### Abstract

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose a feed-forward neural network capable of semi-supervised learning on manifolds without using an explicit graph representation. Our algorithm uses channels that represent localities on the manifold such that correlations between channels represent manifold structure. The proposed neural network has two layers. The first layer learns to build a representation of low-dimensional manifolds in the input data as proposed recently in [8]. The second learns to classify data using both occasional supervision and similarity of the manifold representation of the data. The channel carrying label information for the second layer is assumed to be “silent” most of the time. Learning in both layers is Hebbian, making our network design biologically plausible. We experimentally demonstrate the effect of semi-supervised learning on non-trivial manifolds.

Original language | English (US) |
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Title of host publication | Artificial Neural Networks and Machine Learning – ICANN 2019 |

Subtitle of host publication | Theoretical Neural Computation - 28th International Conference on Artificial Neural Networks, 2019, Proceedings |

Editors | Igor V. Tetko, Pavel Karpov, Fabian Theis, Vera Kurková |

Publisher | Springer Verlag |

Pages | 375-386 |

Number of pages | 12 |

ISBN (Print) | 9783030304867 |

DOIs | |

State | Published - Jan 1 2019 |

Event | 28th International Conference on Artificial Neural Networks, ICANN 2019 - Munich, Germany Duration: Sep 17 2019 → Sep 19 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11727 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 28th International Conference on Artificial Neural Networks, ICANN 2019 |
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Country | Germany |

City | Munich |

Period | 9/17/19 → 9/19/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Keywords

- Manifold learning
- Online learning
- Semi-supervised learning

### Cite this

*Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation - 28th International Conference on Artificial Neural Networks, 2019, Proceedings*(pp. 375-386). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11727 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-30487-4_30

}

*Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation - 28th International Conference on Artificial Neural Networks, 2019, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11727 LNCS, Springer Verlag, pp. 375-386, 28th International Conference on Artificial Neural Networks, ICANN 2019, Munich, Germany, 9/17/19. https://doi.org/10.1007/978-3-030-30487-4_30

**A Neural Network for Semi-supervised Learning on Manifolds.** / Genkin, Alexander; Sengupta, Anirvan M.; Chklovskii, Dmitri.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A Neural Network for Semi-supervised Learning on Manifolds

AU - Genkin, Alexander

AU - Sengupta, Anirvan M.

AU - Chklovskii, Dmitri

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose a feed-forward neural network capable of semi-supervised learning on manifolds without using an explicit graph representation. Our algorithm uses channels that represent localities on the manifold such that correlations between channels represent manifold structure. The proposed neural network has two layers. The first layer learns to build a representation of low-dimensional manifolds in the input data as proposed recently in [8]. The second learns to classify data using both occasional supervision and similarity of the manifold representation of the data. The channel carrying label information for the second layer is assumed to be “silent” most of the time. Learning in both layers is Hebbian, making our network design biologically plausible. We experimentally demonstrate the effect of semi-supervised learning on non-trivial manifolds.

AB - Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose a feed-forward neural network capable of semi-supervised learning on manifolds without using an explicit graph representation. Our algorithm uses channels that represent localities on the manifold such that correlations between channels represent manifold structure. The proposed neural network has two layers. The first layer learns to build a representation of low-dimensional manifolds in the input data as proposed recently in [8]. The second learns to classify data using both occasional supervision and similarity of the manifold representation of the data. The channel carrying label information for the second layer is assumed to be “silent” most of the time. Learning in both layers is Hebbian, making our network design biologically plausible. We experimentally demonstrate the effect of semi-supervised learning on non-trivial manifolds.

KW - Manifold learning

KW - Online learning

KW - Semi-supervised learning

UR - http://www.scopus.com/inward/record.url?scp=85072872064&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072872064&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-30487-4_30

DO - 10.1007/978-3-030-30487-4_30

M3 - Conference contribution

AN - SCOPUS:85072872064

SN - 9783030304867

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 375

EP - 386

BT - Artificial Neural Networks and Machine Learning – ICANN 2019

A2 - Tetko, Igor V.

A2 - Karpov, Pavel

A2 - Theis, Fabian

A2 - Kurková, Vera

PB - Springer Verlag

ER -