Overall you did a great job explaining the mathematics of unsupervised categorization but you missed one point in your end-matter.

The initial Monera classification was not a bad category at the time because when it was created there wasn't enough data to split out different subcategories. All the researchers had were a bunch of fuzzy spots wiggling under a microscope. You touched on this in the Amazon.com example. Just because the categories you have now are good for your current data doesn't mean that they will remain the same with further data.