finches.Rmd

---
title: "Archetype analysis of Darwin's finches"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Useful libraries (optional)

Remove the following two lines if you want to use other tools for plotting. You might have to install ggplot2 and ggfortify using `install.package(ggplot2)` and`install.package(ggfority)`. You can also use something else to plot. In particular, [autoplot](https://cran.r-project.org/web/packages/ggfortify/vignettes/plot_pca.html) (available through ggplot and ggfortify might be useful to look at the PCA results.)
```{r}

library(ggplot2)
library(ggfortify)
```

## Tasks

Follow the following steps to perform an archetype analysis of the finch data.

* Read the data from `data/finches.csv` (`read.csv` should do the trick).
* Plot the data. Can you already infer archetypes? It is challenging in 5 dimensions, right?
* Perform a principal component analysis (PCA).
    * `princomp` is recommended.
    * If you need a refresher on PCA, check out this interactive explanation: https://setosa.io/ev/principal-component-analysis/.
* Determine how much of the variance in the data is captured by the individual principal components.
* Plot the first two principle components. How many archetypes can you identify in the plot?
* Look at the feature loadings (`pca_result$loadings`). You can also `autoplot` or `biplot` to generate a [biplot](https://en.wikipedia.org/wiki/Biplot) of the components and loadings. What are the contributions of the features to the first two principal components?
* Compute the convex hull (`chull` is recommended) and highlight it in the PCA plot.
* Bonus points: based on the points in the convex hull, determine the triangle with the largest surface (spanned by three points in the convex hull).