### Abstract

To solve multiple classification problems with M (geq 3) categories, many studies have been devoted using N (geq lceillog-{2}Mrceil) binary ({0, 1}) classifiers, where these systems are known as binary Error-Correcting Output Codes (binary ECOC). As an extended version of the binary ECOC, the ternary ({0,∗1}) ECOC have also been discussed, where ternary classifiers classify data into positive examples when the element is 1, into negative examples when the element is 0, and no classification when the element is. In this paper, we discuss the ternary ECOC system from the view point of the system evaluation model based on rate-distortion function. First, we discuss a table of M code words with length N which is given by a ternary matrix W of M rows and N columns. Next, by leveraging the benchmark data for multiclass document classification which is widely used in Japan, the relationships between the probability of classification error P_{e} and the number of the ternary classifiers N for a given M are experimentally investigated. In addition, by assuming the M-dimensional Normal distribution for a classification data model, the relationship between P_{e} and N for a given M is also examined. Finally, we show by the system evaluation model that the ternary ECOC systems have desirable properties such as 'Flexible', 'Elastic', and 'Effective Elastic', when M becomes large.

Original language | English |
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Title of host publication | 2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2893-2898 |

Number of pages | 6 |

ISBN (Electronic) | 9781728145693 |

DOIs | |

Publication status | Published - 2019 Oct |

Event | 2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019 - Bari, Italy Duration: 2019 Oct 6 → 2019 Oct 9 |

### Publication series

Name | Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics |
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Volume | 2019-October |

ISSN (Print) | 1062-922X |

### Conference

Conference | 2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019 |
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Country | Italy |

City | Bari |

Period | 19/10/6 → 19/10/9 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Systems Engineering
- Human-Computer Interaction

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## Cite this

*2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019*(pp. 2893-2898). [8914295] (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics; Vol. 2019-October). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SMC.2019.8914295