Kohonen Learning Procedure K-Means vs Lloyd's K-means

K-means maybe the most common data quantization method, used widely for many different domain of problems. Even it relies on very simple idea, it proposes satisfying results in a computationally efficient environment.

Underneath of the formula of K-means optimization, the objective is to minimize the distance between data points to its closest centroid (cluster center). Here we can write the objective as;

$argmin sum_{i=1}^{k}sum_{x_j in S_i} ||x_j - mu_i||^2$

$mu_i$ is the closest centroid to instance $x_j$.