  In this paper, we introduce a general extension of linear sparse component
analysis (SCA) approaches to postnonlinear (PNL) mixtures. In particular, and
contrary to the state-of-art methods, our approaches use a weak sparsity source
assumption: we look for tiny temporal zones where only one source is active. We
investigate two nonlinear single-source confidence measures, using the mutual
information and a local linear tangent space approximation (LTSA). For this
latter measure, we derive two extensions of linear single-source measures,
respectively based on correlation (LTSA-correlation) and eigenvalues
(LTSA-PCA). A second novelty of our approach consists of applying functional
data clustering techniques to the scattered observations in the above
single-source zones, thus allowing us to accurately estimate them.We first
study a classical approach using a B-spline approximation, and then two
approaches which locally approximate the nonlinear functions as lines. Finally,
we extend our PNL methods to more general nonlinear mixtures. Combining
single-source zones and functional data clustering allows us to tackle speech
signals, which has never been performed by other PNL-SCA methods. We
investigate the performance of our approaches with simulated PNL mixtures of
real speech signals. Both the mutual information and the LTSA-correlation
measures are better-suited to detecting single-source zones than the LTSA-PCA
measure. We also find local-linear-approximation-based clustering approaches to
be more flexible and more accurate than the B-spline one.
