I am learning about the k-means clustering algorithm. I have read that one of the characteristics of this algorithm is that it can get trapped in a local minimum, and that a simple way to increase the chance of finding a global optimum is to restart the algorithm with different random seeds. I understand the basic concept of the algorithm, which initialises arbitrary centroids/means in the first iteration and then assigns data points to these clusters. The centroids are then updated after the points are all assigned, and points are re-assigned again. The algorithm continues to iterate until the clusters do not change anymore.
However, I am having trouble understanding exactly what is meant by a local minimum in the context of this algorithm. Any insights are appreciated.