# A Neural Network with Local Learning Rules for Minor Subspace Analysis

arXiv: https://arxiv.org/abs/2102.05501 · HTML: https://mlsanity.com/paper/2102.05501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 10 Feb 2021.

## Builds on (most cited first, 7 of 7)

- [A Hebbian/Anti-Hebbian Neural Network for Linear Subspace Learning: A Derivation from Multidimensional Scaling of Streaming Data](https://mlsanity.com/paper/1503.00669/) (2015)
- [Why do similarity matching objectives lead to Hebbian/anti-Hebbian networks?](https://mlsanity.com/paper/1703.07914/) (2017)
- [Neuroscience-inspired online unsupervised learning algorithms](https://mlsanity.com/paper/1908.01867/) (2019)
- [A Normative Theory of Adaptive Dimensionality Reduction in Neural Networks](https://mlsanity.com/paper/1511.09426/) (2015)
- [A biologically plausible neural network for multi-channel Canonical Correlation Analysis](https://mlsanity.com/paper/2010.00525/) (2020)
- [A Spiking Neural Network with Local Learning Rules Derived From Nonnegative Similarity Matching](https://mlsanity.com/paper/1902.01429/) (2019)
- [Efficient Principal Subspace Projection of Streaming Data Through Fast Similarity Matching](https://mlsanity.com/paper/1808.02083/) (2018)

## Built on by (most cited first, 1 of 1)

- [A Normative and Biologically Plausible Algorithm for Independent Component Analysis](https://mlsanity.com/paper/2111.08858/) (2021)

## Abstract (arXiv)

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.