2 pca_OMBbk
#> 8 Petal.Width -0.0669 PC2 pca_OMBbk
#> 9 Sepal.Length 0.720 PC3 pca_OMBbk
#> 10 Sepal.Width -0.244 PC3 pca_OMBbk
#> 11 Petal.Length -0.142 PC3 pca_OMBbk
#> 12 Petal.Width -0.634 PC3 pca_OMBbk
#> 13 Sepal.Length 0.261 PC4 pca_OMBbk
#> 14 Sepal.Width -0.124 PC4 pca_OMBbk
#> 15 Petal.Length -0.801 PC4 pca_OMBbk
#> 16 Petal.Width 0.524 PC4 pca_OMBbk
Using FactoMineR:
# Using FactoMineR ----
library(FactoMineR)
pca_facto <- FactoMineR::PCA(iris[, 1:4])
Using stats
# Using stats ----
pca_stats <- stats::prcomp(~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data = iris, scale = TRUE, center = TRUE)
Now lets try to compare the content of the objects we just made:
# Equivalent objects:
prep_rec %>% tidy(2, type = "variance"); pca_facto$eig; summary(pca_stats)
#> # A tibble: 16 × 4
#> terms value component id
#> <chr> <dbl> <int> <chr>
#> 1 variance 2.92 1 pca_OMBbk
#> 2 variance 0.914 2 pca_OMBbk
#> 3 variance 0.147 3 pca_OMBbk
#> 4 variance 0.0207 4 pca_OMBbk
#> 5 cumulative variance 2.92 1 pca_OMBbk
#> 6 cumulative variance 3.83 2 pca_OMBbk
#> 7 cumulative variance 3.98 3 pca_OMBbk
#> 8 cumulative variance 4 4 pca_OMBbk
#> 9 percent variance 73.0 1 pca_OMBbk
#> 10 percent variance 22.9 2 pca_OMBbk
#> 11 percent variance 3.67 3 pca_OMBbk
#> 12 percent variance 0.518 4 pca_OMBbk
#> 13 cumulative percent variance 73.0 1 pca_OMBbk
#> 14 cumulative percent variance 95.8 2 pca_OMBbk
#> 15 cumulative percent variance 99.5 3 pca_OMBbk
#> 16 cumulative percent variance 100 4 pca_OMBbk
#> eigenvalue percentage of variance cumulative percentage of variance
#> comp 1 2.91849782 72.9624454 72.96245
#> comp 2 0.91403047 22.8507618 95.81321
#> comp 3 0.14675688 3.6689219 99.48213
#> comp 4 0.02071484 0.5178709 100.00000
#> Importance of components:
#> PC1 PC2 PC3 PC4
#> Standard deviation 1.7084 0.9560 0.38309 0.14393
#> Proportion of Variance 0.7296 0.2285 0.03669 0.00518
#> Cumulative Proportion 0.7296 0.9581 0.99482 1.00000
Now, why are these different?
# Why are these different?
prep_rec %>% tidy(2, type = "coef"); pca_stats$rotation # --> different form $var from an abject made with FactoMineR::PCA()
#> # A tibble: 16 × 4
#> terms value component id
#> <chr> <dbl> <chr> <chr>
#> 1 Sepal.Length 0.521 PC1 pca_OMBbk
#> 2 Sepal.Width -0.269 PC1 pca_OMBbk
#> 3 Petal.Length 0.580 PC1 pca_OMBbk
#> 4 Petal.Width 0.565 PC1 pca_OMBbk
#> 5 Sepal.Length -0.377 PC2 pca_OMBbk
#> 6 Sepal.Width -0.923 PC2 pca_OMBbk
#> 7 Petal.Length -0.0245 PC2 pca_OMBbk
#> 8 Petal.Width -0.0669 PC2 pca_OMBbk
#> 9 Sepal.Length 0.720 PC3 pca_OMBbk
#> 10 Sepal.Width -0.244 PC3 pca_OMBbk
#> 11 Petal.Length -0.142 PC3 pca_OMBbk
#> 12 Petal.Width -0.634 PC3 pca_OMBbk
#> 13 Sepal.Length 0.261 PC4 pca_OMBbk
#> 14 Sepal.Width -0.124 PC4 pca_OMBbk
#> 15 Petal.Length -0.801 PC4 pca_OMBbk
#> 16 Petal.Width 0.524 PC4 pca_OMBbk
#> PC1 PC2 PC3 PC4
#> Sepal.Length 0.5210659 -0.37741762 0.7195664 0.2612863
#> Sepal.Width -0.2693474 -0.92329566 -0.2443818 -0.1235096
#> Petal.Length 0.5804131 -0.02449161 -0.1421264 -0.8014492
#> Petal.Width 0.5648565 -0.06694199 -0.6342727 0.5235971
pca_facto$var
#> $coord
#> Dim.1 Dim.2 Dim.3 Dim.4
#> Sepal.Length 0.8901688 0.36082989 -0.27565767 -0.03760602
#> Sepal.Width -0.4601427 0.88271627 0.09361987 0.01777631
#> Petal.Length 0.9915552 0.02341519 0.05444699 0.11534978
#> Petal.Width 0.9649790 0.06399985 0.24298265 -0.07535950
#>
#> $cor
#> Dim.1 Dim.2 Dim.3 Dim.4
#> Sepal.Length 0.8901688 0.36082989 -0.27565767 -0.03760602
#> Sepal.Width -0.4601427 0.88271627 0.09361987 0.01777631
#> Petal.Length 0.9915552 0.02341519 0.05444699 0.11534978
#> Petal.Width 0.9649790 0.06399985 0.24298265 -0.07535950
#>
#> $cos2
#> Dim.1 Dim.2 Dim.3 Dim.4
#> Sepal.Length 0.7924004 0.130198208 0.075987149 0.0014142127
#> Sepal.Width 0.2117313 0.779188012 0.008764681 0.0003159971
#> Petal.Length 0.9831817 0.000548271 0.002964475 0.0133055723
#> Petal.Width 0.9311844 0.004095980 0.059040571 0.0056790544
#>
#> $contrib
#> Dim.1 Dim.2 Dim.3 Dim.4
#> Sepal.Length 27.150969 14.24440565 51.777574 6.827052
#> Sepal.Width 7.254804 85.24748749 5.972245 1.525463
#> Petal.Length 33.687936 0.05998389 2.019990 64.232089
#> Petal.Width 31.906291 0.44812296 40.230191 27.415396
Created on 2023-10-31 with reprex v2.0.2
Solution
The first plot can be made by mapping the first two principal components to the X and Y axes respectively. To match the example you shared I label the points using ggrepel.
library(tidyverse)
library(recipes)
library(ggrepel)
library(ggforce)
iris_pca <- recipe(~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data = iris) %>%
step_normalize(all_numeric_predictors()) %>%
step_pca(all_predictors(), res = TRUE) %>%
prep()
iris_pca %>%
bake(new_data = NULL) %>%
mutate(id = row_number()) %>%
ggplot(aes(PC1, PC2)) +
geom_point() +
geom_text_repel(aes(label = id)) +
geom_hline(yintercept = 0, lty = 2) +
geom_vline(xintercept = 0, lty = 2) +
coord_equal() +
theme_bw()
Getting the values for the circle plot requires getting the loadings from the prepped object. This is what matrix = 'v' is doing in the following.
tidy(iris_pca, 2, matrix = 'v') %>%
pivot_wider(names_from = component, values_from = value) %>%
ggplot() +
geom_segment(aes(x = 0, y = 0, xend = PC1, yend = PC2)) +
geom_label_repel(aes(x = PC1, y = PC2, label = terms)) +
geom_circle(aes(x0 = 0, y0 = 0, r = 1)) +
coord_equal() +
theme_bw()
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