Monaural Separation and Classification of Mixed Signals : a Support-vector Regression Perspective

We address the problem of extracting multiple independent sources from a single mixture signal. Standard independentcomponent analysis approaches fail when the number of sources is greater than the number of mixtures. For this case, the sparse-decomposition method [1] has been proposed. The method relies on a dictionary of atomic signals and recovers the degree to which various dictionary atoms are present in the mixture. We show that the sparse-decomposition method is equivalent to a form of support-vector regression (SVR). The training inputs for the SVR are the dictionary atoms, and the corresponding targets are the dot product of the mixture and atom vectors. The SVR perspective provides a new interpretation of the sparse-decomposition method’s hyperparameter, and allows us to generalize and improve the method. The most important insight is that the sources do not have to be identical to dictionary atoms, but rather we can accommodate a many-to-one mapping of source signals to dictionary atoms—a classification of sorts—characterized by a known nonlinear transformation with unknown parameters. The limitation of the SVR perspective is that it cannot recover the signal strength of an atom in the mixture; rather, it can only recover whether or not a particular atom was present. In experiments, we show that our model can handle difficult problems involving classification of sources. Our model may be particularly useful for speech signal processing and CDMA-based mobile communication, where in both cases we have knowledge about the invariances in the signal.