## Abstract

Non-negative matrix factorisation covers a variety of algorithms that attempt to

represent a given, large, data matrix as a sum of low rank matrices with a prescribed sign pattern. There are intuitave advantages to this approach, but also theoretical and computational challenges. In this exploratory paper we investigate the use of non-negative matrix factorisation algorithms as a means to reorder the nodes in a large network. This gives a set of alternatives to the more traditional approach of using the singular value decomposition. We describe and implement a range of recently proposed algorithms and evaluate their performance on synthetically constructed test data and on a real data set arising in cancer research.

represent a given, large, data matrix as a sum of low rank matrices with a prescribed sign pattern. There are intuitave advantages to this approach, but also theoretical and computational challenges. In this exploratory paper we investigate the use of non-negative matrix factorisation algorithms as a means to reorder the nodes in a large network. This gives a set of alternatives to the more traditional approach of using the singular value decomposition. We describe and implement a range of recently proposed algorithms and evaluate their performance on synthetically constructed test data and on a real data set arising in cancer research.

Original language | English |
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Pages (from-to) | 39-53 |

Number of pages | 16 |

Journal | Monografias de la Real Academia de Ciencias de Zaragoza |

Volume | 33 |

Publication status | Published - 2010 |

## Keywords

- matrix factorisation
- data matrix
- cancer research