I have to find number of clusters for 1D data. All clusters are assumed to have a gaussian distribution (so there is a big number of same points). I have a robust "agglomerative clustering + EM"-based algorithm which is able to find cluster centers.
The number of clusters varies (in different data sets) from $1$ to $10$, but number of points in my 1D datasets varies from hundreds to hundreds of thousands. And that is the problem, because my algorithm is running pretty slow for high number of points.
Is there any simple method how to reduce number of points? The accuracy of cluster centers does not matter for me, I just only want to have fast detection.
Is it OK to select each k-th point and apply clustering algorithm on that selection. Or do I need something else like counting number of same points and leave out some percent of same points?