Does scipy's kmeans2 algorithm also weigh initial centroids set when using minit='matrix'?

Question

I was playing around with scipy's kmeans2 algorithm until I noticed a problem. Consider the following code:

x = np.array([[0.1, 0.0], [0.0, 0.1], [1.1, 1.0], [1.0, 1.1]])
c = np.array([[3,3], [4, 4]])

kmeans2(x, c, minit = 'matrix', iter=100)

You'd expect this code (rather deviously) to just converge to a solution with the following centroids: [0.05, 0.05] and [1.05, 1.05] . However, the code returns this:

 (array([[ 0.55,  0.55],
   [ 4.  ,  4.  ]]), array([0, 0, 0, 0], dtype=int32))

It seems like the k-means algorithm takes its initial centroids into account when finding the new centroids. Why is this? How can I prevent this from happening?

Answer 1

I haven't really worked on this for a while but I randomly got this Eureka-moment in which I figured out why my problem was occuring:
Although the results seem kinda strange, if you look at how k-means works, these results are actually easy to explain: in the first epoch of k-means, the four data points are all assigned to the [3, 3] centroid, because that centroid is closest to all data points. The mean of the data points is [ 0.55, 0.55] . No matter how many epochs you do after, the centroid initialised as [3, 3] will stay the same (because it's not 'attracted' to any other data points, there aren't any) and the other centroid (initialised as [4, 4] ) will stay put because none of the data points are closer to this centroid than to the other. That's it.