Another Interpretation as Clustering

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 $\mu_k$ as cluster centroids, the a posteriori probability in equation (6) as a membership degree of each micro-energy and the log-likelihood $P_{\bar{\theta}}(x,n,k)$ as a distance function between centroid $\mu_k$ and a micro-energy, thus the $Q$ function in equation (3) turns out to be the objective function for fuzzy clustering. We call this concept ``Harmonic Clustering.''