  We develop a biologically-plausible learning rule called Triplet BCM that
provably converges to the class means of general mixture models. This rule
generalizes the classical BCM neural rule, and provides a novel interpretation
of classical BCM as performing a kind of tensor decomposition. It achieves a
substantial generalization over classical BCM by incorporating triplets of
samples from the mixtures, which provides a novel information processing
interpretation to spike-timing-dependent plasticity. We provide complete proofs
of convergence of this learning rule, and an extended discussion of the
connection between BCM and tensor learning.
