I have data points that are generated with the $n$ normal distributions with the same $\sigma$ and different means.
I do not know $n$, but I know that $1 \leq n \leq 4$. I know the possible set of means, i.e., $\mu = -2,-1, 0, 1, 2$ (so the number of potential means is bigger than expected number of clusters).
Mclust from R package works well and solves the problem in a nice way. The problem is that there are a lot of data points and Mclust works too slow (I guess it would work faster if it could take into account prior information of $\mu$ vector).
Is there a way to solve this problem in a fast and efficient way? I am trying to do mixtools, it is faster than Mclust, the problem is that I do not know number of clusters $n$ and this way of solving the problem is making huge mistakes when $n$ was initially wrong. Should I just apply BIC and do a greedy search for optimal $n$? Or are there more efficient ways?
I would appreciate links to the theory/approach that can help (so I do not expect that it was already implemented).