Optimal Bayesian Risk-based Multi-class Classification

doi:10.1117/3.2540669.ch5

Book: Optimal Bayesian Classification

Author(s): Lori A. Dalton, Edward R. Dougherty

Published: 2020

https://doi.org/10.1117/3.2540669.ch5

Author Affiliations +

Abstract

In this chapter we consider classification under multiple classes and allow for different types of error to be associated with different levels of risk or loss. A few classical classification algorithms naturally permit multiple classes and arbitrary loss functions; for example, a plug-in rule takes the functional form for an optimal Bayes decision rule under a given modeling assumption and substitutes sample estimates of model parameters in place of the true parameters. This can be done with LDA and QDA for multiple classes with arbitrary loss functions, which essentially assume that the underlying classconditional densities are Gaussian with equal or unequal covariances, respectively.