The objectives for this week are:

- Think critically about cluster analysis
- Learn about distance metrics
- Apply the \(k\)-means cluster algorithm

The lab uses cluster analysis to analyse the happy paintings by Bob Ross. This was the subject of the 538 post, “A Statistical Analysis of the Work of Bob Ross”.

We have taken the painting images from the sales site, read the images into R, and resized them all to be 20 by 20 pixels. Each painting has been classified into one of 8 classes based on the title of the painting. This is the data that you will work with.

Each row corresponds to one painting, and the rgb color values at each pixel are in each column. With a \(20\times20\) image, this leads to \(400\times3=1200\) columns.

We have given you a set of 178 paintings. Your job is to cluster the data and thus organise the paintings.

Here is one of the original paintings and how it appears after image processing: