Basics of Clustering Using k-Means

Twelve customers. Two columns. Every number printed on the page.

A bakery owner wants to treat different kinds of regular differently. She has measurements for all twelve of her regulars and no categories, because nobody has ever sorted them. That is the whole setup, and it is enough to build clustering from nothing.

This book works k-means through completely on data small enough that you can check every calculation yourself. Not a survey. Not a tour of the literature. One method, one dataset, followed until it works and then pushed until it breaks.

What you will actually see:

• Why no straight line separates these twelve customers correctly, established by testing roughly six million of them rather than asserting it
• What "alike" means when a machine has to compute it, and where a group is located when it has four members and no address
• k-means run from a deliberately poor start, one step at a time, until nothing moves
• Two quality scores disagreeing about the same grouping, one calling it an improvement and the other a deterioration, and why the disagreement is the useful part
• The run that converges to an answer seven times worse than the best available, reports success, and gives you no warning
• How recording spend in cents instead of dollars hands 100 percent of the decision to one column and silently changes every group
  
  By the end you will know how to run k-means, how to choose k, and, more usefully, how to tell when the answer it hands you should not be trusted.
  

No statistics background assumed. Arithmetic and the rule about right triangles are the only mathematics used.