Geometric Properties of Naive Bayes in Nominal Domains

It is well known that the naive Bayesian classiier is linear in binary domains. However, little work is done on the learnability of the naive Bayesian classiier in nominal domains, a general case of binary domains. This paper explores the geometric properties of the naive Bayesian classiier in nominal domains. First we propose a three-layer measure for the linearity of functions in nominal domains: hard linear, soft nonlinear, and hard nonlinear. We examine the learnability of the naive Bayesian classiier in terms of that linearity measure. We show that the naive Bayesian classiier can learn some hard linear and some soft nonlinear nominal functions, but still cannot learn any hard nonlinear functions.