How to normalize data by mapping data points from one mixture of multivariate normal distributions to another mixture
I am trying to normalize multivariate time series data. The data set (spectrograms from temporal EEG) come from sources that differ widely in their noise characteristics, scaling, and presence of artefacts. However, I have good reasons to believe that the distribution of data points in all cases can be well represented by a mixture of multivariate normal (MVN) distributions. For any given data set, the mean and covariance of these MVN distributions may be somewhat different, but the number of kernels will remain the same. To normalize the data before further processing, I would hence like to
fit a mixture of MVN distributions to each individual data set,
find a bijective mapping to some reference mixture of MVN distribution,
transform the original data points to the corresponding values in the reference.
Does such a procedure exist, and where can I read up on it?
If such a procedure is non-standard, how would I go about steps 2 & 3 efficiently? Each data set contains 100k data points, and I have on the order of 100 data sets. Is there a closed form algebraic expression, given two sets of MVN distributions?