A Recommendation on How to Teach K-Means in Introductory Analytics Courses

Abstract

We teach K-Means clustering in introductory data analytics courses because it is one of the simplest and most widely used unsupervised machine learning algorithms. However, one drawback of this algorithm is that it does not offer a clear method to determine the appropriate number of clusters; it does not have a built-in mechanism for K selection. What is usually taught as the solution for the K Selection problem is the so-called elbow method, where we look at the incremental changes in some quality metric (usually, the sum of squared errors, SSE), trying to find a sudden change. In addition to SSE, we can find many other metrics and methods in the literature. In this paper, we survey several of them, and conclude that the Variance Ratio Criterion (VRC) is an appropriate metric we should consider teaching for K Selection. From a pedagogical perspective, VRC has desirable mathematical properties, which help emphasize the statistical underpinnings of the algorithm, thereby reinforcing the students’ understanding through experiential learning. We also list the key concepts targeted by the VRC approach and provide ideas for assignments.