I am looking to do k-means clustering on a set of 10-dimensional points. The catch: there are 10^10 points.
I am looking for just the center and size of the largest clusters (let's say 10 to 100 clusters); I don't care about what cluster each point ends up in. Using k-means specifically is not important; I am just looking for a similar effect, any approximate k-means or related algorithm would be great (minibatch-SGD means, ...). Since GMM is in a sense the same problem as k-means, doing GMM on the same size data is also interesting.
At this scale, subsampling the data probably doesn't change the result significantly: the odds of finding the same top 10 clusters using a 1/10000th sample of the data are very good. But even then, that is a 10^6 point problem which is on/beyond the edge of tractable.