A Neural Network with Local Learning Rules for Minor Subspace Analysis
This work addresses a gap in neuromorphic hardware and biological modeling by providing a biologically plausible solution for MSA, which is incremental as it builds on existing methods for principal subspace analysis.
The authors tackled the lack of biologically plausible neural networks for minor subspace analysis (MSA), a fundamental signal processing task, by introducing a novel similarity matching objective and deriving an adaptive algorithm that maps onto a neural network with local learning rules, achieving competitive convergence rates.
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.