K-Means Clustering in a PCA Subspace

In a previous post, we saw a list of the top 250 offensive players in MLB history constructed by Principal Components Analysis (PCA), which transforms high-dimensional data to its lower-dimensional principal components while retaining a high percentage of the sample variation. The PCA projection of high-dimensional data onto a convenient lower-dimensional subspace allows accessible data visualization and provides an opportunity for data segmentation. Segmentation can add detail and structure to a PCA biplot like the one seen below for the reduced MLB players' career batting data.

In practice, it is quite common that PCA is used to project high-dimensional data onto a lower-dimensional space, then have the K-means clustering algorithm be applied in a PCA subspace. Below is the result of automatic segmentation of baseball hitters into groups by applying K-means clustering on the first few principal components that account for the lion’s share of the sample variance.