### Abstract

Given a set of sample patterns for two pattern classes, some simple expressions for the upper bound of the probability of error for a linear pattern classifier and the optimal linear discriminant function minimizing the upper bound are obtained. Using these results, if the tolerable probability of error of classifying patterns in the two pattern classes is not smaller than this upper bound, not only a linear pattern classifier is known to be feasible, but also a satisfactory linear discriminant function is given. The results presented here are independent of the probability distribution of the patterns in the pattern classes. For some special cases, a smaller upper bound is found.

Original language | English (US) |
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Pages (from-to) | 321-322 |

Number of pages | 2 |

Journal | Proceedings of the IEEE |

Volume | 56 |

Issue number | 3 |

DOIs | |

State | Published - 1968 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

**On the Upper Bound of the Probability of Error of a Linear Pattern Classifier for Probabilistic Pattern Classes.** / Yau, Sik-Sang; Lin, T. T.

Research output: Contribution to journal › Article

*Proceedings of the IEEE*, vol. 56, no. 3, pp. 321-322. https://doi.org/10.1109/PROC.1968.6274

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TY - JOUR

T1 - On the Upper Bound of the Probability of Error of a Linear Pattern Classifier for Probabilistic Pattern Classes

AU - Yau, Sik-Sang

AU - Lin, T. T.

PY - 1968

Y1 - 1968

N2 - Given a set of sample patterns for two pattern classes, some simple expressions for the upper bound of the probability of error for a linear pattern classifier and the optimal linear discriminant function minimizing the upper bound are obtained. Using these results, if the tolerable probability of error of classifying patterns in the two pattern classes is not smaller than this upper bound, not only a linear pattern classifier is known to be feasible, but also a satisfactory linear discriminant function is given. The results presented here are independent of the probability distribution of the patterns in the pattern classes. For some special cases, a smaller upper bound is found.

AB - Given a set of sample patterns for two pattern classes, some simple expressions for the upper bound of the probability of error for a linear pattern classifier and the optimal linear discriminant function minimizing the upper bound are obtained. Using these results, if the tolerable probability of error of classifying patterns in the two pattern classes is not smaller than this upper bound, not only a linear pattern classifier is known to be feasible, but also a satisfactory linear discriminant function is given. The results presented here are independent of the probability distribution of the patterns in the pattern classes. For some special cases, a smaller upper bound is found.

UR - http://www.scopus.com/inward/record.url?scp=84932363006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84932363006&partnerID=8YFLogxK

U2 - 10.1109/PROC.1968.6274

DO - 10.1109/PROC.1968.6274

M3 - Article

AN - SCOPUS:84932363006

VL - 56

SP - 321

EP - 322

JO - Proceedings of the IEEE

JF - Proceedings of the IEEE

SN - 0018-9219

IS - 3

ER -