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For the problem of independent component analysis we propose an alternative solution to determining $n$ independent sources from $n$ channels using a geometric approach. The resulting algorithm inherits many properties of the then applicable simplex algorithm, namely computational tractability even in high dimensions ($n geq 100$), and yields demixing estimates comparable to standard algorithms (e.g. FastICA) for extremely small sample sizes ($N = 50$). Our results are corroborated by demixingdoi:10.24355/dbbs.084-201306131536-0 fatcat:mmtnygkh7nhx5e72rhyqxh37ha