Median-based clustering for underdetermined blind signal processing

In underdetermined blind source separation, more sources are to be extracted from less observed mixtures without knowing both sources and mixing matrix. k-means-style clustering algorithms are commonly used to do this algorithmically given sufficiently sparse sources, but in any case other than deterministic sources, this lacks theoretical justification. After establishing that mean-based algorithms converge to wrong solutions in practice, we propose a median-based clustering scheme. Theoretical justification as well as algorithmic realizations (both online and batch) are given and illustrated by some examples.