Author: Alexander Davis
Date: 2024-01-31

# Using matsindf for principal components analysis

#### Alexander Davis

#### 2024-01-31

## 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)
    #> # A tibble: 5 × 4
    #>   flower   species dimension    length
    #>   <chr>    <chr>   <chr>         <dbl>
    #> 1 flower_1 setosa  Sepal.Length    5.1
    #> 2 flower_1 setosa  Sepal.Width     3.5
    #> 3 flower_1 setosa  Petal.Length    1.4
    #> 4 flower_1 setosa  Petal.Width     0.2
    #> 5 flower_2 setosa  Sepal.Length    4.9

## 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)
    #>       flower component projection
    #> 1   flower_1       PC1 -2.2571412
    #> 2  flower_10       PC1 -2.1770349
    #> 3 flower_100       PC1  0.2558734
    #> 4 flower_101       PC1  1.8384100
    #> 5 flower_102       PC1  1.1540156

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)
    #> # A tibble: 5 × 4
    #>   flower   species component projection
    #>   <chr>    <chr>   <chr>          <dbl>
    #> 1 flower_1 setosa  PC1          -2.26
    #> 2 flower_1 setosa  PC2          -0.478
    #> 3 flower_1 setosa  PC3           0.127
    #> 4 flower_1 setosa  PC4          -0.0241
    #> 5 flower_2 setosa  PC1          -2.07

… 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()

As expected, we see that the distribution of measurements differs across the three species of iris.

## Conclusion

`matsindf` simplifies tasks that are otherwise much more difficult.