Possible solution to large data sets?

[riversdark]

This has already been mentioned in another issue, but I thought it merits its own thread, and besides the other one hasn't been updated for quite a while.

Since the algorithm complexity is $O(n^3)$, the computation can get quite costly quite quickly, both time-wise and memory-wise. Are there any solutions or approximation algorithms to address this problem?

In the other thread a data size of 55K was already considered a big data set, and I have a data set that is thousands of times its size... Any hope?