I am solving a clustering problem on a trivial dataset with the k-means algorithm. I am running a couple of tests and, from time to time, one centroid doesn't attract any points, i.e. I've got an empty cluster (see the purple "x" in the picture).

What should I do? Shall I delete it and go on with the remaining centroids or just stop updating its value? Why?

In the picture each colour represents a cluster and each "X" is its centroid (marked with the number of the iteration in which it has been computed).

  [1]: https://i.sstatic.net/jMllj.png