### Abstract

Many problems require a notion of distance between a set of points in a metric space, e.g., clustering data points in an N-dimensional space, object retrieval in pattern recognition, and image segmentation. However, these applications often require that the distances must be a metric, meaning that they must satisfy a set of conditions, with triangle inequality being the focus of this paper. Given an dissimilarity matrix with triangle inequality violations, the metric nearness problem requires to find a closest distance matrix, which satisfies the triangle inequality condition. This paper introduces a new deep learning approach for approximating a nearest matrix with more efficient runtime complexity than existing algorithms. We have experimented with several deep learning architectures, and our experimental results demonstrate that deep neural networks can learn to construct a close-distance matrix efficiently by removing most of the triangular inequality violations.

Original language | English |
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Title of host publication | Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings |

Editors | Jacek M. Zurada, Witold Pedrycz, Leszek Rutkowski, Rafał Scherer, Marcin Korytkowski, Ryszard Tadeusiewicz |

Publisher | Springer Verlag |

Pages | 62-72 |

Number of pages | 11 |

ISBN (Print) | 9783030209117 |

DOIs | |

Publication status | Published - Jan 1 2019 |

Event | 18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019 - Zakopane, Poland Duration: Jun 16 2019 → Jun 20 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 | 11508 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019 |
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Country | Poland |

City | Zakopane |

Period | 6/16/19 → 6/20/19 |

### Keywords

- Convolutional neural networks
- Deep learning
- Matrix analysis
- Metric nearness problem

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Artificial Intelligence and Soft Computing - 18th International Conference, ICAISC 2019, Proceedings*(pp. 62-72). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11508 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-030-20912-4_6