MULTIVARIATE DISCRIMINANT-ANALYSIS AND MAXIMUM PENALIZED LIKELIHOOD DENSITY-ESTIMATION

A new theoretical point of view is discussed in the framework of densi ty estimation. The multivariate true density, viewed as a prior or pen alizing factor in a Bayesian framework, is modelled by a Gibbs potenti al. Estimating the density consists in maximizing the posterior. For e fficiency of time, we are interested in an approximate estimator ($) o ver cap f = B pi of the true density f, where B is a stochastic operat or and pi is the raw histogram. Then, we investigate the discriminatio n problem, introducing an adaptive bandwidth depending on the k neares t neighbours and chosen to optimize the cross-validation criterion. Ou r final classification algorithm referred to as APML for approximate p enalized maximum likelihood compares favourably in terms of error rate and time efficiency with other algorithms tested, including multinorm al, nearest neighbour and convex hull classifiers.