  The development of neuromorphic hardware and modeling of biological neural
networks requires algorithms with local learning rules. Artificial neural
networks using local learning rules to perform principal subspace analysis
(PSA) and clustering have recently been derived from principled objective
functions. However, no biologically plausible networks exist for minor subspace
analysis (MSA), a fundamental signal processing task. MSA extracts the
lowest-variance subspace of the input signal covariance matrix. Here, we
introduce a novel similarity matching objective for extracting the minor
subspace, Minor Subspace Similarity Matching (MSSM). Moreover, we derive an
adaptive MSSM algorithm that naturally maps onto a novel neural network with
local learning rules and gives numerical results showing that our method
converges at a competitive rate.
