  The extraction of nonstationary signals from blind and semi-blind
multivariate observations is a recurrent problem. Numerous algorithms have been
developed for this problem, which are based on the exact or approximate joint
diagonalization of second or higher order cumulant matrices/tensors of
multichannel data. While a great body of research has been dedicated to joint
diagonalization algorithms, the selection of the diagonalized matrix/tensor set
remains highly problem-specific. Herein, various methods for nonstationarity
identification are reviewed and a new general framework based on hypothesis
testing is proposed, which results in a classification/clustering perspective
to semi-blind source separation of nonstationary components. The proposed
method is applied to noninvasive fetal ECG extraction, as case study.
