As far as I know k-means picks the initial centers randomly. Since they're based on pure luck, they can be selected really badly. The K-means++ algorithm tries to solve this problem, by spreading the initial centers evenly.
Do the two algorithms guarantee the same results? Or it is possible that the poorly chosen initial centroids lead to a bad result, not matter how many iterations.
Lets say there is a given dataset and a given number of desired clusters. We run a k-means algorithm as long as it converged (no more center move). Is there an exact solution to this cluster problem (given SSE), or k-means will produce sometimes different result at rerun?
If there is more than one solution to a clustering problem (given dataset, given number of clusters) , does K-means++ guarantee a better result, or just a faster? By better I mean lower SSE.
The reason I am asking these questions is because I am on the hunt for a k-means algorithm for clustering a huge dataset. I have found some k-means++, but there are some CUDA implementations too. As you already know CUDA is using the GPU, and it can run more hundreds of threads parallel. (So it can really speed up the whole process). But none of the CUDA implementations - which I have found so far - have k-means++ initialization.