Using matsindf for principal components analysis
In matsindf: Matrices in Data Frames

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(datasets)
library(dplyr)
library(ggplot2)
library(matsindf)
library(tidyr)

Introduction

When working with tidy data, it can be challenging to use R operations that take in matrices. But the functions in matsindf make it easier.

Data

We will illustrate how to handle these cases with matsindf functions by doing principal components analysis (PCA) on the classic Fisher iris dataset, often used to illustrate PCA. We will be using a "long" input table, in which each measurement, rather than each flower, is a single row.

long_iris <- datasets::iris %>%
  dplyr::mutate(flower = sprintf("flower_%d", 1:nrow(datasets::iris))) %>%
  tidyr::pivot_longer(
    cols = c(-Species, -flower), names_to = "dimension", values_to = "length"
  ) %>%
  dplyr::rename(species = Species) %>%
  dplyr::select(flower, species, dimension, length) %>%
  dplyr::mutate(species = as.character(species))

head(long_iris, n = 5)

Generate PCA results

Using matsindf, we can convert to a matrix, apply PCA, and then convert back to a long format table.

long_pca_embeddings <- long_iris %>%
  collapse_to_matrices(
    rownames = "flower", colnames = "dimension", matvals = "length"
  ) %>%
  dplyr::transmute(projection = lapply(length, function(mat)
    stats::prcomp(mat, center = TRUE, scale = TRUE)$x
  )) %>%
  expand_to_tidy(
    rownames = "flower", colnames = "component", matvals = "projection"
  )
head(long_pca_embeddings, n = 5)

The result are the coordinates of the iris data along the principal components, as a long format table. We just need to add back the species column ...

long_pca_withspecies <- long_iris %>%
  dplyr::select(flower, species) %>%
  dplyr::distinct() %>%
  dplyr::left_join(long_pca_embeddings, by = "flower")
head(long_pca_withspecies, n = 5)

... followed by the familiar PCA plot.

long_pca_withspecies %>%
  tidyr::pivot_wider(
    id_cols = c(flower, species), names_from = component,
    values_from = projection
  ) %>%
  ggplot2::ggplot(ggplot2::aes(x = PC1, y = PC2, colour = species)) + 
  ggplot2::geom_point() +
  ggplot2::labs(colour = ggplot2::element_blank()) +
  ggplot2::theme_bw() +
  ggplot2::coord_equal()