15 Monaural Speech Separation by Support Vector Machines: Bridging the Divide Between Supervised and Unsupervised Learning Methods

We address the problem of identifying multiple independent speech sources from a single signal that is a mixture of the sources. Because the problem is ill-posed, standard independent component analysis (ICA) approaches which try to invert the mixing matrix fail. We show how the unsupervised problem can be transformed into a supervised regression task which is then solved by supportvector regression (SVR). It turns out that the linear SVR approach is equivalent to the sparse-decomposition method proposed by [1, 2]. However, we can extend the method to nonlinear ICA by applying the “kernel trick.” Beyond the kernel trick, the SVM perspective provides a new interpretation of the sparse-decomposition method’s hyperparameter which is related to the input noise. The limitation of the SVM perspective is that, for the nonlinear case, it can recover only whether or not a mixture component is present; it cannot recover the strength of the component. In experiments, we show that our model can handle difficult problems and is especially well suited for speech signal separation.