From another viewpoint, this ML procedure can be understood as a
clustering method under a harmonic constraint between Gaussian mixture
components where spectral density function is considered as a statistical
distribution of micro-energies along frequency axis.
As we regard as cluster centroids, the a posteriori probability
in equation (6) as a membership degree of each
micro-energy and the log-likelihood
as a
distance function between centroid
and a micro-energy, thus the
function in equation (3) turns out to be the
objective function for fuzzy clustering. We call this concept
``Harmonic Clustering.''