Is there any strategy or hack to give different importance to the different dimension of the data?
That means, that distances into one direction are penalized harder than into other directions, when fitting a GMM on multidimensional data. Options I considered:
- Preprocessing: Simple scaling of the dimensions won't work, as the GMM will just learn a similarly scaled variance.
- Manipulate the EM-algorithm: I tried to scale the covariance matrix after each M-step into the direction of the less important dimensions. Moderate success.
I am a bit surprised, I cannot find information on this quite obvious usecase.
