Eureka! For a two-dimensional analogy, imagine a horizontal rubber sheet that is fixed at certain points representing the input samples. Get hold of the sheet at one of the cluster centroids and stretch or "distort" it by pulling that point horizontally away from the centroid. The amount of distortion you introduce is like the cost function that the clustering algorithm tries to minimise.

Eureka! For a two-dimensional analogy, imagine a horizontal rubber sheet that is fixed at certain points representing the input samples. Get hold of the sheet at one of the cluster centroids and stretch or "distort" it by pulling that point horizontally away from the true centroid. The amount of distortion you introduce is like the cost function that the clustering algorithm tries to minimise.