### Abstract

We show that the decision function of a radial basis function (RBF) classifier is equivalent in form to the Bayes-optimal discriminant associated with a special kind of mixture-based statistical model. The relevant mixture model is a type of mixture-of-experts model for which class labels, like continuous-valued features, are assumed to have been generated randomly, conditional on the mixture component of origin. The new interpretation shows that RBF classifiers effectively assume a probability model, which, moreover, is easily determined given the designed RBF. This interpretation also suggests a statistical learning objective as an alternative to standard methods for designing the RBF-equivalent models. The statistical objective is especially useful for incorporating unlabeled data to enhance learning. Finally, it is observed that any new data to classify are simply additional unlabeled data. Thus, we suggest a combined learning and use paradigm, to be invoked whenever there are new data to classify.

Original language | English (US) |
---|---|

Pages (from-to) | 281-293 |

Number of pages | 13 |

Journal | Neural Computation |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Feb 15 1998 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Arts and Humanities (miscellaneous)
- Cognitive Neuroscience

### Cite this

*Neural Computation*,

*10*(2), 281-293. https://doi.org/10.1162/089976698300017764

}

*Neural Computation*, vol. 10, no. 2, pp. 281-293. https://doi.org/10.1162/089976698300017764

**Combined Learning and Use for a Mixture Model Equivalent to the RBF Classifier.** / Miller, David Jonathan; Uyar, Hasan S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Combined Learning and Use for a Mixture Model Equivalent to the RBF Classifier

AU - Miller, David Jonathan

AU - Uyar, Hasan S.

PY - 1998/2/15

Y1 - 1998/2/15

N2 - We show that the decision function of a radial basis function (RBF) classifier is equivalent in form to the Bayes-optimal discriminant associated with a special kind of mixture-based statistical model. The relevant mixture model is a type of mixture-of-experts model for which class labels, like continuous-valued features, are assumed to have been generated randomly, conditional on the mixture component of origin. The new interpretation shows that RBF classifiers effectively assume a probability model, which, moreover, is easily determined given the designed RBF. This interpretation also suggests a statistical learning objective as an alternative to standard methods for designing the RBF-equivalent models. The statistical objective is especially useful for incorporating unlabeled data to enhance learning. Finally, it is observed that any new data to classify are simply additional unlabeled data. Thus, we suggest a combined learning and use paradigm, to be invoked whenever there are new data to classify.

AB - We show that the decision function of a radial basis function (RBF) classifier is equivalent in form to the Bayes-optimal discriminant associated with a special kind of mixture-based statistical model. The relevant mixture model is a type of mixture-of-experts model for which class labels, like continuous-valued features, are assumed to have been generated randomly, conditional on the mixture component of origin. The new interpretation shows that RBF classifiers effectively assume a probability model, which, moreover, is easily determined given the designed RBF. This interpretation also suggests a statistical learning objective as an alternative to standard methods for designing the RBF-equivalent models. The statistical objective is especially useful for incorporating unlabeled data to enhance learning. Finally, it is observed that any new data to classify are simply additional unlabeled data. Thus, we suggest a combined learning and use paradigm, to be invoked whenever there are new data to classify.

UR - http://www.scopus.com/inward/record.url?scp=0000307012&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000307012&partnerID=8YFLogxK

U2 - 10.1162/089976698300017764

DO - 10.1162/089976698300017764

M3 - Article

AN - SCOPUS:0000307012

VL - 10

SP - 281

EP - 293

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 2

ER -