Identification and clustering limitations

The performance of the clustering algorithm will depend on the distance between points of different clusters. If clusters still overlap or come too close after preprocessing, spectral clustering will not be possible. This cluster ``separability'' depends mainly on the nonlinearity $\textbf{f}$ and the mixing matrix.

Furthermore, it is assumed that the different sources have double sided distributions. By applying spectral clustering, it is then possible to distinguish $2n$ clusters, one for each sidelobe of the $n$ distributions. And since the nonlinearities are assumed to be linear for small input values, determining which pair of clusters correspond to the same source can be done by looking at which clusters have the same slopes close to the origin. Finally, $n$ clusters are obtained, corresponding to the $n$ sources.