### Abstract

In statistical pattern recognition, the Bayesian decision theory gives a decision that minimizes the expected probability of misclassification as long as the true distributions are given. However, in most practical situations, the true distributions are unknown, and the parameters of the distributions are usually estimated from training sample vectors. It is well known that estimated parameters contain estimation errors when the sample size is small, and the errors have a negative influence on recognition performance. Among the estimation errors of parameters, the estimation errors of eigenvectors have not been sufficiently considered. In this paper, we present a method to estimate the true Mahalanobis distance from the sample eigenvectors (the eigenvectors of sample covariance matrix) by considering the estimation errors of eigenvectors. Recognition experiments show that the true Mahalanobis distance can be estimated, and better recognition accuracy is achieved by applying the proposed method without many training samples and any hyperparameters.

Original language | English |
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Pages (from-to) | 30-38 |

Number of pages | 9 |

Journal | Systems and Computers in Japan |

Volume | 35 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2004 Aug |

### Keywords

- Discriminant function
- Eigenvector
- Estimation error
- Mahalanobis distance
- Pattern recognition

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Hardware and Architecture
- Computational Theory and Mathematics

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## Cite this

*Systems and Computers in Japan*,

*35*(9), 30-38. https://doi.org/10.1002/scj.10519