Hands-On Unsupervised Learning with Python

K-means

K-means is the simplest implementation of the principle of maximum separation and maximum internal cohesion. Let's suppose we have a dataset X ∈ ℜ^M×N (that is, M N-dimensional samples) that we want to split into K clusters and a set of K centroids corresponding to the means of the samples assigned to each cluster K_j:

The set M and the centroids have an additional index (as a superscript) indicating the iterative step. Starting from an initial guess M⁽⁰⁾, K-means tries to minimize an objective function called inertia (that is, the total average intra-cluster distance between samples assigned to a cluster K_j and its centroid μ_j):