PROBABILITY DENSITY-ESTIMATION USING ELLIPTIC BASIS FUNCTIONS

Elliptical basis function (EBF) networks are introduced as a new nonpa rametric method of estimating probability density functions for proces s data. Unlike Parzen window density estimators that use identical hyp erspherical basis functions, the EBF method uses elliptical basis func tions adapted to the local character of the data. This technique overc omes the spikiness problem associated with Parzen windows, where in hi gh dimension, they can fail to produce smooth probability density esti mates. The EBF estimator produces valid density functions that converg e to the underlying distribution of the data in the limit of an infini te number of training examples. A technique based on statistical cross validation is introduced for evaluating different density estimators. The criterion is a measure of how well the density estimator estimate s the density of data not used in the training. The EBF density estima tion method and the evaluation technique are demonstrated using severa l examples of fault diagnosis.