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次へ: Multi-pitch Detection Algorithm 上へ: A Maximum Likelihood Formulation 戻る: Model Parameter Estimation using

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.''