Maximin location: Discretization not always works

Why Discretization Works for Naive Bayesian Classifiers

This paper explains why well-known dis-cretization methods, such as entropy-based and ten-bin, work well for naive Bayesian classiiers with continuous variables, regardless of their complexities. These methods usually assume that discretized variables have Dirichlet priors. Since perfect aggrega-tion holds for Dirichlets, we can show that, generally, a wide variety of discretization methods can...

Subquadratic algorithms for the weighted maximin facility location problem

Let S be a set of n points in the plane, and let each point p of S have a positive weight w(p). We consider the problem of positioning a point x inside a compact region R ⊆ R such that min{ w(p)−1 · d(x, p) ; p ∈ S } is maximized. Based on the parametric search paradigm, we give the first subquadratic algorithms for this problem, with running time O(n log n). Furthermore, we shall introduce the...

Not Always Buried Deep

KLP Not Always Efficient

The size of the nondominated set of a vector set is greatly dependent on the size of the original vector set N and the dimension of the vector M . Theoretical analysis shows that when M = O(log N) the original set has big nondominated set which may be the original set itself, and in the case M = O(log N), a classical algorithm (KLP) for finding nondominated set has complexity of KLP higher than...

On Why Discretization Works for Naive-Bayes Classifiers

We investigate why discretization is effective in naive-Bayes learning. We prove a theorem that identifies particular conditions under which discretization will result in naiveBayes classifiers delivering the same probability estimates as would be obtained if the correct probability density functions were employed. We discuss the factors that might affect naive-Bayes classification error under ...